%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP044^1 : 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 : n007.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 10:23:48 AM UTC 2026
% Result : Theorem 12.87s 2.36s
% Output : CNFRefutation 12.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 145
% Syntax : Number of formulae : 2191 ( 796 unt; 0 typ; 0 def)
% Number of atoms : 13388 (8951 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 19082 (3583 ~;3788 |; 77 &;11416 @)
% ( 0 <=>; 218 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 10 ( 9 usr)
% Number of type conns : 835 ( 835 >; 0 *; 0 +; 0 <<)
% Number of symbols : 152 ( 149 usr; 19 con; 0-3 aty)
% Number of variables : 4823 ( 34 ^;4779 !; 10 ?;4823 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_list_a,type,
list_a: $tType ).
thf(tp_list_list_a,type,
list_list_a: $tType ).
thf(tp_list_nat,type,
list_nat: $tType ).
thf(tp_list_poly_a,type,
list_poly_a: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_poly_a,type,
poly_a: $tType ).
thf(tp_poly_nat,type,
poly_nat: $tType ).
thf(tp_poly_poly_a,type,
poly_poly_a: $tType ).
thf(tp_append_a,type,
append_a: list_a > list_a > list_a ).
thf(tp_append_nat,type,
append_nat: list_nat > list_nat > list_nat ).
thf(tp_append_poly_a,type,
append_poly_a: list_poly_a > list_poly_a > list_poly_a ).
thf(tp_coeffs_a,type,
coeffs_a: poly_a > list_a ).
thf(tp_coeffs_nat,type,
coeffs_nat: poly_nat > list_nat ).
thf(tp_coeffs_poly_a,type,
coeffs_poly_a: poly_poly_a > list_poly_a ).
thf(tp_cons_a,type,
cons_a: a > list_a > list_a ).
thf(tp_cons_list_a,type,
cons_list_a: list_a > list_list_a > list_list_a ).
thf(tp_cons_nat,type,
cons_nat: nat > list_nat > list_nat ).
thf(tp_cons_poly_a,type,
cons_poly_a: poly_a > list_poly_a > list_poly_a ).
thf(tp_descar1375166517sums_a,type,
descar1375166517sums_a: list_a > list_a ).
thf(tp_descar2095969287nges_a,type,
descar2095969287nges_a: list_a > nat ).
thf(tp_descar226543321ms_nat,type,
descar226543321ms_nat: list_nat > list_nat ).
thf(tp_descar282223555poly_a,type,
descar282223555poly_a: list_poly_a > list_poly_a ).
thf(tp_descar357075861poly_a,type,
descar357075861poly_a: list_poly_a > nat ).
thf(tp_descar434775507poly_a,type,
descar434775507poly_a: poly_a > poly_poly_a > poly_poly_a ).
thf(tp_descar466059845root_a,type,
descar466059845root_a: a > poly_a > poly_a ).
thf(tp_g,type,
g: poly_a ).
thf(tp_is_zero_a,type,
is_zero_a: poly_a > $o ).
thf(tp_is_zero_poly_a,type,
is_zero_poly_a: poly_poly_a > $o ).
thf(tp_nil_a,type,
nil_a: list_a ).
thf(tp_nil_list_a,type,
nil_list_a: list_list_a ).
thf(tp_nil_nat,type,
nil_nat: list_nat ).
thf(tp_nil_poly_a,type,
nil_poly_a: list_poly_a ).
thf(tp_null_a,type,
null_a: list_a > $o ).
thf(tp_null_poly_a,type,
null_poly_a: list_poly_a > $o ).
thf(tp_one_one_a,type,
one_one_a: a ).
thf(tp_one_one_nat,type,
one_one_nat: nat ).
thf(tp_one_one_poly_a,type,
one_one_poly_a: poly_a ).
thf(tp_one_one_poly_nat,type,
one_one_poly_nat: poly_nat ).
thf(tp_one_one_poly_poly_a,type,
one_one_poly_poly_a: poly_poly_a ).
thf(tp_ord_less_a,type,
ord_less_a: a > a > $o ).
thf(tp_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(tp_ord_less_poly_a,type,
ord_less_poly_a: poly_a > poly_a > $o ).
thf(tp_pCons_a,type,
pCons_a: a > poly_a > poly_a ).
thf(tp_pCons_nat,type,
pCons_nat: nat > poly_nat > poly_nat ).
thf(tp_pCons_poly_a,type,
pCons_poly_a: poly_a > poly_poly_a > poly_poly_a ).
thf(tp_poly_a2,type,
poly_a2: list_a > poly_a ).
thf(tp_poly_nat2,type,
poly_nat2: list_nat > poly_nat ).
thf(tp_poly_poly_a2,type,
poly_poly_a2: list_poly_a > poly_poly_a ).
thf(tp_sK10_Y2,type,
sK10_Y2: ( list_a > list_a > $o ) > a ).
thf(tp_sK11_SY336,type,
sK11_SY336: ( list_a > list_a > $o ) > list_a ).
thf(tp_sK12_X2,type,
sK12_X2: ( list_a > list_a > $o ) > a ).
thf(tp_sK13_SY337,type,
sK13_SY337: ( list_a > list_a > $o ) > list_a ).
thf(tp_sK14_X2,type,
sK14_X2: ( list_a > list_a > $o ) > a ).
thf(tp_sK15_SY338,type,
sK15_SY338: ( list_a > list_a > $o ) > list_a ).
thf(tp_sK16_SY340,type,
sK16_SY340: ( list_a > list_a > $o ) > list_a ).
thf(tp_sK17_X_1,type,
sK17_X_1: ( list_a > list_a > $o ) > list_a ).
thf(tp_sK18_X2,type,
sK18_X2: ( list_a > $o ) > a ).
thf(tp_sK19_SY341,type,
sK19_SY341: ( list_a > $o ) > a ).
thf(tp_sK1_N2,type,
sK1_N2: ( nat > $o ) > nat ).
thf(tp_sK20_SY343,type,
sK20_SY343: ( list_a > $o ) > list_a ).
thf(tp_sK21_X2,type,
sK21_X2: ( list_a > $o ) > a ).
thf(tp_sK22_X2,type,
sK22_X2: list_a > a ).
thf(tp_sK23_SY344,type,
sK23_SY344: list_a > list_a ).
thf(tp_sK24_X2,type,
sK24_X2: ( list_a > $o ) > a ).
thf(tp_sK25_SY345,type,
sK25_SY345: ( list_a > $o ) > list_a ).
thf(tp_sK26_X2,type,
sK26_X2: ( list_a > list_a > $o ) > a ).
thf(tp_sK27_SY350,type,
sK27_SY350: ( list_a > list_a > $o ) > list_a ).
thf(tp_sK28_SY353,type,
sK28_SY353: ( list_a > list_a > $o ) > a ).
thf(tp_sK29_SY355,type,
sK29_SY355: ( list_a > list_a > $o ) > list_a ).
thf(tp_sK2_X213,type,
sK2_X213: list_a > a ).
thf(tp_sK30_Xs2,type,
sK30_Xs2: ( list_a > list_a > $o ) > list_a ).
thf(tp_sK31_X_1,type,
sK31_X_1: ( list_a > list_a > $o ) > list_a ).
thf(tp_sK32_X2,type,
sK32_X2: list_a > a ).
thf(tp_sK33_SY356,type,
sK33_SY356: list_a > a ).
thf(tp_sK34_SY358,type,
sK34_SY358: list_a > list_a ).
thf(tp_sK35_X2,type,
sK35_X2: list_a > a ).
thf(tp_sK36_P5,type,
sK36_P5: ( ( a > a > $o ) > list_a > $o ) > a > a > $o ).
thf(tp_sK37_SY359,type,
sK37_SY359: ( ( a > a > $o ) > list_a > $o ) > a ).
thf(tp_sK38_SY361,type,
sK38_SY361: ( ( a > a > $o ) > list_a > $o ) > list_a ).
thf(tp_sK39_P5,type,
sK39_P5: ( ( a > a > $o ) > list_a > $o ) > a > a > $o ).
thf(tp_sK3_SY328,type,
sK3_SY328: list_a > list_a ).
thf(tp_sK40_X2,type,
sK40_X2: ( list_a > $o ) > a ).
thf(tp_sK41_SY362,type,
sK41_SY362: ( list_a > $o ) > a ).
thf(tp_sK42_SY364,type,
sK42_SY364: ( list_a > $o ) > list_a ).
thf(tp_sK43_X2,type,
sK43_X2: ( list_a > $o ) > a ).
thf(tp_sK44_P5,type,
sK44_P5: ( ( a > a > $o ) > list_a > $o ) > a > a > $o ).
thf(tp_sK45_SY365,type,
sK45_SY365: ( ( a > a > $o ) > list_a > $o ) > a ).
thf(tp_sK46_SY368,type,
sK46_SY368: ( ( a > a > $o ) > list_a > $o ) > a ).
thf(tp_sK47_SY370,type,
sK47_SY370: ( ( a > a > $o ) > list_a > $o ) > list_a ).
thf(tp_sK48_P5,type,
sK48_P5: ( ( a > a > $o ) > list_a > $o ) > a > a > $o ).
thf(tp_sK49_SY371,type,
sK49_SY371: ( ( a > a > $o ) > list_a > $o ) > a ).
thf(tp_sK4_X1,type,
sK4_X1: ( list_a > $o ) > a ).
thf(tp_sK50_P5,type,
sK50_P5: ( ( a > a > $o ) > list_a > $o ) > a > a > $o ).
thf(tp_sK51_X2,type,
sK51_X2: ( list_a > $o ) > list_a > a ).
thf(tp_sK52_SY372,type,
sK52_SY372: ( list_a > $o ) > list_a > list_a ).
thf(tp_sK53_X2,type,
sK53_X2: ( list_a > $o ) > list_a > a ).
thf(tp_sK54_F2,type,
sK54_F2: ( a > a ) > ( ( a > a ) > list_a > list_a > $o ) > a > a ).
thf(tp_sK55_SY373,type,
sK55_SY373: ( a > a ) > ( ( a > a ) > list_a > list_a > $o ) > a ).
thf(tp_sK56_SY376,type,
sK56_SY376: ( a > a ) > ( ( a > a ) > list_a > list_a > $o ) > list_a ).
thf(tp_sK57_SY378,type,
sK57_SY378: ( a > a ) > ( ( a > a ) > list_a > list_a > $o ) > list_a ).
thf(tp_sK58_F2,type,
sK58_F2: ( a > a ) > ( ( a > a ) > list_a > list_a > $o ) > a > a ).
thf(tp_sK59_SY379,type,
sK59_SY379: ( a > a ) > ( ( a > a ) > list_a > list_a > $o ) > list_a ).
thf(tp_sK5_SY329,type,
sK5_SY329: ( list_a > $o ) > list_a ).
thf(tp_sK60_X2,type,
sK60_X2: list_a > a ).
thf(tp_sK61_SY380,type,
sK61_SY380: list_a > list_a ).
thf(tp_sK62_X2,type,
sK62_X2: ( list_a > $o ) > a ).
thf(tp_sK63_SY381,type,
sK63_SY381: ( list_a > $o ) > list_a ).
thf(tp_sK64_X2,type,
sK64_X2: list_a > a ).
thf(tp_sK65_SY382,type,
sK65_SY382: list_a > a ).
thf(tp_sK66_SY384,type,
sK66_SY384: list_a > list_a ).
thf(tp_sK67_X2,type,
sK67_X2: list_a > a ).
thf(tp_sK68_Y2,type,
sK68_Y2: ( list_a > list_a > $o ) > a ).
thf(tp_sK69_SY385,type,
sK69_SY385: ( list_a > list_a > $o ) > list_a ).
thf(tp_sK6_X2,type,
sK6_X2: ( list_a > list_a > $o ) > a ).
thf(tp_sK70_Xs2,type,
sK70_Xs2: ( list_a > list_a > $o ) > list_a ).
thf(tp_sK71_X2,type,
sK71_X2: ( list_a > list_a > $o ) > a ).
thf(tp_sK72_SY386,type,
sK72_SY386: ( list_a > list_a > $o ) > list_a ).
thf(tp_sK73_SY389,type,
sK73_SY389: ( list_a > list_a > $o ) > a ).
thf(tp_sK74_SY391,type,
sK74_SY391: ( list_a > list_a > $o ) > list_a ).
thf(tp_sK75_X2,type,
sK75_X2: ( list_a > list_a > $o ) > a ).
thf(tp_sK76_SY392,type,
sK76_SY392: ( list_a > list_a > $o ) > list_a ).
thf(tp_sK77_SY395,type,
sK77_SY395: ( list_a > list_a > $o ) > a ).
thf(tp_sK78_SY397,type,
sK78_SY397: ( list_a > list_a > $o ) > list_a ).
thf(tp_sK79_V,type,
sK79_V: ( list_a > list_a > $o ) > a ).
thf(tp_sK7_SY330,type,
sK7_SY330: ( list_a > list_a > $o ) > list_a ).
thf(tp_sK80_SY398,type,
sK80_SY398: ( list_a > list_a > $o ) > list_a ).
thf(tp_sK81_Xs2,type,
sK81_Xs2: ( list_a > list_a > $o ) > list_a ).
thf(tp_sK82_A2,type,
sK82_A2: ( poly_a > $o ) > a ).
thf(tp_sK83_SY399,type,
sK83_SY399: ( poly_a > $o ) > poly_a ).
thf(tp_sK84_A2,type,
sK84_A2: ( poly_a > poly_a > $o ) > a ).
thf(tp_sK85_SY400,type,
sK85_SY400: ( poly_a > poly_a > $o ) > poly_a ).
thf(tp_sK86_SY403,type,
sK86_SY403: ( poly_a > poly_a > $o ) > a ).
thf(tp_sK87_SY405,type,
sK87_SY405: ( poly_a > poly_a > $o ) > poly_a ).
thf(tp_sK88_A2,type,
sK88_A2: ( poly_a > $o ) > a ).
thf(tp_sK89_SY406,type,
sK89_SY406: ( poly_a > $o ) > poly_a ).
thf(tp_sK8_SY333,type,
sK8_SY333: ( list_a > list_a > $o ) > a ).
thf(tp_sK90_SY508,type,
sK90_SY508: list_a > a ).
thf(tp_sK91_SY569,type,
sK91_SY569: list_a > list_a ).
thf(tp_sK92_SY508,type,
sK92_SY508: list_a > a > list_a > a ).
thf(tp_sK93_SY575,type,
sK93_SY575: a > list_a > list_a > list_a ).
thf(tp_sK9_SY335,type,
sK9_SY335: ( list_a > list_a > $o ) > list_a ).
thf(tp_smult_a,type,
smult_a: a > poly_a > poly_a ).
thf(tp_smult_nat,type,
smult_nat: nat > poly_nat > poly_nat ).
thf(tp_smult_poly_a,type,
smult_poly_a: poly_a > poly_poly_a > poly_poly_a ).
thf(tp_times_times_a,type,
times_times_a: a > a > a ).
thf(tp_times_times_nat,type,
times_times_nat: nat > nat > nat ).
thf(tp_times_times_poly_a,type,
times_times_poly_a: poly_a > poly_a > poly_a ).
thf(tp_uminus_uminus_a,type,
uminus_uminus_a: a > a ).
thf(tp_uminus_uminus_poly_a,type,
uminus_uminus_poly_a: poly_a > poly_a ).
thf(tp_v,type,
v: poly_a > nat ).
thf(tp_xs,type,
xs: list_a ).
thf(tp_ys,type,
ys: list_a ).
thf(tp_zero_z2096148049poly_a,type,
zero_z2096148049poly_a: poly_poly_a ).
thf(tp_zero_zero_a,type,
zero_zero_a: a ).
thf(tp_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(tp_zero_zero_poly_a,type,
zero_zero_poly_a: poly_a ).
thf(tp_zero_zero_poly_nat,type,
zero_zero_poly_nat: poly_nat ).
thf(2,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_344_nat__mult__eq__cancel__disj) ).
thf(5,axiom,
! [N: nat] :
( ( times_times_nat @ zero_zero_nat @ N )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_mult__0) ).
thf(8,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_bot__nat__0_Oextremum__strict) ).
thf(9,axiom,
! [P3: nat > $o,N: nat] :
( ( P3 @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ~ ( P3 @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P3 @ M2 ) ) ) )
=> ( P3 @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_infinite__descent0) ).
thf(10,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_gr__implies__not0) ).
thf(11,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_less__zeroE) ).
thf(12,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_not__less0) ).
thf(13,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_not__gr0) ).
thf(14,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_gr0I) ).
thf(28,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_318_mult__cancel1) ).
thf(29,axiom,
! [M: nat] :
( ( times_times_nat @ M @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_mult__0__right) ).
thf(30,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_316_mult__is__0) ).
thf(31,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_bot__nat__0_Onot__eq__extremum) ).
thf(32,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_less__nat__zero__code) ).
thf(33,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_neq0__conv) ).
thf(34,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_312_mult__cancel2) ).
thf(81,axiom,
null_a @ nil_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_null__rec_I2_J) ).
thf(82,axiom,
! [Xs: list_a] :
( ( Xs = nil_a )
= ( null_a @ Xs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_eq__Nil__null) ).
thf(83,axiom,
! [X: a,Xs: list_a] :
~ ( null_a @ ( cons_a @ X @ Xs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_null__rec_I1_J) ).
thf(84,axiom,
! [Xs: list_a,Ys2: list_a] :
( ( Xs = Ys2 )
=> ( Xs
= ( append_a @ nil_a @ Ys2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_eq__Nil__appendI) ).
thf(85,axiom,
! [Ys2: list_a] :
( ( append_a @ nil_a @ Ys2 )
= Ys2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_append__Nil) ).
thf(86,axiom,
! [A: list_a] :
( ( append_a @ nil_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_append_Oleft__neutral) ).
thf(87,axiom,
! [X: a,Xs1: list_a,Ys2: list_a,Xs: list_a,Zs: list_a] :
( ( ( cons_a @ X @ Xs1 )
= Ys2 )
=> ( ( Xs
= ( append_a @ Xs1 @ Zs ) )
=> ( ( cons_a @ X @ Xs )
= ( append_a @ Ys2 @ Zs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_Cons__eq__appendI) ).
thf(88,axiom,
! [X: a,Xs: list_a,Ys2: list_a] :
( ( append_a @ ( cons_a @ X @ Xs ) @ Ys2 )
= ( cons_a @ X @ ( append_a @ Xs @ Ys2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_append__Cons) ).
thf(89,axiom,
! [X21: a,X22: list_a] :
( nil_a
!= ( cons_a @ X21 @ X22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_list_Odistinct_I1_J) ).
thf(90,axiom,
! [List: list_a,X21: a,X22: list_a] :
( ( List
= ( cons_a @ X21 @ X22 ) )
=> ( List != nil_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_list_OdiscI) ).
thf(91,axiom,
! [Y3: list_a] :
( ( Y3 != nil_a )
=> ~ ! [X213: a,X223: list_a] :
( Y3
!= ( cons_a @ X213 @ X223 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_list_Oexhaust) ).
thf(92,axiom,
! [P3: list_a > $o,List: list_a] :
( ( P3 @ nil_a )
=> ( ! [X1: a,X23: list_a] :
( ( P3 @ X23 )
=> ( P3 @ ( cons_a @ X1 @ X23 ) ) )
=> ( P3 @ List ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_list_Oinducts) ).
thf(93,axiom,
! [Xs: list_a] :
( ( Xs != nil_a )
= ( ? [Y4: a,Ys3: list_a] :
( Xs
= ( cons_a @ Y4 @ Ys3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_neq__Nil__conv) ).
thf(94,axiom,
! [P3: list_a > list_a > $o,Xs: list_a,Ys2: list_a] :
( ( P3 @ nil_a @ nil_a )
=> ( ! [X2: a,Xs2: list_a] : ( P3 @ ( cons_a @ X2 @ Xs2 ) @ nil_a )
=> ( ! [Y2: a,Ys: list_a] : ( P3 @ nil_a @ ( cons_a @ Y2 @ Ys ) )
=> ( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
( ( P3 @ Xs2 @ Ys )
=> ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) )
=> ( P3 @ Xs @ Ys2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_list__induct2_H) ).
thf(95,axiom,
! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
( ! [X_1: list_a] : ( P3 @ nil_a @ X_1 )
=> ( ! [X2: a,Xs2: list_a,Ys: list_a] :
( ( P3 @ Ys @ Xs2 )
=> ( P3 @ ( cons_a @ X2 @ Xs2 ) @ Ys ) )
=> ( P3 @ A0 @ A1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_splice_Oinduct) ).
thf(96,axiom,
! [P3: list_a > $o,Xs: list_a] :
( ( P3 @ nil_a )
=> ( ! [X2: a] : ( P3 @ ( cons_a @ X2 @ nil_a ) )
=> ( ! [X2: a,Y2: a,Zs2: list_a] :
( ( P3 @ Zs2 )
=> ( ( P3 @ ( cons_a @ Y2 @ Zs2 ) )
=> ( P3 @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Zs2 ) ) ) ) )
=> ( P3 @ Xs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_induct__list012) ).
thf(97,axiom,
! [X: list_a] :
( ! [X2: a,Xs2: list_a] :
( X
!= ( cons_a @ X2 @ Xs2 ) )
=> ( X = nil_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_min__list_Ocases) ).
thf(98,axiom,
! [P3: list_a > $o,A0: list_a] :
( ! [X2: a,Xs2: list_a] :
( ! [X212: a,X222: list_a] :
( ( Xs2
= ( cons_a @ X212 @ X222 ) )
=> ( P3 @ Xs2 ) )
=> ( P3 @ ( cons_a @ X2 @ Xs2 ) ) )
=> ( ( P3 @ nil_a )
=> ( P3 @ A0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_min__list_Oinduct) ).
thf(99,axiom,
! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
( ! [X_1: list_a] : ( P3 @ nil_a @ X_1 )
=> ( ! [Xs2: list_a] : ( P3 @ Xs2 @ nil_a )
=> ( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
( ( P3 @ Xs2 @ ( cons_a @ Y2 @ Ys ) )
=> ( ( P3 @ ( cons_a @ X2 @ Xs2 ) @ Ys )
=> ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) ) )
=> ( P3 @ A0 @ A1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_shuffles_Oinduct) ).
thf(101,axiom,
! [X: list_a] :
( ( X != nil_a )
=> ( ! [X2: a] :
( X
!= ( cons_a @ X2 @ nil_a ) )
=> ~ ! [X2: a,Y2: a,Xs2: list_a] :
( X
!= ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_remdups__adj_Ocases) ).
thf(102,axiom,
! [P3: ( a > a > $o ) > list_a > $o,A0: a > a > $o,A1: list_a] :
( ! [P5: a > a > $o] : ( P3 @ P5 @ nil_a )
=> ( ! [P5: a > a > $o,X2: a,Ys: list_a] :
( ( P3 @ P5 @ Ys )
=> ( P3 @ P5 @ ( cons_a @ X2 @ Ys ) ) )
=> ( P3 @ A0 @ A1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_sorted__wrt_Oinduct) ).
thf(103,axiom,
! [P3: list_a > $o,A0: list_a] :
( ( P3 @ nil_a )
=> ( ! [X2: a] : ( P3 @ ( cons_a @ X2 @ nil_a ) )
=> ( ! [X2: a,Y2: a,Xs2: list_a] :
( ( ( X2 = Y2 )
=> ( P3 @ ( cons_a @ X2 @ Xs2 ) ) )
=> ( ( ( X2 != Y2 )
=> ( P3 @ ( cons_a @ Y2 @ Xs2 ) ) )
=> ( P3 @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) ) )
=> ( P3 @ A0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_remdups__adj_Oinduct) ).
thf(104,axiom,
! [P3: ( a > a > $o ) > list_a > $o,A0: a > a > $o,A1: list_a] :
( ! [P5: a > a > $o] : ( P3 @ P5 @ nil_a )
=> ( ! [P5: a > a > $o,X2: a] : ( P3 @ P5 @ ( cons_a @ X2 @ nil_a ) )
=> ( ! [P5: a > a > $o,X2: a,Y2: a,Xs2: list_a] :
( ( P3 @ P5 @ ( cons_a @ Y2 @ Xs2 ) )
=> ( P3 @ P5 @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) )
=> ( P3 @ A0 @ A1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_successively_Oinduct) ).
thf(105,axiom,
! [Xs: list_a,P3: list_a > $o] :
( ( Xs != nil_a )
=> ( ! [X2: a] : ( P3 @ ( cons_a @ X2 @ nil_a ) )
=> ( ! [X2: a,Xs2: list_a] :
( ( Xs2 != nil_a )
=> ( ( P3 @ Xs2 )
=> ( P3 @ ( cons_a @ X2 @ Xs2 ) ) ) )
=> ( P3 @ Xs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_list__nonempty__induct) ).
thf(106,axiom,
! [P3: ( a > a ) > list_a > list_a > $o,A0: a > a,A1: list_a,A22: list_a] :
( ! [F2: a > a,X_1: list_a] : ( P3 @ F2 @ nil_a @ X_1 )
=> ( ! [F2: a > a,A2: a,As2: list_a,Bs: list_a] :
( ( P3 @ F2 @ As2 @ ( cons_a @ ( F2 @ A2 ) @ Bs ) )
=> ( P3 @ F2 @ ( cons_a @ A2 @ As2 ) @ Bs ) )
=> ( P3 @ A0 @ A1 @ A22 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_map__tailrec__rev_Oinduct) ).
thf(107,axiom,
! [X: list_a] :
( ( X != nil_a )
=> ~ ! [X2: a,Ys: list_a] :
( X
!= ( cons_a @ X2 @ Ys ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_strict__sorted_Ocases) ).
thf(108,axiom,
! [P3: list_a > $o,A0: list_a] :
( ( P3 @ nil_a )
=> ( ! [X2: a,Ys: list_a] :
( ( P3 @ Ys )
=> ( P3 @ ( cons_a @ X2 @ Ys ) ) )
=> ( P3 @ A0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_strict__sorted_Oinduct) ).
thf(127,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_zero__neq__one) ).
thf(128,axiom,
zero_zero_a != one_one_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_zero__neq__one) ).
thf(129,axiom,
zero_zero_poly_a != one_one_poly_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_zero__neq__one) ).
thf(130,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
!= zero_zero_nat )
=> ( ( A != zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_mult__not__zero) ).
thf(131,axiom,
! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
!= zero_zero_poly_a )
=> ( ( A != zero_zero_poly_a )
& ( B != zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_mult__not__zero) ).
thf(132,axiom,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
!= zero_zero_a )
=> ( ( A != zero_zero_a )
& ( B != zero_zero_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_mult__not__zero) ).
thf(133,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_divisors__zero) ).
thf(134,axiom,
! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= zero_zero_poly_a )
=> ( ( A = zero_zero_poly_a )
| ( B = zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_divisors__zero) ).
thf(135,axiom,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= zero_zero_a )
=> ( ( A = zero_zero_a )
| ( B = zero_zero_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_divisors__zero) ).
thf(136,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ A @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_no__zero__divisors) ).
thf(137,axiom,
! [A: poly_a,B: poly_a] :
( ( A != zero_zero_poly_a )
=> ( ( B != zero_zero_poly_a )
=> ( ( times_times_poly_a @ A @ B )
!= zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_no__zero__divisors) ).
thf(138,axiom,
! [A: a,B: a] :
( ( A != zero_zero_a )
=> ( ( B != zero_zero_a )
=> ( ( times_times_a @ A @ B )
!= zero_zero_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_no__zero__divisors) ).
thf(139,axiom,
! [C: nat,A: nat,B: nat] :
( ( C != zero_zero_nat )
=> ( ( ( times_times_nat @ C @ A )
= ( times_times_nat @ C @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_mult__left__cancel) ).
thf(140,axiom,
! [C: poly_a,A: poly_a,B: poly_a] :
( ( C != zero_zero_poly_a )
=> ( ( ( times_times_poly_a @ C @ A )
= ( times_times_poly_a @ C @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_mult__left__cancel) ).
thf(141,axiom,
! [C: a,A: a,B: a] :
( ( C != zero_zero_a )
=> ( ( ( times_times_a @ C @ A )
= ( times_times_a @ C @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_mult__left__cancel) ).
thf(142,axiom,
! [C: nat,A: nat,B: nat] :
( ( C != zero_zero_nat )
=> ( ( ( times_times_nat @ A @ C )
= ( times_times_nat @ B @ C ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_mult__right__cancel) ).
thf(143,axiom,
! [C: poly_a,A: poly_a,B: poly_a] :
( ( C != zero_zero_poly_a )
=> ( ( ( times_times_poly_a @ A @ C )
= ( times_times_poly_a @ B @ C ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_mult__right__cancel) ).
thf(144,axiom,
! [C: a,A: a,B: a] :
( ( C != zero_zero_a )
=> ( ( ( times_times_a @ A @ C )
= ( times_times_a @ B @ C ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_mult__right__cancel) ).
thf(145,axiom,
~ ( ord_less_poly_a @ zero_zero_poly_a @ zero_zero_poly_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_less__numeral__extra_I3_J) ).
thf(146,axiom,
~ ( ord_less_a @ zero_zero_a @ zero_zero_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_less__numeral__extra_I3_J) ).
thf(147,axiom,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_less__numeral__extra_I3_J) ).
thf(148,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_gr__zeroI) ).
thf(149,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_not__less__zero) ).
thf(150,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_gr__implies__not__zero) ).
thf(151,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_zero__less__iff__neq__zero) ).
thf(156,axiom,
! [X: a,Xs: list_a] :
( ( cons_a @ X @ Xs )
!= Xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_not__Cons__self2) ).
thf(171,axiom,
! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_zero__reorient) ).
thf(172,axiom,
! [X: a] :
( ( zero_zero_a = X )
= ( X = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_zero__reorient) ).
thf(173,axiom,
! [X: poly_a] :
( ( zero_zero_poly_a = X )
= ( X = zero_zero_poly_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_zero__reorient) ).
thf(175,axiom,
! [Xs: list_a] :
( ( append_a @ Xs @ nil_a )
= Xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_append__Nil2) ).
thf(176,axiom,
! [Xs: list_a,Ys2: list_a] :
( ( ( append_a @ Xs @ Ys2 )
= Xs )
= ( Ys2 = nil_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_append__self__conv) ).
thf(177,axiom,
! [Xs: list_a,Ys2: list_a] :
( ( Xs
= ( append_a @ Xs @ Ys2 ) )
= ( Ys2 = nil_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_self__append__conv) ).
thf(178,axiom,
! [Xs: list_a,Ys2: list_a] :
( ( ( append_a @ Xs @ Ys2 )
= Ys2 )
= ( Xs = nil_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_append__self__conv2) ).
thf(179,axiom,
! [Ys2: list_a,Xs: list_a] :
( ( Ys2
= ( append_a @ Xs @ Ys2 ) )
= ( Xs = nil_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_self__append__conv2) ).
thf(180,axiom,
! [Xs: list_a,Ys2: list_a] :
( ( nil_a
= ( append_a @ Xs @ Ys2 ) )
= ( ( Xs = nil_a )
& ( Ys2 = nil_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_Nil__is__append__conv) ).
thf(181,axiom,
! [Xs: list_a,Ys2: list_a] :
( ( ( append_a @ Xs @ Ys2 )
= nil_a )
= ( ( Xs = nil_a )
& ( Ys2 = nil_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_append__is__Nil__conv) ).
thf(182,axiom,
! [A: list_a] :
( ( append_a @ A @ nil_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_append_Oright__neutral) ).
thf(197,axiom,
( ( uminus_uminus_a @ zero_zero_a )
= zero_zero_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_add_Oinverse__neutral) ).
thf(198,axiom,
( ( uminus_uminus_poly_a @ zero_zero_poly_a )
= zero_zero_poly_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_add_Oinverse__neutral) ).
thf(199,axiom,
! [A: a] :
( ( zero_zero_a
= ( uminus_uminus_a @ A ) )
= ( zero_zero_a = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_neg__0__equal__iff__equal) ).
thf(200,axiom,
! [A: poly_a] :
( ( zero_zero_poly_a
= ( uminus_uminus_poly_a @ A ) )
= ( zero_zero_poly_a = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_neg__0__equal__iff__equal) ).
thf(201,axiom,
! [A: a] :
( ( ( uminus_uminus_a @ A )
= zero_zero_a )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_neg__equal__0__iff__equal) ).
thf(202,axiom,
! [A: poly_a] :
( ( ( uminus_uminus_poly_a @ A )
= zero_zero_poly_a )
= ( A = zero_zero_poly_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_neg__equal__0__iff__equal) ).
thf(203,axiom,
! [A: a] :
( ( A
= ( uminus_uminus_a @ A ) )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_equal__neg__zero) ).
thf(204,axiom,
! [A: poly_a] :
( ( A
= ( uminus_uminus_poly_a @ A ) )
= ( A = zero_zero_poly_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_equal__neg__zero) ).
thf(205,axiom,
! [A: a] :
( ( ( uminus_uminus_a @ A )
= A )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_neg__equal__zero) ).
thf(206,axiom,
! [A: poly_a] :
( ( ( uminus_uminus_poly_a @ A )
= A )
= ( A = zero_zero_poly_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_neg__equal__zero) ).
thf(207,axiom,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_mult__zero__left) ).
thf(208,axiom,
! [A: poly_a] :
( ( times_times_poly_a @ zero_zero_poly_a @ A )
= zero_zero_poly_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_mult__zero__left) ).
thf(209,axiom,
! [A: a] :
( ( times_times_a @ zero_zero_a @ A )
= zero_zero_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_mult__zero__left) ).
thf(210,axiom,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_mult__zero__right) ).
thf(211,axiom,
! [A: poly_a] :
( ( times_times_poly_a @ A @ zero_zero_poly_a )
= zero_zero_poly_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_mult__zero__right) ).
thf(212,axiom,
! [A: a] :
( ( times_times_a @ A @ zero_zero_a )
= zero_zero_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_mult__zero__right) ).
thf(213,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_mult__eq__0__iff) ).
thf(214,axiom,
! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= zero_zero_poly_a )
= ( ( A = zero_zero_poly_a )
| ( B = zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_mult__eq__0__iff) ).
thf(215,axiom,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= zero_zero_a )
= ( ( A = zero_zero_a )
| ( B = zero_zero_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_mult__eq__0__iff) ).
thf(216,axiom,
! [C: nat,A: nat,B: nat] :
( ( ( times_times_nat @ C @ A )
= ( times_times_nat @ C @ B ) )
= ( ( C = zero_zero_nat )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_mult__cancel__left) ).
thf(217,axiom,
! [C: poly_a,A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ C @ A )
= ( times_times_poly_a @ C @ B ) )
= ( ( C = zero_zero_poly_a )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_mult__cancel__left) ).
thf(218,axiom,
! [C: a,A: a,B: a] :
( ( ( times_times_a @ C @ A )
= ( times_times_a @ C @ B ) )
= ( ( C = zero_zero_a )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_mult__cancel__left) ).
thf(219,axiom,
! [A: nat,C: nat,B: nat] :
( ( ( times_times_nat @ A @ C )
= ( times_times_nat @ B @ C ) )
= ( ( C = zero_zero_nat )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_mult__cancel__right) ).
thf(220,axiom,
! [A: poly_a,C: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ C )
= ( times_times_poly_a @ B @ C ) )
= ( ( C = zero_zero_poly_a )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_mult__cancel__right) ).
thf(221,axiom,
! [A: a,C: a,B: a] :
( ( ( times_times_a @ A @ C )
= ( times_times_a @ B @ C ) )
= ( ( C = zero_zero_a )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_mult__cancel__right) ).
thf(222,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_not__gr__zero) ).
thf(227,axiom,
! [X21: a,X22: list_a,Y21: a,Y22: list_a] :
( ( ( cons_a @ X21 @ X22 )
= ( cons_a @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_list_Oinject) ).
thf(250,axiom,
! [Xs: list_a,X: a,Ys2: list_a,Y3: a] :
( ( ( append_a @ Xs @ ( cons_a @ X @ nil_a ) )
= ( append_a @ Ys2 @ ( cons_a @ Y3 @ nil_a ) ) )
= ( ( Xs = Ys2 )
& ( X = Y3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_append1__eq__conv) ).
thf(254,axiom,
! [A: a,P2: poly_a] :
( ( A != zero_zero_a )
=> ( ( P2 != zero_zero_poly_a )
=> ( ( descar466059845root_a @ A @ P2 )
!= zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_reduce__root__nonzero) ).
thf(257,axiom,
! [X: list_a] :
( ( X != nil_a )
=> ( ! [X2: a] :
( X
!= ( cons_a @ X2 @ nil_a ) )
=> ~ ! [X2: a,Y2: a,Xs2: list_a] :
( X
!= ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_psums_Ocases) ).
thf(259,axiom,
! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
( ( P3 @ Xs2 @ Ys )
=> ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) )
=> ( ! [Xs2: list_a] : ( P3 @ Xs2 @ nil_a )
=> ( ! [Y2: a,Ys: list_a] : ( P3 @ nil_a @ ( cons_a @ Y2 @ Ys ) )
=> ( P3 @ A0 @ A1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_minus__poly__rev__list_Oinduct) ).
thf(260,axiom,
! [P2: poly_a] :
( ( P2 != zero_zero_poly_a )
=> ( ( coeffs_a @ P2 )
!= nil_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_not__0__coeffs__not__Nil) ).
thf(262,axiom,
! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
( ! [Xs2: list_a] : ( P3 @ Xs2 @ nil_a )
=> ( ! [V: a,Va: list_a] : ( P3 @ nil_a @ ( cons_a @ V @ Va ) )
=> ( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
( ( P3 @ Xs2 @ Ys )
=> ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) )
=> ( P3 @ A0 @ A1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_plus__coeffs_Oinduct) ).
thf(263,axiom,
! [P2: poly_a] :
( ( times_times_poly_a @ P2 @ zero_zero_poly_a )
= zero_zero_poly_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_mult__poly__0__right) ).
thf(264,axiom,
! [Q2: poly_a] :
( ( times_times_poly_a @ zero_zero_poly_a @ Q2 )
= zero_zero_poly_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_mult__poly__0__left) ).
thf(265,axiom,
! [P3: poly_a > $o,A0: poly_a] :
( ! [A2: a,P4: poly_a] :
( ( ( P4 != zero_zero_poly_a )
=> ( P3 @ P4 ) )
=> ( P3 @ ( pCons_a @ A2 @ P4 ) ) )
=> ( P3 @ A0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_pderiv_Oinduct) ).
thf(266,axiom,
! [P3: poly_a > poly_a > $o,P2: poly_a,Q2: poly_a] :
( ( P3 @ zero_zero_poly_a @ zero_zero_poly_a )
=> ( ! [A2: a,P4: poly_a,B2: a,Q3: poly_a] :
( ( P3 @ P4 @ Q3 )
=> ( P3 @ ( pCons_a @ A2 @ P4 ) @ ( pCons_a @ B2 @ Q3 ) ) )
=> ( P3 @ P2 @ Q2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_poly__induct2) ).
thf(268,axiom,
! [P3: poly_a > $o,P2: poly_a] :
( ( P3 @ zero_zero_poly_a )
=> ( ! [A2: a,P4: poly_a] :
( ( ( A2 != zero_zero_a )
| ( P4 != zero_zero_poly_a ) )
=> ( ( P3 @ P4 )
=> ( P3 @ ( pCons_a @ A2 @ P4 ) ) ) )
=> ( P3 @ P2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_pCons__induct) ).
thf(271,axiom,
( is_zero_a
= ( ^ [P: poly_a] : ( P = zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_is__zero__null) ).
thf(275,axiom,
( ( descar1375166517sums_a @ nil_a )
= nil_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_psums_Osimps_I1_J) ).
thf(276,axiom,
! [X: a] :
( ( descar1375166517sums_a @ ( cons_a @ X @ nil_a ) )
= ( cons_a @ X @ nil_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_psums_Osimps_I2_J) ).
thf(277,axiom,
( ( poly_a2 @ nil_a )
= zero_zero_poly_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Poly_Osimps_I1_J) ).
thf(278,axiom,
! [A: a,As: list_a] :
( ( poly_a2 @ ( cons_a @ A @ As ) )
= ( pCons_a @ A @ ( poly_a2 @ As ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_Poly_Osimps_I2_J) ).
thf(280,axiom,
! [As: list_a] :
( ( poly_a2 @ ( append_a @ As @ ( cons_a @ zero_zero_a @ nil_a ) ) )
= ( poly_a2 @ As ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_Poly__snoc__zero) ).
thf(284,axiom,
! [X: a] :
( ( descar2095969287nges_a @ ( cons_a @ X @ nil_a ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_sign__changes__singleton) ).
thf(288,axiom,
! [Xs: list_a] :
( ( descar1375166517sums_a @ ( cons_a @ zero_zero_a @ Xs ) )
= ( cons_a @ zero_zero_a @ ( descar1375166517sums_a @ Xs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_psums__0__Cons) ).
thf(291,axiom,
( ( coeffs_a @ zero_zero_poly_a )
= nil_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_coeffs__0__eq__Nil) ).
thf(293,axiom,
! [P2: poly_a] :
( ( ( coeffs_a @ P2 )
= nil_a )
= ( P2 = zero_zero_poly_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_coeffs__eq__Nil) ).
thf(298,axiom,
! [A: a,P2: poly_a] :
( ( ( smult_a @ A @ P2 )
= zero_zero_poly_a )
= ( ( A = zero_zero_a )
| ( P2 = zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_smult__eq__0__iff) ).
thf(302,axiom,
! [P2: poly_a] :
( ( smult_a @ zero_zero_a @ P2 )
= zero_zero_poly_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_smult__0__left) ).
thf(308,axiom,
! [A: a,P2: poly_a] :
( ( ( pCons_a @ A @ P2 )
= zero_zero_poly_a )
= ( ( A = zero_zero_a )
& ( P2 = zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_pCons__eq__0__iff) ).
thf(312,axiom,
( ( pCons_a @ zero_zero_a @ zero_zero_poly_a )
= zero_zero_poly_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_pCons__0__0) ).
thf(316,axiom,
! [A: a] :
( ( smult_a @ A @ zero_zero_poly_a )
= zero_zero_poly_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_smult__0__right) ).
thf(325,axiom,
! [X: a,Xs: list_a] :
( ( descar2095969287nges_a @ ( cons_a @ X @ ( cons_a @ zero_zero_a @ Xs ) ) )
= ( descar2095969287nges_a @ ( cons_a @ X @ Xs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_sign__changes__Cons__Cons__0) ).
thf(327,axiom,
! [Xs: list_a] :
( ( descar2095969287nges_a @ ( cons_a @ zero_zero_a @ Xs ) )
= ( descar2095969287nges_a @ Xs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_sign__changes__0__Cons) ).
thf(331,axiom,
( ( descar2095969287nges_a @ nil_a )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_sign__changes__Nil) ).
thf(333,axiom,
! [P2: poly_a] :
( ( poly_a2 @ ( coeffs_a @ P2 ) )
= P2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Poly__coeffs) ).
thf(335,axiom,
( is_zero_a
= ( ^ [P: poly_a] : ( null_a @ ( coeffs_a @ P ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_is__zero__def) ).
thf(339,axiom,
( ys
= ( append_a @ ( coeffs_a @ g ) @ ( cons_a @ zero_zero_a @ nil_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_ys__def) ).
thf(340,axiom,
! [Xs: list_a,P2: poly_a] :
( ( ( poly_a2 @ Xs )
= P2 )
=> ( ( descar2095969287nges_a @ Xs )
= ( descar2095969287nges_a @ ( coeffs_a @ P2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_sign__changes__coeff__sign__changes) ).
thf(342,axiom,
( ys
= ( descar1375166517sums_a @ xs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_ys) ).
thf(343,axiom,
( ( ^ [Y: poly_a,Z: poly_a] : ( Y = Z ) )
= ( ^ [P: poly_a,Q: poly_a] :
( ( coeffs_a @ P )
= ( coeffs_a @ Q ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_coeffs__eq__iff) ).
thf(345,axiom,
g != zero_zero_poly_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_nz) ).
thf(346,axiom,
( v
= ( ^ [F: poly_a] : ( descar2095969287nges_a @ ( coeffs_a @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_v__def) ).
thf(347,conjecture,
( ( descar2095969287nges_a @ ys )
= ( descar2095969287nges_a @ ( coeffs_a @ g ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(348,negated_conjecture,
( ( ( descar2095969287nges_a @ ys )
= ( descar2095969287nges_a @ ( coeffs_a @ g ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[347]) ).
thf(349,plain,
( ( ( descar2095969287nges_a @ ys )
= ( descar2095969287nges_a @ ( coeffs_a @ g ) ) )
= $false ),
inference(unfold_def,[status(thm)],[348]) ).
thf(350,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)],[2]) ).
thf(351,plain,
( ( ! [N: nat] :
( ( times_times_nat @ zero_zero_nat @ N )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(352,plain,
( ( ! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(353,plain,
( ( ! [P3: nat > $o,N: nat] :
( ( P3 @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ~ ( P3 @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P3 @ M2 ) ) ) )
=> ( P3 @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(354,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(355,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(356,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(357,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(358,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(359,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)],[28]) ).
thf(360,plain,
( ( ! [M: nat] :
( ( times_times_nat @ M @ zero_zero_nat )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(361,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)],[30]) ).
thf(362,plain,
( ( ! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(363,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(364,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(365,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)],[34]) ).
thf(366,plain,
( ( null_a @ nil_a )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(367,plain,
( ( ! [Xs: list_a] :
( ( Xs = nil_a )
= ( null_a @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(368,plain,
( ( ! [X: a,Xs: list_a] :
~ ( null_a @ ( cons_a @ X @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(369,plain,
( ( ! [Xs: list_a,Ys2: list_a] :
( ( Xs = Ys2 )
=> ( Xs
= ( append_a @ nil_a @ Ys2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(370,plain,
( ( ! [Ys2: list_a] :
( ( append_a @ nil_a @ Ys2 )
= Ys2 ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(371,plain,
( ( ! [A: list_a] :
( ( append_a @ nil_a @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(372,plain,
( ( ! [X: a,Xs1: list_a,Ys2: list_a,Xs: list_a,Zs: list_a] :
( ( ( cons_a @ X @ Xs1 )
= Ys2 )
=> ( ( Xs
= ( append_a @ Xs1 @ Zs ) )
=> ( ( cons_a @ X @ Xs )
= ( append_a @ Ys2 @ Zs ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(373,plain,
( ( ! [X: a,Xs: list_a,Ys2: list_a] :
( ( append_a @ ( cons_a @ X @ Xs ) @ Ys2 )
= ( cons_a @ X @ ( append_a @ Xs @ Ys2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(374,plain,
( ( ! [X21: a,X22: list_a] :
( nil_a
!= ( cons_a @ X21 @ X22 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(375,plain,
( ( ! [List: list_a,X21: a,X22: list_a] :
( ( List
= ( cons_a @ X21 @ X22 ) )
=> ( List != nil_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(376,plain,
( ( ! [Y3: list_a] :
( ( Y3 != nil_a )
=> ~ ! [X213: a,X223: list_a] :
( Y3
!= ( cons_a @ X213 @ X223 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(377,plain,
( ( ! [P3: list_a > $o,List: list_a] :
( ( P3 @ nil_a )
=> ( ! [X1: a,X23: list_a] :
( ( P3 @ X23 )
=> ( P3 @ ( cons_a @ X1 @ X23 ) ) )
=> ( P3 @ List ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(378,plain,
( ( ! [Xs: list_a] :
( ( Xs != nil_a )
= ( ? [Y4: a,Ys3: list_a] :
( Xs
= ( cons_a @ Y4 @ Ys3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(379,plain,
( ( ! [P3: list_a > list_a > $o,Xs: list_a,Ys2: list_a] :
( ( P3 @ nil_a @ nil_a )
=> ( ! [X2: a,Xs2: list_a] : ( P3 @ ( cons_a @ X2 @ Xs2 ) @ nil_a )
=> ( ! [Y2: a,Ys: list_a] : ( P3 @ nil_a @ ( cons_a @ Y2 @ Ys ) )
=> ( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
( ( P3 @ Xs2 @ Ys )
=> ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) )
=> ( P3 @ Xs @ Ys2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(380,plain,
( ( ! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
( ! [X_1: list_a] : ( P3 @ nil_a @ X_1 )
=> ( ! [X2: a,Xs2: list_a,Ys: list_a] :
( ( P3 @ Ys @ Xs2 )
=> ( P3 @ ( cons_a @ X2 @ Xs2 ) @ Ys ) )
=> ( P3 @ A0 @ A1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(381,plain,
( ( ! [P3: list_a > $o,Xs: list_a] :
( ( P3 @ nil_a )
=> ( ! [X2: a] : ( P3 @ ( cons_a @ X2 @ nil_a ) )
=> ( ! [X2: a,Y2: a,Zs2: list_a] :
( ( P3 @ Zs2 )
=> ( ( P3 @ ( cons_a @ Y2 @ Zs2 ) )
=> ( P3 @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Zs2 ) ) ) ) )
=> ( P3 @ Xs ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(382,plain,
( ( ! [X: list_a] :
( ! [X2: a,Xs2: list_a] :
( X
!= ( cons_a @ X2 @ Xs2 ) )
=> ( X = nil_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(383,plain,
( ( ! [P3: list_a > $o,A0: list_a] :
( ! [X2: a,Xs2: list_a] :
( ! [X212: a,X222: list_a] :
( ( Xs2
= ( cons_a @ X212 @ X222 ) )
=> ( P3 @ Xs2 ) )
=> ( P3 @ ( cons_a @ X2 @ Xs2 ) ) )
=> ( ( P3 @ nil_a )
=> ( P3 @ A0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(384,plain,
( ( ! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
( ! [X_1: list_a] : ( P3 @ nil_a @ X_1 )
=> ( ! [Xs2: list_a] : ( P3 @ Xs2 @ nil_a )
=> ( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
( ( P3 @ Xs2 @ ( cons_a @ Y2 @ Ys ) )
=> ( ( P3 @ ( cons_a @ X2 @ Xs2 ) @ Ys )
=> ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) ) )
=> ( P3 @ A0 @ A1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(385,plain,
( ( ! [X: list_a] :
( ( X != nil_a )
=> ( ! [X2: a] :
( X
!= ( cons_a @ X2 @ nil_a ) )
=> ~ ! [X2: a,Y2: a,Xs2: list_a] :
( X
!= ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(386,plain,
( ( ! [P3: ( a > a > $o ) > list_a > $o,A0: a > a > $o,A1: list_a] :
( ! [P5: a > a > $o] : ( P3 @ P5 @ nil_a )
=> ( ! [P5: a > a > $o,X2: a,Ys: list_a] :
( ( P3 @ P5 @ Ys )
=> ( P3 @ P5 @ ( cons_a @ X2 @ Ys ) ) )
=> ( P3 @ A0 @ A1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(387,plain,
( ( ! [P3: list_a > $o,A0: list_a] :
( ( P3 @ nil_a )
=> ( ! [X2: a] : ( P3 @ ( cons_a @ X2 @ nil_a ) )
=> ( ! [X2: a,Y2: a,Xs2: list_a] :
( ( ( X2 = Y2 )
=> ( P3 @ ( cons_a @ X2 @ Xs2 ) ) )
=> ( ( ( X2 != Y2 )
=> ( P3 @ ( cons_a @ Y2 @ Xs2 ) ) )
=> ( P3 @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) ) )
=> ( P3 @ A0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(388,plain,
( ( ! [P3: ( a > a > $o ) > list_a > $o,A0: a > a > $o,A1: list_a] :
( ! [P5: a > a > $o] : ( P3 @ P5 @ nil_a )
=> ( ! [P5: a > a > $o,X2: a] : ( P3 @ P5 @ ( cons_a @ X2 @ nil_a ) )
=> ( ! [P5: a > a > $o,X2: a,Y2: a,Xs2: list_a] :
( ( P3 @ P5 @ ( cons_a @ Y2 @ Xs2 ) )
=> ( P3 @ P5 @ ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) )
=> ( P3 @ A0 @ A1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(389,plain,
( ( ! [Xs: list_a,P3: list_a > $o] :
( ( Xs != nil_a )
=> ( ! [X2: a] : ( P3 @ ( cons_a @ X2 @ nil_a ) )
=> ( ! [X2: a,Xs2: list_a] :
( ( Xs2 != nil_a )
=> ( ( P3 @ Xs2 )
=> ( P3 @ ( cons_a @ X2 @ Xs2 ) ) ) )
=> ( P3 @ Xs ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(390,plain,
( ( ! [P3: ( a > a ) > list_a > list_a > $o,A0: a > a,A1: list_a,A22: list_a] :
( ! [F2: a > a,X_1: list_a] : ( P3 @ F2 @ nil_a @ X_1 )
=> ( ! [F2: a > a,A2: a,As2: list_a,Bs: list_a] :
( ( P3 @ F2 @ As2 @ ( cons_a @ ( F2 @ A2 ) @ Bs ) )
=> ( P3 @ F2 @ ( cons_a @ A2 @ As2 ) @ Bs ) )
=> ( P3 @ A0 @ A1 @ A22 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(391,plain,
( ( ! [X: list_a] :
( ( X != nil_a )
=> ~ ! [X2: a,Ys: list_a] :
( X
!= ( cons_a @ X2 @ Ys ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(392,plain,
( ( ! [P3: list_a > $o,A0: list_a] :
( ( P3 @ nil_a )
=> ( ! [X2: a,Ys: list_a] :
( ( P3 @ Ys )
=> ( P3 @ ( cons_a @ X2 @ Ys ) ) )
=> ( P3 @ A0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(393,plain,
( ( zero_zero_nat != one_one_nat )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(394,plain,
( ( zero_zero_a != one_one_a )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(395,plain,
( ( zero_zero_poly_a != one_one_poly_a )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(396,plain,
( ( ! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
!= zero_zero_nat )
=> ( ( A != zero_zero_nat )
& ( B != zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(397,plain,
( ( ! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
!= zero_zero_poly_a )
=> ( ( A != zero_zero_poly_a )
& ( B != zero_zero_poly_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(398,plain,
( ( ! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
!= zero_zero_a )
=> ( ( A != zero_zero_a )
& ( B != zero_zero_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(399,plain,
( ( ! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(400,plain,
( ( ! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= zero_zero_poly_a )
=> ( ( A = zero_zero_poly_a )
| ( B = zero_zero_poly_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(401,plain,
( ( ! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= zero_zero_a )
=> ( ( A = zero_zero_a )
| ( B = zero_zero_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(402,plain,
( ( ! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ A @ B )
!= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(403,plain,
( ( ! [A: poly_a,B: poly_a] :
( ( A != zero_zero_poly_a )
=> ( ( B != zero_zero_poly_a )
=> ( ( times_times_poly_a @ A @ B )
!= zero_zero_poly_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(404,plain,
( ( ! [A: a,B: a] :
( ( A != zero_zero_a )
=> ( ( B != zero_zero_a )
=> ( ( times_times_a @ A @ B )
!= zero_zero_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(405,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( C != zero_zero_nat )
=> ( ( ( times_times_nat @ C @ A )
= ( times_times_nat @ C @ B ) )
= ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(406,plain,
( ( ! [C: poly_a,A: poly_a,B: poly_a] :
( ( C != zero_zero_poly_a )
=> ( ( ( times_times_poly_a @ C @ A )
= ( times_times_poly_a @ C @ B ) )
= ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(407,plain,
( ( ! [C: a,A: a,B: a] :
( ( C != zero_zero_a )
=> ( ( ( times_times_a @ C @ A )
= ( times_times_a @ C @ B ) )
= ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(408,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( C != zero_zero_nat )
=> ( ( ( times_times_nat @ A @ C )
= ( times_times_nat @ B @ C ) )
= ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(409,plain,
( ( ! [C: poly_a,A: poly_a,B: poly_a] :
( ( C != zero_zero_poly_a )
=> ( ( ( times_times_poly_a @ A @ C )
= ( times_times_poly_a @ B @ C ) )
= ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(410,plain,
( ( ! [C: a,A: a,B: a] :
( ( C != zero_zero_a )
=> ( ( ( times_times_a @ A @ C )
= ( times_times_a @ B @ C ) )
= ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(411,plain,
( ( ~ ( ord_less_poly_a @ zero_zero_poly_a @ zero_zero_poly_a ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(412,plain,
( ( ~ ( ord_less_a @ zero_zero_a @ zero_zero_a ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(413,plain,
( ( ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(414,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(415,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(416,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(417,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(418,plain,
( ( ! [X: a,Xs: list_a] :
( ( cons_a @ X @ Xs )
!= Xs ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(419,plain,
( ( ! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(420,plain,
( ( ! [X: a] :
( ( zero_zero_a = X )
= ( X = zero_zero_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(421,plain,
( ( ! [X: poly_a] :
( ( zero_zero_poly_a = X )
= ( X = zero_zero_poly_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(422,plain,
( ( ! [Xs: list_a] :
( ( append_a @ Xs @ nil_a )
= Xs ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(423,plain,
( ( ! [Xs: list_a,Ys2: list_a] :
( ( ( append_a @ Xs @ Ys2 )
= Xs )
= ( Ys2 = nil_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(424,plain,
( ( ! [Xs: list_a,Ys2: list_a] :
( ( Xs
= ( append_a @ Xs @ Ys2 ) )
= ( Ys2 = nil_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(425,plain,
( ( ! [Xs: list_a,Ys2: list_a] :
( ( ( append_a @ Xs @ Ys2 )
= Ys2 )
= ( Xs = nil_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(426,plain,
( ( ! [Ys2: list_a,Xs: list_a] :
( ( Ys2
= ( append_a @ Xs @ Ys2 ) )
= ( Xs = nil_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(427,plain,
( ( ! [Xs: list_a,Ys2: list_a] :
( ( nil_a
= ( append_a @ Xs @ Ys2 ) )
= ( ( Xs = nil_a )
& ( Ys2 = nil_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(428,plain,
( ( ! [Xs: list_a,Ys2: list_a] :
( ( ( append_a @ Xs @ Ys2 )
= nil_a )
= ( ( Xs = nil_a )
& ( Ys2 = nil_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(429,plain,
( ( ! [A: list_a] :
( ( append_a @ A @ nil_a )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(430,plain,
( ( ( uminus_uminus_a @ zero_zero_a )
= zero_zero_a )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(431,plain,
( ( ( uminus_uminus_poly_a @ zero_zero_poly_a )
= zero_zero_poly_a )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(432,plain,
( ( ! [A: a] :
( ( zero_zero_a
= ( uminus_uminus_a @ A ) )
= ( zero_zero_a = A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(433,plain,
( ( ! [A: poly_a] :
( ( zero_zero_poly_a
= ( uminus_uminus_poly_a @ A ) )
= ( zero_zero_poly_a = A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(434,plain,
( ( ! [A: a] :
( ( ( uminus_uminus_a @ A )
= zero_zero_a )
= ( A = zero_zero_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(435,plain,
( ( ! [A: poly_a] :
( ( ( uminus_uminus_poly_a @ A )
= zero_zero_poly_a )
= ( A = zero_zero_poly_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(436,plain,
( ( ! [A: a] :
( ( A
= ( uminus_uminus_a @ A ) )
= ( A = zero_zero_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(437,plain,
( ( ! [A: poly_a] :
( ( A
= ( uminus_uminus_poly_a @ A ) )
= ( A = zero_zero_poly_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(438,plain,
( ( ! [A: a] :
( ( ( uminus_uminus_a @ A )
= A )
= ( A = zero_zero_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(439,plain,
( ( ! [A: poly_a] :
( ( ( uminus_uminus_poly_a @ A )
= A )
= ( A = zero_zero_poly_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(440,plain,
( ( ! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(441,plain,
( ( ! [A: poly_a] :
( ( times_times_poly_a @ zero_zero_poly_a @ A )
= zero_zero_poly_a ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(442,plain,
( ( ! [A: a] :
( ( times_times_a @ zero_zero_a @ A )
= zero_zero_a ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(443,plain,
( ( ! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(444,plain,
( ( ! [A: poly_a] :
( ( times_times_poly_a @ A @ zero_zero_poly_a )
= zero_zero_poly_a ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(445,plain,
( ( ! [A: a] :
( ( times_times_a @ A @ zero_zero_a )
= zero_zero_a ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(446,plain,
( ( ! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(447,plain,
( ( ! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= zero_zero_poly_a )
= ( ( A = zero_zero_poly_a )
| ( B = zero_zero_poly_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(448,plain,
( ( ! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= zero_zero_a )
= ( ( A = zero_zero_a )
| ( B = zero_zero_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(449,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( ( times_times_nat @ C @ A )
= ( times_times_nat @ C @ B ) )
= ( ( C = zero_zero_nat )
| ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(450,plain,
( ( ! [C: poly_a,A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ C @ A )
= ( times_times_poly_a @ C @ B ) )
= ( ( C = zero_zero_poly_a )
| ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(451,plain,
( ( ! [C: a,A: a,B: a] :
( ( ( times_times_a @ C @ A )
= ( times_times_a @ C @ B ) )
= ( ( C = zero_zero_a )
| ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(452,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ( times_times_nat @ A @ C )
= ( times_times_nat @ B @ C ) )
= ( ( C = zero_zero_nat )
| ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(453,plain,
( ( ! [A: poly_a,C: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ C )
= ( times_times_poly_a @ B @ C ) )
= ( ( C = zero_zero_poly_a )
| ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(454,plain,
( ( ! [A: a,C: a,B: a] :
( ( ( times_times_a @ A @ C )
= ( times_times_a @ B @ C ) )
= ( ( C = zero_zero_a )
| ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(455,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(456,plain,
( ( ! [X21: a,X22: list_a,Y21: a,Y22: list_a] :
( ( ( cons_a @ X21 @ X22 )
= ( cons_a @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(457,plain,
( ( ! [Xs: list_a,X: a,Ys2: list_a,Y3: a] :
( ( ( append_a @ Xs @ ( cons_a @ X @ nil_a ) )
= ( append_a @ Ys2 @ ( cons_a @ Y3 @ nil_a ) ) )
= ( ( Xs = Ys2 )
& ( X = Y3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(458,plain,
( ( ! [A: a,P2: poly_a] :
( ( A != zero_zero_a )
=> ( ( P2 != zero_zero_poly_a )
=> ( ( descar466059845root_a @ A @ P2 )
!= zero_zero_poly_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(459,plain,
( ( ! [X: list_a] :
( ( X != nil_a )
=> ( ! [X2: a] :
( X
!= ( cons_a @ X2 @ nil_a ) )
=> ~ ! [X2: a,Y2: a,Xs2: list_a] :
( X
!= ( cons_a @ X2 @ ( cons_a @ Y2 @ Xs2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(460,plain,
( ( ! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
( ( P3 @ Xs2 @ Ys )
=> ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) )
=> ( ! [Xs2: list_a] : ( P3 @ Xs2 @ nil_a )
=> ( ! [Y2: a,Ys: list_a] : ( P3 @ nil_a @ ( cons_a @ Y2 @ Ys ) )
=> ( P3 @ A0 @ A1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(461,plain,
( ( ! [P3: list_a > list_a > $o,A0: list_a,A1: list_a] :
( ! [Xs2: list_a] : ( P3 @ Xs2 @ nil_a )
=> ( ! [V: a,Va: list_a] : ( P3 @ nil_a @ ( cons_a @ V @ Va ) )
=> ( ! [X2: a,Xs2: list_a,Y2: a,Ys: list_a] :
( ( P3 @ Xs2 @ Ys )
=> ( P3 @ ( cons_a @ X2 @ Xs2 ) @ ( cons_a @ Y2 @ Ys ) ) )
=> ( P3 @ A0 @ A1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(462,plain,
( ( ! [P2: poly_a] :
( ( times_times_poly_a @ P2 @ zero_zero_poly_a )
= zero_zero_poly_a ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(463,plain,
( ( ! [Q2: poly_a] :
( ( times_times_poly_a @ zero_zero_poly_a @ Q2 )
= zero_zero_poly_a ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(464,plain,
( ( ! [P3: poly_a > $o,A0: poly_a] :
( ! [A2: a,P4: poly_a] :
( ( ( P4 != zero_zero_poly_a )
=> ( P3 @ P4 ) )
=> ( P3 @ ( pCons_a @ A2 @ P4 ) ) )
=> ( P3 @ A0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(465,plain,
( ( ! [P3: poly_a > poly_a > $o,P2: poly_a,Q2: poly_a] :
( ( P3 @ zero_zero_poly_a @ zero_zero_poly_a )
=> ( ! [A2: a,P4: poly_a,B2: a,Q3: poly_a] :
( ( P3 @ P4 @ Q3 )
=> ( P3 @ ( pCons_a @ A2 @ P4 ) @ ( pCons_a @ B2 @ Q3 ) ) )
=> ( P3 @ P2 @ Q2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(466,plain,
( ( ! [P3: poly_a > $o,P2: poly_a] :
( ( P3 @ zero_zero_poly_a )
=> ( ! [A2: a,P4: poly_a] :
( ( ( A2 != zero_zero_a )
| ( P4 != zero_zero_poly_a ) )
=> ( ( P3 @ P4 )
=> ( P3 @ ( pCons_a @ A2 @ P4 ) ) ) )
=> ( P3 @ P2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(467,plain,
( ( is_zero_a
= ( ^ [P: poly_a] : ( P = zero_zero_poly_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(468,plain,
( ( ( descar1375166517sums_a @ nil_a )
= nil_a )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(469,plain,
( ( ! [X: a] :
( ( descar1375166517sums_a @ ( cons_a @ X @ nil_a ) )
= ( cons_a @ X @ nil_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(470,plain,
( ( ( poly_a2 @ nil_a )
= zero_zero_poly_a )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(471,plain,
( ( ! [A: a,As: list_a] :
( ( poly_a2 @ ( cons_a @ A @ As ) )
= ( pCons_a @ A @ ( poly_a2 @ As ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(472,plain,
( ( ! [As: list_a] :
( ( poly_a2 @ ( append_a @ As @ ( cons_a @ zero_zero_a @ nil_a ) ) )
= ( poly_a2 @ As ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(473,plain,
( ( ! [X: a] :
( ( descar2095969287nges_a @ ( cons_a @ X @ nil_a ) )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(474,plain,
( ( ! [Xs: list_a] :
( ( descar1375166517sums_a @ ( cons_a @ zero_zero_a @ Xs ) )
= ( cons_a @ zero_zero_a @ ( descar1375166517sums_a @ Xs ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(475,plain,
( ( ! [A: a,P2: poly_a] :
( ( ( smult_a @ A @ P2 )
= zero_zero_poly_a )
= ( ( A = zero_zero_a )
| ( P2 = zero_zero_poly_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(476,plain,
( ( ! [P2: poly_a] :
( ( smult_a @ zero_zero_a @ P2 )
= zero_zero_poly_a ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(477,plain,
( ( ! [A: a,P2: poly_a] :
( ( ( pCons_a @ A @ P2 )
= zero_zero_poly_a )
= ( ( A = zero_zero_a )
& ( P2 = zero_zero_poly_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(478,plain,
( ( ( pCons_a @ zero_zero_a @ zero_zero_poly_a )
= zero_zero_poly_a )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(479,plain,
( ( ! [A: a] :
( ( smult_a @ A @ zero_zero_poly_a )
= zero_zero_poly_a ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(480,plain,
( ( ys
= ( append_a @ ( coeffs_a @ g ) @ ( cons_a @ zero_zero_a @ nil_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(481,plain,
( ( ! [P2: poly_a] :
( ( P2 != zero_zero_poly_a )
=> ( ( coeffs_a @ P2 )
!= nil_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(482,plain,
( ( ( coeffs_a @ zero_zero_poly_a )
= nil_a )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(483,plain,
( ( ! [P2: poly_a] :
( ( ( coeffs_a @ P2 )
= nil_a )
= ( P2 = zero_zero_poly_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(484,plain,
( ( ! [X: a,Xs: list_a] :
( ( descar2095969287nges_a @ ( cons_a @ X @ ( cons_a @ zero_zero_a @ Xs ) ) )
= ( descar2095969287nges_a @ ( cons_a @ X @ Xs ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(485,plain,
( ( ! [Xs: list_a] :
( ( descar2095969287nges_a @ ( cons_a @ zero_zero_a @ Xs ) )
= ( descar2095969287nges_a @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(486,plain,
( ( ( descar2095969287nges_a @ nil_a )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(487,plain,
( ( ! [P2: poly_a] :
( ( poly_a2 @ ( coeffs_a @ P2 ) )
= P2 ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(488,plain,
( ( is_zero_a
= ( ^ [P: poly_a] : ( null_a @ ( coeffs_a @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(489,plain,
( ( ! [Xs: list_a,P2: poly_a] :
( ( ( poly_a2 @ Xs )
= P2 )
=> ( ( descar2095969287nges_a @ Xs )
= ( descar2095969287nges_a @ ( coeffs_a @ P2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(490,plain,
( ( ys
= ( descar1375166517sums_a @ xs ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(491,plain,
( ( ( ^ [Y: poly_a,Z: poly_a] : ( Y = Z ) )
= ( ^ [P: poly_a,Q: poly_a] :
( ( coeffs_a @ P )
= ( coeffs_a @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(492,plain,
( ( g != zero_zero_poly_a )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(493,plain,
( ( v
= ( ^ [F: poly_a] : ( descar2095969287nges_a @ ( coeffs_a @ F ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(494,plain,
( ( ( descar2095969287nges_a @ ys )
!= ( descar2095969287nges_a @ ( coeffs_a @ g ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[349]) ).
thf(495,plain,
( ( ! [P3: nat > $o] :
( ~ ( P3 @ zero_zero_nat )
| ( ( ord_less_nat @ zero_zero_nat @ ( sK1_N2 @ P3 ) )
& ~ ( P3 @ ( sK1_N2 @ P3 ) )
& ! [SY327: nat] :
( ~ ( ord_less_nat @ SY327 @ ( sK1_N2 @ P3 ) )
| ( P3 @ SY327 ) ) )
| ! [N: nat] : ( P3 @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[353]) ).
thf(496,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
| ( N != zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[354]) ).
thf(497,plain,
( ( ! [N: nat] :
( ( N = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[358]) ).
thf(498,plain,
( ( ! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[362]) ).
thf(499,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[364]) ).
thf(500,plain,
( ( ! [Xs: list_a,Ys2: list_a] :
( ( Xs != Ys2 )
| ( Xs
= ( append_a @ nil_a @ Ys2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[369]) ).
thf(501,plain,
( ( ! [X: a,Xs1: list_a,Ys2: list_a] :
( ( ( cons_a @ X @ Xs1 )
!= Ys2 )
| ! [Xs: list_a,Zs: list_a] :
( ( Xs
!= ( append_a @ Xs1 @ Zs ) )
| ( ( cons_a @ X @ Xs )
= ( append_a @ Ys2 @ Zs ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[372]) ).
thf(502,plain,
( ( ! [X21: a,X22: list_a] :
( nil_a
!= ( cons_a @ X21 @ X22 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[374]) ).
thf(503,plain,
( ( ! [List: list_a] :
( ! [X21: a,X22: list_a] :
( List
!= ( cons_a @ X21 @ X22 ) )
| ( List != nil_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[375]) ).
thf(504,plain,
( ( ! [Y3: list_a] :
( ( Y3 = nil_a )
| ( Y3
= ( cons_a @ ( sK2_X213 @ Y3 ) @ ( sK3_SY328 @ Y3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[376]) ).
thf(505,plain,
( ( ! [P3: list_a > $o] :
( ~ ( P3 @ nil_a )
| ( ( P3 @ ( sK5_SY329 @ P3 ) )
& ~ ( P3 @ ( cons_a @ ( sK4_X1 @ P3 ) @ ( sK5_SY329 @ P3 ) ) ) )
| ! [List: list_a] : ( P3 @ List ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[377]) ).
thf(506,plain,
( ( ! [Xs: list_a] :
( ( Xs != nil_a )
= ( ? [Y4: a,Ys3: list_a] :
( Xs
= ( cons_a @ Y4 @ Ys3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[378]) ).
thf(507,plain,
( ( ! [P3: list_a > list_a > $o] :
( ~ ( P3 @ nil_a @ nil_a )
| ~ ( P3 @ ( cons_a @ ( sK12_X2 @ P3 ) @ ( sK13_SY337 @ P3 ) ) @ nil_a )
| ~ ( P3 @ nil_a @ ( cons_a @ ( sK10_Y2 @ P3 ) @ ( sK11_SY336 @ P3 ) ) )
| ( ( P3 @ ( sK7_SY330 @ P3 ) @ ( sK9_SY335 @ P3 ) )
& ~ ( P3 @ ( cons_a @ ( sK6_X2 @ P3 ) @ ( sK7_SY330 @ P3 ) ) @ ( cons_a @ ( sK8_SY333 @ P3 ) @ ( sK9_SY335 @ P3 ) ) ) )
| ! [Xs: list_a,Ys2: list_a] : ( P3 @ Xs @ Ys2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[379]) ).
thf(508,plain,
( ( ! [P3: list_a > list_a > $o] :
( ~ ( P3 @ nil_a @ ( sK17_X_1 @ P3 ) )
| ( ( P3 @ ( sK16_SY340 @ P3 ) @ ( sK15_SY338 @ P3 ) )
& ~ ( P3 @ ( cons_a @ ( sK14_X2 @ P3 ) @ ( sK15_SY338 @ P3 ) ) @ ( sK16_SY340 @ P3 ) ) )
| ! [A0: list_a,A1: list_a] : ( P3 @ A0 @ A1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[380]) ).
thf(509,plain,
( ( ! [P3: list_a > $o] :
( ~ ( P3 @ nil_a )
| ~ ( P3 @ ( cons_a @ ( sK21_X2 @ P3 ) @ nil_a ) )
| ( ( P3 @ ( sK20_SY343 @ P3 ) )
& ( P3 @ ( cons_a @ ( sK19_SY341 @ P3 ) @ ( sK20_SY343 @ P3 ) ) )
& ~ ( P3 @ ( cons_a @ ( sK18_X2 @ P3 ) @ ( cons_a @ ( sK19_SY341 @ P3 ) @ ( sK20_SY343 @ P3 ) ) ) ) )
| ! [Xs: list_a] : ( P3 @ Xs ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[381]) ).
thf(510,plain,
( ( ! [X: list_a] :
( ( X
= ( cons_a @ ( sK22_X2 @ X ) @ ( sK23_SY344 @ X ) ) )
| ( X = nil_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[382]) ).
thf(511,plain,
( ( ! [P3: list_a > $o] :
( ( ( ! [SY348: a,SY349: list_a] :
( ( sK25_SY345 @ P3 )
!= ( cons_a @ SY348 @ SY349 ) )
| ( P3 @ ( sK25_SY345 @ P3 ) ) )
& ~ ( P3 @ ( cons_a @ ( sK24_X2 @ P3 ) @ ( sK25_SY345 @ P3 ) ) ) )
| ~ ( P3 @ nil_a )
| ! [A0: list_a] : ( P3 @ A0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[383]) ).
thf(512,plain,
( ( ! [P3: list_a > list_a > $o] :
( ~ ( P3 @ nil_a @ ( sK31_X_1 @ P3 ) )
| ~ ( P3 @ ( sK30_Xs2 @ P3 ) @ nil_a )
| ( ( P3 @ ( sK27_SY350 @ P3 ) @ ( cons_a @ ( sK28_SY353 @ P3 ) @ ( sK29_SY355 @ P3 ) ) )
& ( P3 @ ( cons_a @ ( sK26_X2 @ P3 ) @ ( sK27_SY350 @ P3 ) ) @ ( sK29_SY355 @ P3 ) )
& ~ ( P3 @ ( cons_a @ ( sK26_X2 @ P3 ) @ ( sK27_SY350 @ P3 ) ) @ ( cons_a @ ( sK28_SY353 @ P3 ) @ ( sK29_SY355 @ P3 ) ) ) )
| ! [A0: list_a,A1: list_a] : ( P3 @ A0 @ A1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[384]) ).
thf(513,plain,
( ( ! [X: list_a] :
( ( X = nil_a )
| ( X
= ( cons_a @ ( sK35_X2 @ X ) @ nil_a ) )
| ( X
= ( cons_a @ ( sK32_X2 @ X ) @ ( cons_a @ ( sK33_SY356 @ X ) @ ( sK34_SY358 @ X ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[385]) ).
thf(514,plain,
( ( ! [P3: ( a > a > $o ) > list_a > $o] :
( ~ ( P3 @ ( sK39_P5 @ P3 ) @ nil_a )
| ( ( P3 @ ( sK36_P5 @ P3 ) @ ( sK38_SY361 @ P3 ) )
& ~ ( P3 @ ( sK36_P5 @ P3 ) @ ( cons_a @ ( sK37_SY359 @ P3 ) @ ( sK38_SY361 @ P3 ) ) ) )
| ! [A0: a > a > $o,A1: list_a] : ( P3 @ A0 @ A1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[386]) ).
thf(515,plain,
( ( ! [P3: list_a > $o] :
( ~ ( P3 @ nil_a )
| ~ ( P3 @ ( cons_a @ ( sK43_X2 @ P3 ) @ nil_a ) )
| ( ( ( ( sK40_X2 @ P3 )
!= ( sK41_SY362 @ P3 ) )
| ( P3 @ ( cons_a @ ( sK40_X2 @ P3 ) @ ( sK42_SY364 @ P3 ) ) ) )
& ( ( ( sK40_X2 @ P3 )
= ( sK41_SY362 @ P3 ) )
| ( P3 @ ( cons_a @ ( sK41_SY362 @ P3 ) @ ( sK42_SY364 @ P3 ) ) ) )
& ~ ( P3 @ ( cons_a @ ( sK40_X2 @ P3 ) @ ( cons_a @ ( sK41_SY362 @ P3 ) @ ( sK42_SY364 @ P3 ) ) ) ) )
| ! [A0: list_a] : ( P3 @ A0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[387]) ).
thf(516,plain,
( ( ! [P3: ( a > a > $o ) > list_a > $o] :
( ~ ( P3 @ ( sK50_P5 @ P3 ) @ nil_a )
| ~ ( P3 @ ( sK48_P5 @ P3 ) @ ( cons_a @ ( sK49_SY371 @ P3 ) @ nil_a ) )
| ( ( P3 @ ( sK44_P5 @ P3 ) @ ( cons_a @ ( sK46_SY368 @ P3 ) @ ( sK47_SY370 @ P3 ) ) )
& ~ ( P3 @ ( sK44_P5 @ P3 ) @ ( cons_a @ ( sK45_SY365 @ P3 ) @ ( cons_a @ ( sK46_SY368 @ P3 ) @ ( sK47_SY370 @ P3 ) ) ) ) )
| ! [A0: a > a > $o,A1: list_a] : ( P3 @ A0 @ A1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[388]) ).
thf(517,plain,
( ( ! [Xs: list_a] :
( ( Xs = nil_a )
| ! [P3: list_a > $o] :
( ~ ( P3 @ ( cons_a @ ( sK53_X2 @ P3 @ Xs ) @ nil_a ) )
| ( ( ( sK52_SY372 @ P3 @ Xs )
!= nil_a )
& ( P3 @ ( sK52_SY372 @ P3 @ Xs ) )
& ~ ( P3 @ ( cons_a @ ( sK51_X2 @ P3 @ Xs ) @ ( sK52_SY372 @ P3 @ Xs ) ) ) )
| ( P3 @ Xs ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[389]) ).
thf(518,plain,
( ( ! [P3: ( a > a ) > list_a > list_a > $o,A0: a > a] :
( ~ ( P3 @ ( sK58_F2 @ A0 @ P3 ) @ nil_a @ ( sK59_SY379 @ A0 @ P3 ) )
| ( ( P3 @ ( sK54_F2 @ A0 @ P3 ) @ ( sK56_SY376 @ A0 @ P3 ) @ ( cons_a @ ( sK54_F2 @ A0 @ P3 @ ( sK55_SY373 @ A0 @ P3 ) ) @ ( sK57_SY378 @ A0 @ P3 ) ) )
& ~ ( P3 @ ( sK54_F2 @ A0 @ P3 ) @ ( cons_a @ ( sK55_SY373 @ A0 @ P3 ) @ ( sK56_SY376 @ A0 @ P3 ) ) @ ( sK57_SY378 @ A0 @ P3 ) ) )
| ! [A1: list_a,A22: list_a] : ( P3 @ A0 @ A1 @ A22 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[390]) ).
thf(519,plain,
( ( ! [X: list_a] :
( ( X = nil_a )
| ( X
= ( cons_a @ ( sK60_X2 @ X ) @ ( sK61_SY380 @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[391]) ).
thf(520,plain,
( ( ! [P3: list_a > $o] :
( ~ ( P3 @ nil_a )
| ( ( P3 @ ( sK63_SY381 @ P3 ) )
& ~ ( P3 @ ( cons_a @ ( sK62_X2 @ P3 ) @ ( sK63_SY381 @ P3 ) ) ) )
| ! [A0: list_a] : ( P3 @ A0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[392]) ).
thf(521,plain,
( ( zero_zero_nat != one_one_nat )
= $true ),
inference(extcnf_combined,[status(esa)],[393]) ).
thf(522,plain,
( ( zero_zero_a != one_one_a )
= $true ),
inference(extcnf_combined,[status(esa)],[394]) ).
thf(523,plain,
( ( zero_zero_poly_a != one_one_poly_a )
= $true ),
inference(extcnf_combined,[status(esa)],[395]) ).
thf(524,plain,
( ( ! [A: nat] :
( ! [B: nat] :
( ( times_times_nat @ A @ B )
= zero_zero_nat )
| ( A != zero_zero_nat ) )
& ! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
| ( B != zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[396]) ).
thf(525,plain,
( ( ! [A: poly_a] :
( ! [B: poly_a] :
( ( times_times_poly_a @ A @ B )
= zero_zero_poly_a )
| ( A != zero_zero_poly_a ) )
& ! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= zero_zero_poly_a )
| ( B != zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[397]) ).
thf(526,plain,
( ( ! [A: a] :
( ! [B: a] :
( ( times_times_a @ A @ B )
= zero_zero_a )
| ( A != zero_zero_a ) )
& ! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= zero_zero_a )
| ( B != zero_zero_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[398]) ).
thf(527,plain,
( ( ! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
!= zero_zero_nat )
| ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[399]) ).
thf(528,plain,
( ( ! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
!= zero_zero_poly_a )
| ( A = zero_zero_poly_a )
| ( B = zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[400]) ).
thf(529,plain,
( ( ! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
!= zero_zero_a )
| ( A = zero_zero_a )
| ( B = zero_zero_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[401]) ).
thf(530,plain,
( ( ! [A: nat] :
( ( A = zero_zero_nat )
| ! [B: nat] :
( ( B = zero_zero_nat )
| ( ( times_times_nat @ A @ B )
!= zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[402]) ).
thf(531,plain,
( ( ! [A: poly_a] :
( ( A = zero_zero_poly_a )
| ! [B: poly_a] :
( ( B = zero_zero_poly_a )
| ( ( times_times_poly_a @ A @ B )
!= zero_zero_poly_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[403]) ).
thf(532,plain,
( ( ! [A: a] :
( ( A = zero_zero_a )
| ! [B: a] :
( ( B = zero_zero_a )
| ( ( times_times_a @ A @ B )
!= zero_zero_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[404]) ).
thf(533,plain,
( ( ! [C: nat] :
( ( C = zero_zero_nat )
| ! [A: nat,B: nat] :
( ( ( times_times_nat @ C @ A )
= ( times_times_nat @ C @ B ) )
= ( A = B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[405]) ).
thf(534,plain,
( ( ! [C: poly_a] :
( ( C = zero_zero_poly_a )
| ! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ C @ A )
= ( times_times_poly_a @ C @ B ) )
= ( A = B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[406]) ).
thf(535,plain,
( ( ! [C: a] :
( ( C = zero_zero_a )
| ! [A: a,B: a] :
( ( ( times_times_a @ C @ A )
= ( times_times_a @ C @ B ) )
= ( A = B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[407]) ).
thf(536,plain,
( ( ! [C: nat] :
( ( C = zero_zero_nat )
| ! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ C )
= ( times_times_nat @ B @ C ) )
= ( A = B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[408]) ).
thf(537,plain,
( ( ! [C: poly_a] :
( ( C = zero_zero_poly_a )
| ! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ C )
= ( times_times_poly_a @ B @ C ) )
= ( A = B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[409]) ).
thf(538,plain,
( ( ! [C: a] :
( ( C = zero_zero_a )
| ! [A: a,B: a] :
( ( ( times_times_a @ A @ C )
= ( times_times_a @ B @ C ) )
= ( A = B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[410]) ).
thf(539,plain,
( ( ! [N: nat] :
( ( N = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[414]) ).
thf(540,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
| ( N != zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[416]) ).
thf(541,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[417]) ).
thf(542,plain,
( ( ! [X: a,Xs: list_a] :
( ( cons_a @ X @ Xs )
!= Xs ) )
= $true ),
inference(extcnf_combined,[status(esa)],[418]) ).
thf(543,plain,
( ( ! [A: a] :
( ( A = zero_zero_a )
| ! [P2: poly_a] :
( ( P2 = zero_zero_poly_a )
| ( ( descar466059845root_a @ A @ P2 )
!= zero_zero_poly_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[458]) ).
thf(544,plain,
( ( ! [X: list_a] :
( ( X = nil_a )
| ( X
= ( cons_a @ ( sK67_X2 @ X ) @ nil_a ) )
| ( X
= ( cons_a @ ( sK64_X2 @ X ) @ ( cons_a @ ( sK65_SY382 @ X ) @ ( sK66_SY384 @ X ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[459]) ).
thf(545,plain,
( ( ! [P3: list_a > list_a > $o] :
( ( ( P3 @ ( sK72_SY386 @ P3 ) @ ( sK74_SY391 @ P3 ) )
& ~ ( P3 @ ( cons_a @ ( sK71_X2 @ P3 ) @ ( sK72_SY386 @ P3 ) ) @ ( cons_a @ ( sK73_SY389 @ P3 ) @ ( sK74_SY391 @ P3 ) ) ) )
| ~ ( P3 @ ( sK70_Xs2 @ P3 ) @ nil_a )
| ~ ( P3 @ nil_a @ ( cons_a @ ( sK68_Y2 @ P3 ) @ ( sK69_SY385 @ P3 ) ) )
| ! [A0: list_a,A1: list_a] : ( P3 @ A0 @ A1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[460]) ).
thf(546,plain,
( ( ! [P3: list_a > list_a > $o] :
( ~ ( P3 @ ( sK81_Xs2 @ P3 ) @ nil_a )
| ~ ( P3 @ nil_a @ ( cons_a @ ( sK79_V @ P3 ) @ ( sK80_SY398 @ P3 ) ) )
| ( ( P3 @ ( sK76_SY392 @ P3 ) @ ( sK78_SY397 @ P3 ) )
& ~ ( P3 @ ( cons_a @ ( sK75_X2 @ P3 ) @ ( sK76_SY392 @ P3 ) ) @ ( cons_a @ ( sK77_SY395 @ P3 ) @ ( sK78_SY397 @ P3 ) ) ) )
| ! [A0: list_a,A1: list_a] : ( P3 @ A0 @ A1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[461]) ).
thf(547,plain,
( ( ! [P3: poly_a > $o] :
( ( ( ( ( sK83_SY399 @ P3 )
= zero_zero_poly_a )
| ( P3 @ ( sK83_SY399 @ P3 ) ) )
& ~ ( P3 @ ( pCons_a @ ( sK82_A2 @ P3 ) @ ( sK83_SY399 @ P3 ) ) ) )
| ! [A0: poly_a] : ( P3 @ A0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[464]) ).
thf(548,plain,
( ( ! [P3: poly_a > poly_a > $o] :
( ~ ( P3 @ zero_zero_poly_a @ zero_zero_poly_a )
| ( ( P3 @ ( sK85_SY400 @ P3 ) @ ( sK87_SY405 @ P3 ) )
& ~ ( P3 @ ( pCons_a @ ( sK84_A2 @ P3 ) @ ( sK85_SY400 @ P3 ) ) @ ( pCons_a @ ( sK86_SY403 @ P3 ) @ ( sK87_SY405 @ P3 ) ) ) )
| ! [P2: poly_a,Q2: poly_a] : ( P3 @ P2 @ Q2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[465]) ).
thf(549,plain,
( ( ! [P3: poly_a > $o] :
( ~ ( P3 @ zero_zero_poly_a )
| ( ( ( ( sK88_A2 @ P3 )
!= zero_zero_a )
| ( ( sK89_SY406 @ P3 )
!= zero_zero_poly_a ) )
& ( P3 @ ( sK89_SY406 @ P3 ) )
& ~ ( P3 @ ( pCons_a @ ( sK88_A2 @ P3 ) @ ( sK89_SY406 @ P3 ) ) ) )
| ! [P2: poly_a] : ( P3 @ P2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[466]) ).
thf(550,plain,
( ( ! [P2: poly_a] :
( ( P2 = zero_zero_poly_a )
| ( ( coeffs_a @ P2 )
!= nil_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[481]) ).
thf(551,plain,
( ( ! [Xs: list_a,P2: poly_a] :
( ( ( poly_a2 @ Xs )
!= P2 )
| ( ( descar2095969287nges_a @ Xs )
= ( descar2095969287nges_a @ ( coeffs_a @ P2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[489]) ).
thf(552,plain,
( ( g != zero_zero_poly_a )
= $true ),
inference(extcnf_combined,[status(esa)],[492]) ).
thf(553,plain,
( ( v
= ( ^ [F: poly_a] : ( descar2095969287nges_a @ ( coeffs_a @ F ) ) ) )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(554,plain,
( ( g != zero_zero_poly_a )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(555,plain,
( ( ( ^ [Y: poly_a,Z: poly_a] : ( Y = Z ) )
= ( ^ [P: poly_a,Q: poly_a] :
( ( coeffs_a @ P )
= ( coeffs_a @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(556,plain,
( ( ys
= ( descar1375166517sums_a @ xs ) )
= $true ),
inference(copy,[status(thm)],[490]) ).
thf(557,plain,
( ( ! [Xs: list_a,P2: poly_a] :
( ( ( poly_a2 @ Xs )
!= P2 )
| ( ( descar2095969287nges_a @ Xs )
= ( descar2095969287nges_a @ ( coeffs_a @ P2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[551]) ).
thf(558,plain,
( ( is_zero_a
= ( ^ [P: poly_a] : ( null_a @ ( coeffs_a @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(559,plain,
( ( ! [P2: poly_a] :
( ( poly_a2 @ ( coeffs_a @ P2 ) )
= P2 ) )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(560,plain,
( ( ( descar2095969287nges_a @ nil_a )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(561,plain,
( ( ! [Xs: list_a] :
( ( descar2095969287nges_a @ ( cons_a @ zero_zero_a @ Xs ) )
= ( descar2095969287nges_a @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(562,plain,
( ( ! [X: a,Xs: list_a] :
( ( descar2095969287nges_a @ ( cons_a @ X @ ( cons_a @ zero_zero_a @ Xs ) ) )
= ( descar2095969287nges_a @ ( cons_a @ X @ Xs ) ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(563,plain,
( ( ! [P2: poly_a] :
( ( ( coeffs_a @ P2 )
= nil_a )
= ( P2 = zero_zero_poly_a ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(564,plain,
( ( ( coeffs_a @ zero_zero_poly_a )
= nil_a )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(565,plain,
( ( ! [P2: poly_a] :
( ( P2 = zero_zero_poly_a )
| ( ( coeffs_a @ P2 )
!= nil_a ) ) )
= $true ),
inference(copy,[status(thm)],[550]) ).
thf(566,plain,
( ( ys
= ( append_a @ ( coeffs_a @ g ) @ ( cons_a @ zero_zero_a @ nil_a ) ) )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(567,plain,
( ( ! [A: a] :
( ( smult_a @ A @ zero_zero_poly_a )
= zero_zero_poly_a ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(568,plain,
( ( ( pCons_a @ zero_zero_a @ zero_zero_poly_a )
= zero_zero_poly_a )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(569,plain,
( ( ! [A: a,P2: poly_a] :
( ( ( pCons_a @ A @ P2 )
= zero_zero_poly_a )
= ( ( A = zero_zero_a )
& ( P2 = zero_zero_poly_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(570,plain,
( ( ! [P2: poly_a] :
( ( smult_a @ zero_zero_a @ P2 )
= zero_zero_poly_a ) )
= $true ),
inference(copy,[status(thm)],[476]) ).
thf(571,plain,
( ( ! [A: a,P2: poly_a] :
( ( ( smult_a @ A @ P2 )
= zero_zero_poly_a )
= ( ( A = zero_zero_a )
| ( P2 = zero_zero_poly_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(572,plain,
( ( ! [Xs: list_a] :
( ( descar1375166517sums_a @ ( cons_a @ zero_zero_a @ Xs ) )
= ( cons_a @ zero_zero_a @ ( descar1375166517sums_a @ Xs ) ) ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(573,plain,
( ( ! [X: a] :
( ( descar2095969287nges_a @ ( cons_a @ X @ nil_a ) )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(574,plain,
( ( ! [As: list_a] :
( ( poly_a2 @ ( append_a @ As @ ( cons_a @ zero_zero_a @ nil_a ) ) )
= ( poly_a2 @ As ) ) )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(575,plain,
( ( ! [A: a,As: list_a] :
( ( poly_a2 @ ( cons_a @ A @ As ) )
= ( pCons_a @ A @ ( poly_a2 @ As ) ) ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(576,plain,
( ( ( poly_a2 @ nil_a )
= zero_zero_poly_a )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(577,plain,
( ( ! [X: a] :
( ( descar1375166517sums_a @ ( cons_a @ X @ nil_a ) )
= ( cons_a @ X @ nil_a ) ) )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(578,plain,
( ( ( descar1375166517sums_a @ nil_a )
= nil_a )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(579,plain,
( ( is_zero_a
= ( ^ [P: poly_a] : ( P = zero_zero_poly_a ) ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(580,plain,
( ( ! [P3: poly_a > $o] :
( ~ ( P3 @ zero_zero_poly_a )
| ( ( ( ( sK88_A2 @ P3 )
!= zero_zero_a )
| ( ( sK89_SY406 @ P3 )
!= zero_zero_poly_a ) )
& ( P3 @ ( sK89_SY406 @ P3 ) )
& ~ ( P3 @ ( pCons_a @ ( sK88_A2 @ P3 ) @ ( sK89_SY406 @ P3 ) ) ) )
| ! [P2: poly_a] : ( P3 @ P2 ) ) )
= $true ),
inference(copy,[status(thm)],[549]) ).
thf(581,plain,
( ( ! [P3: poly_a > poly_a > $o] :
( ~ ( P3 @ zero_zero_poly_a @ zero_zero_poly_a )
| ( ( P3 @ ( sK85_SY400 @ P3 ) @ ( sK87_SY405 @ P3 ) )
& ~ ( P3 @ ( pCons_a @ ( sK84_A2 @ P3 ) @ ( sK85_SY400 @ P3 ) ) @ ( pCons_a @ ( sK86_SY403 @ P3 ) @ ( sK87_SY405 @ P3 ) ) ) )
| ! [P2: poly_a,Q2: poly_a] : ( P3 @ P2 @ Q2 ) ) )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(582,plain,
( ( ! [P3: poly_a > $o] :
( ( ( ( ( sK83_SY399 @ P3 )
= zero_zero_poly_a )
| ( P3 @ ( sK83_SY399 @ P3 ) ) )
& ~ ( P3 @ ( pCons_a @ ( sK82_A2 @ P3 ) @ ( sK83_SY399 @ P3 ) ) ) )
| ! [A0: poly_a] : ( P3 @ A0 ) ) )
= $true ),
inference(copy,[status(thm)],[547]) ).
thf(583,plain,
( ( ! [Q2: poly_a] :
( ( times_times_poly_a @ zero_zero_poly_a @ Q2 )
= zero_zero_poly_a ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(584,plain,
( ( ! [P2: poly_a] :
( ( times_times_poly_a @ P2 @ zero_zero_poly_a )
= zero_zero_poly_a ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(585,plain,
( ( ! [P3: list_a > list_a > $o] :
( ~ ( P3 @ ( sK81_Xs2 @ P3 ) @ nil_a )
| ~ ( P3 @ nil_a @ ( cons_a @ ( sK79_V @ P3 ) @ ( sK80_SY398 @ P3 ) ) )
| ( ( P3 @ ( sK76_SY392 @ P3 ) @ ( sK78_SY397 @ P3 ) )
& ~ ( P3 @ ( cons_a @ ( sK75_X2 @ P3 ) @ ( sK76_SY392 @ P3 ) ) @ ( cons_a @ ( sK77_SY395 @ P3 ) @ ( sK78_SY397 @ P3 ) ) ) )
| ! [A0: list_a,A1: list_a] : ( P3 @ A0 @ A1 ) ) )
= $true ),
inference(copy,[status(thm)],[546]) ).
thf(586,plain,
( ( ! [P3: list_a > list_a > $o] :
( ( ( P3 @ ( sK72_SY386 @ P3 ) @ ( sK74_SY391 @ P3 ) )
& ~ ( P3 @ ( cons_a @ ( sK71_X2 @ P3 ) @ ( sK72_SY386 @ P3 ) ) @ ( cons_a @ ( sK73_SY389 @ P3 ) @ ( sK74_SY391 @ P3 ) ) ) )
| ~ ( P3 @ ( sK70_Xs2 @ P3 ) @ nil_a )
| ~ ( P3 @ nil_a @ ( cons_a @ ( sK68_Y2 @ P3 ) @ ( sK69_SY385 @ P3 ) ) )
| ! [A0: list_a,A1: list_a] : ( P3 @ A0 @ A1 ) ) )
= $true ),
inference(copy,[status(thm)],[545]) ).
thf(587,plain,
( ( ! [X: list_a] :
( ( X = nil_a )
| ( X
= ( cons_a @ ( sK67_X2 @ X ) @ nil_a ) )
| ( X
= ( cons_a @ ( sK64_X2 @ X ) @ ( cons_a @ ( sK65_SY382 @ X ) @ ( sK66_SY384 @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[544]) ).
thf(588,plain,
( ( ! [A: a] :
( ( A = zero_zero_a )
| ! [P2: poly_a] :
( ( P2 = zero_zero_poly_a )
| ( ( descar466059845root_a @ A @ P2 )
!= zero_zero_poly_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[543]) ).
thf(589,plain,
( ( ! [Xs: list_a,X: a,Ys2: list_a,Y3: a] :
( ( ( append_a @ Xs @ ( cons_a @ X @ nil_a ) )
= ( append_a @ Ys2 @ ( cons_a @ Y3 @ nil_a ) ) )
= ( ( Xs = Ys2 )
& ( X = Y3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(590,plain,
( ( ! [X21: a,X22: list_a,Y21: a,Y22: list_a] :
( ( ( cons_a @ X21 @ X22 )
= ( cons_a @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 ) ) ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(591,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(592,plain,
( ( ! [A: a,C: a,B: a] :
( ( ( times_times_a @ A @ C )
= ( times_times_a @ B @ C ) )
= ( ( C = zero_zero_a )
| ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[454]) ).
thf(593,plain,
( ( ! [A: poly_a,C: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ C )
= ( times_times_poly_a @ B @ C ) )
= ( ( C = zero_zero_poly_a )
| ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(594,plain,
( ( ! [A: nat,C: nat,B: nat] :
( ( ( times_times_nat @ A @ C )
= ( times_times_nat @ B @ C ) )
= ( ( C = zero_zero_nat )
| ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(595,plain,
( ( ! [C: a,A: a,B: a] :
( ( ( times_times_a @ C @ A )
= ( times_times_a @ C @ B ) )
= ( ( C = zero_zero_a )
| ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(596,plain,
( ( ! [C: poly_a,A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ C @ A )
= ( times_times_poly_a @ C @ B ) )
= ( ( C = zero_zero_poly_a )
| ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(597,plain,
( ( ! [C: nat,A: nat,B: nat] :
( ( ( times_times_nat @ C @ A )
= ( times_times_nat @ C @ B ) )
= ( ( C = zero_zero_nat )
| ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(598,plain,
( ( ! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= zero_zero_a )
= ( ( A = zero_zero_a )
| ( B = zero_zero_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(599,plain,
( ( ! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= zero_zero_poly_a )
= ( ( A = zero_zero_poly_a )
| ( B = zero_zero_poly_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(600,plain,
( ( ! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[446]) ).
thf(601,plain,
( ( ! [A: a] :
( ( times_times_a @ A @ zero_zero_a )
= zero_zero_a ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(602,plain,
( ( ! [A: poly_a] :
( ( times_times_poly_a @ A @ zero_zero_poly_a )
= zero_zero_poly_a ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(603,plain,
( ( ! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(604,plain,
( ( ! [A: a] :
( ( times_times_a @ zero_zero_a @ A )
= zero_zero_a ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(605,plain,
( ( ! [A: poly_a] :
( ( times_times_poly_a @ zero_zero_poly_a @ A )
= zero_zero_poly_a ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(606,plain,
( ( ! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(607,plain,
( ( ! [A: poly_a] :
( ( ( uminus_uminus_poly_a @ A )
= A )
= ( A = zero_zero_poly_a ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(608,plain,
( ( ! [A: a] :
( ( ( uminus_uminus_a @ A )
= A )
= ( A = zero_zero_a ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(609,plain,
( ( ! [A: poly_a] :
( ( A
= ( uminus_uminus_poly_a @ A ) )
= ( A = zero_zero_poly_a ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(610,plain,
( ( ! [A: a] :
( ( A
= ( uminus_uminus_a @ A ) )
= ( A = zero_zero_a ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(611,plain,
( ( ! [A: poly_a] :
( ( ( uminus_uminus_poly_a @ A )
= zero_zero_poly_a )
= ( A = zero_zero_poly_a ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(612,plain,
( ( ! [A: a] :
( ( ( uminus_uminus_a @ A )
= zero_zero_a )
= ( A = zero_zero_a ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(613,plain,
( ( ! [A: poly_a] :
( ( zero_zero_poly_a
= ( uminus_uminus_poly_a @ A ) )
= ( zero_zero_poly_a = A ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(614,plain,
( ( ! [A: a] :
( ( zero_zero_a
= ( uminus_uminus_a @ A ) )
= ( zero_zero_a = A ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(615,plain,
( ( ( uminus_uminus_poly_a @ zero_zero_poly_a )
= zero_zero_poly_a )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(616,plain,
( ( ( uminus_uminus_a @ zero_zero_a )
= zero_zero_a )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(617,plain,
( ( ! [A: list_a] :
( ( append_a @ A @ nil_a )
= A ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(618,plain,
( ( ! [Xs: list_a,Ys2: list_a] :
( ( ( append_a @ Xs @ Ys2 )
= nil_a )
= ( ( Xs = nil_a )
& ( Ys2 = nil_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(619,plain,
( ( ! [Xs: list_a,Ys2: list_a] :
( ( nil_a
= ( append_a @ Xs @ Ys2 ) )
= ( ( Xs = nil_a )
& ( Ys2 = nil_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(620,plain,
( ( ! [Ys2: list_a,Xs: list_a] :
( ( Ys2
= ( append_a @ Xs @ Ys2 ) )
= ( Xs = nil_a ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(621,plain,
( ( ! [Xs: list_a,Ys2: list_a] :
( ( ( append_a @ Xs @ Ys2 )
= Ys2 )
= ( Xs = nil_a ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(622,plain,
( ( ! [Xs: list_a,Ys2: list_a] :
( ( Xs
= ( append_a @ Xs @ Ys2 ) )
= ( Ys2 = nil_a ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(623,plain,
( ( ! [Xs: list_a,Ys2: list_a] :
( ( ( append_a @ Xs @ Ys2 )
= Xs )
= ( Ys2 = nil_a ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(624,plain,
( ( ! [Xs: list_a] :
( ( append_a @ Xs @ nil_a )
= Xs ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(625,plain,
( ( ! [X: poly_a] :
( ( zero_zero_poly_a = X )
= ( X = zero_zero_poly_a ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(626,plain,
( ( ! [X: a] :
( ( zero_zero_a = X )
= ( X = zero_zero_a ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(627,plain,
( ( ! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(628,plain,
( ( ! [X: a,Xs: list_a] :
( ( cons_a @ X @ Xs )
!= Xs ) )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(629,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(630,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
| ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[540]) ).
thf(631,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(632,plain,
( ( ! [N: nat] :
( ( N = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[539]) ).
thf(633,plain,
( ( ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(634,plain,
( ( ~ ( ord_less_a @ zero_zero_a @ zero_zero_a ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(635,plain,
( ( ~ ( ord_less_poly_a @ zero_zero_poly_a @ zero_zero_poly_a ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(636,plain,
( ( ! [C: a] :
( ( C = zero_zero_a )
| ! [A: a,B: a] :
( ( ( times_times_a @ A @ C )
= ( times_times_a @ B @ C ) )
= ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(637,plain,
( ( ! [C: poly_a] :
( ( C = zero_zero_poly_a )
| ! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ C )
= ( times_times_poly_a @ B @ C ) )
= ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(638,plain,
( ( ! [C: nat] :
( ( C = zero_zero_nat )
| ! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ C )
= ( times_times_nat @ B @ C ) )
= ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(639,plain,
( ( ! [C: a] :
( ( C = zero_zero_a )
| ! [A: a,B: a] :
( ( ( times_times_a @ C @ A )
= ( times_times_a @ C @ B ) )
= ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(640,plain,
( ( ! [C: poly_a] :
( ( C = zero_zero_poly_a )
| ! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ C @ A )
= ( times_times_poly_a @ C @ B ) )
= ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(641,plain,
( ( ! [C: nat] :
( ( C = zero_zero_nat )
| ! [A: nat,B: nat] :
( ( ( times_times_nat @ C @ A )
= ( times_times_nat @ C @ B ) )
= ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(642,plain,
( ( ! [A: a] :
( ( A = zero_zero_a )
| ! [B: a] :
( ( B = zero_zero_a )
| ( ( times_times_a @ A @ B )
!= zero_zero_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(643,plain,
( ( ! [A: poly_a] :
( ( A = zero_zero_poly_a )
| ! [B: poly_a] :
( ( B = zero_zero_poly_a )
| ( ( times_times_poly_a @ A @ B )
!= zero_zero_poly_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(644,plain,
( ( ! [A: nat] :
( ( A = zero_zero_nat )
| ! [B: nat] :
( ( B = zero_zero_nat )
| ( ( times_times_nat @ A @ B )
!= zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(645,plain,
( ( ! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
!= zero_zero_a )
| ( A = zero_zero_a )
| ( B = zero_zero_a ) ) )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(646,plain,
( ( ! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
!= zero_zero_poly_a )
| ( A = zero_zero_poly_a )
| ( B = zero_zero_poly_a ) ) )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(647,plain,
( ( ! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
!= zero_zero_nat )
| ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(648,plain,
( ( ! [A: a] :
( ! [B: a] :
( ( times_times_a @ A @ B )
= zero_zero_a )
| ( A != zero_zero_a ) )
& ! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= zero_zero_a )
| ( B != zero_zero_a ) ) )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(649,plain,
( ( ! [A: poly_a] :
( ! [B: poly_a] :
( ( times_times_poly_a @ A @ B )
= zero_zero_poly_a )
| ( A != zero_zero_poly_a ) )
& ! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= zero_zero_poly_a )
| ( B != zero_zero_poly_a ) ) )
= $true ),
inference(copy,[status(thm)],[525]) ).
thf(650,plain,
( ( ! [A: nat] :
( ! [B: nat] :
( ( times_times_nat @ A @ B )
= zero_zero_nat )
| ( A != zero_zero_nat ) )
& ! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
| ( B != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[524]) ).
thf(651,plain,
( ( zero_zero_poly_a != one_one_poly_a )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(652,plain,
( ( zero_zero_a != one_one_a )
= $true ),
inference(copy,[status(thm)],[522]) ).
thf(653,plain,
( ( zero_zero_nat != one_one_nat )
= $true ),
inference(copy,[status(thm)],[521]) ).
thf(654,plain,
( ( ! [P3: list_a > $o] :
( ~ ( P3 @ nil_a )
| ( ( P3 @ ( sK63_SY381 @ P3 ) )
& ~ ( P3 @ ( cons_a @ ( sK62_X2 @ P3 ) @ ( sK63_SY381 @ P3 ) ) ) )
| ! [A0: list_a] : ( P3 @ A0 ) ) )
= $true ),
inference(copy,[status(thm)],[520]) ).
thf(655,plain,
( ( ! [X: list_a] :
( ( X = nil_a )
| ( X
= ( cons_a @ ( sK60_X2 @ X ) @ ( sK61_SY380 @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(656,plain,
( ( ! [P3: ( a > a ) > list_a > list_a > $o,A0: a > a] :
( ~ ( P3 @ ( sK58_F2 @ A0 @ P3 ) @ nil_a @ ( sK59_SY379 @ A0 @ P3 ) )
| ( ( P3 @ ( sK54_F2 @ A0 @ P3 ) @ ( sK56_SY376 @ A0 @ P3 ) @ ( cons_a @ ( sK54_F2 @ A0 @ P3 @ ( sK55_SY373 @ A0 @ P3 ) ) @ ( sK57_SY378 @ A0 @ P3 ) ) )
& ~ ( P3 @ ( sK54_F2 @ A0 @ P3 ) @ ( cons_a @ ( sK55_SY373 @ A0 @ P3 ) @ ( sK56_SY376 @ A0 @ P3 ) ) @ ( sK57_SY378 @ A0 @ P3 ) ) )
| ! [A1: list_a,A22: list_a] : ( P3 @ A0 @ A1 @ A22 ) ) )
= $true ),
inference(copy,[status(thm)],[518]) ).
thf(657,plain,
( ( ! [Xs: list_a] :
( ( Xs = nil_a )
| ! [P3: list_a > $o] :
( ~ ( P3 @ ( cons_a @ ( sK53_X2 @ P3 @ Xs ) @ nil_a ) )
| ( ( ( sK52_SY372 @ P3 @ Xs )
!= nil_a )
& ( P3 @ ( sK52_SY372 @ P3 @ Xs ) )
& ~ ( P3 @ ( cons_a @ ( sK51_X2 @ P3 @ Xs ) @ ( sK52_SY372 @ P3 @ Xs ) ) ) )
| ( P3 @ Xs ) ) ) )
= $true ),
inference(copy,[status(thm)],[517]) ).
thf(658,plain,
( ( ! [P3: ( a > a > $o ) > list_a > $o] :
( ~ ( P3 @ ( sK50_P5 @ P3 ) @ nil_a )
| ~ ( P3 @ ( sK48_P5 @ P3 ) @ ( cons_a @ ( sK49_SY371 @ P3 ) @ nil_a ) )
| ( ( P3 @ ( sK44_P5 @ P3 ) @ ( cons_a @ ( sK46_SY368 @ P3 ) @ ( sK47_SY370 @ P3 ) ) )
& ~ ( P3 @ ( sK44_P5 @ P3 ) @ ( cons_a @ ( sK45_SY365 @ P3 ) @ ( cons_a @ ( sK46_SY368 @ P3 ) @ ( sK47_SY370 @ P3 ) ) ) ) )
| ! [A0: a > a > $o,A1: list_a] : ( P3 @ A0 @ A1 ) ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(659,plain,
( ( ! [P3: list_a > $o] :
( ~ ( P3 @ nil_a )
| ~ ( P3 @ ( cons_a @ ( sK43_X2 @ P3 ) @ nil_a ) )
| ( ( ( ( sK40_X2 @ P3 )
!= ( sK41_SY362 @ P3 ) )
| ( P3 @ ( cons_a @ ( sK40_X2 @ P3 ) @ ( sK42_SY364 @ P3 ) ) ) )
& ( ( ( sK40_X2 @ P3 )
= ( sK41_SY362 @ P3 ) )
| ( P3 @ ( cons_a @ ( sK41_SY362 @ P3 ) @ ( sK42_SY364 @ P3 ) ) ) )
& ~ ( P3 @ ( cons_a @ ( sK40_X2 @ P3 ) @ ( cons_a @ ( sK41_SY362 @ P3 ) @ ( sK42_SY364 @ P3 ) ) ) ) )
| ! [A0: list_a] : ( P3 @ A0 ) ) )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(660,plain,
( ( ! [P3: ( a > a > $o ) > list_a > $o] :
( ~ ( P3 @ ( sK39_P5 @ P3 ) @ nil_a )
| ( ( P3 @ ( sK36_P5 @ P3 ) @ ( sK38_SY361 @ P3 ) )
& ~ ( P3 @ ( sK36_P5 @ P3 ) @ ( cons_a @ ( sK37_SY359 @ P3 ) @ ( sK38_SY361 @ P3 ) ) ) )
| ! [A0: a > a > $o,A1: list_a] : ( P3 @ A0 @ A1 ) ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(661,plain,
( ( ! [X: list_a] :
( ( X = nil_a )
| ( X
= ( cons_a @ ( sK35_X2 @ X ) @ nil_a ) )
| ( X
= ( cons_a @ ( sK32_X2 @ X ) @ ( cons_a @ ( sK33_SY356 @ X ) @ ( sK34_SY358 @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[513]) ).
thf(662,plain,
( ( ! [P3: list_a > list_a > $o] :
( ~ ( P3 @ nil_a @ ( sK31_X_1 @ P3 ) )
| ~ ( P3 @ ( sK30_Xs2 @ P3 ) @ nil_a )
| ( ( P3 @ ( sK27_SY350 @ P3 ) @ ( cons_a @ ( sK28_SY353 @ P3 ) @ ( sK29_SY355 @ P3 ) ) )
& ( P3 @ ( cons_a @ ( sK26_X2 @ P3 ) @ ( sK27_SY350 @ P3 ) ) @ ( sK29_SY355 @ P3 ) )
& ~ ( P3 @ ( cons_a @ ( sK26_X2 @ P3 ) @ ( sK27_SY350 @ P3 ) ) @ ( cons_a @ ( sK28_SY353 @ P3 ) @ ( sK29_SY355 @ P3 ) ) ) )
| ! [A0: list_a,A1: list_a] : ( P3 @ A0 @ A1 ) ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(663,plain,
( ( ! [P3: list_a > $o] :
( ( ( ! [SY348: a,SY349: list_a] :
( ( sK25_SY345 @ P3 )
!= ( cons_a @ SY348 @ SY349 ) )
| ( P3 @ ( sK25_SY345 @ P3 ) ) )
& ~ ( P3 @ ( cons_a @ ( sK24_X2 @ P3 ) @ ( sK25_SY345 @ P3 ) ) ) )
| ~ ( P3 @ nil_a )
| ! [A0: list_a] : ( P3 @ A0 ) ) )
= $true ),
inference(copy,[status(thm)],[511]) ).
thf(664,plain,
( ( ! [X: list_a] :
( ( X
= ( cons_a @ ( sK22_X2 @ X ) @ ( sK23_SY344 @ X ) ) )
| ( X = nil_a ) ) )
= $true ),
inference(copy,[status(thm)],[510]) ).
thf(665,plain,
( ( ! [P3: list_a > $o] :
( ~ ( P3 @ nil_a )
| ~ ( P3 @ ( cons_a @ ( sK21_X2 @ P3 ) @ nil_a ) )
| ( ( P3 @ ( sK20_SY343 @ P3 ) )
& ( P3 @ ( cons_a @ ( sK19_SY341 @ P3 ) @ ( sK20_SY343 @ P3 ) ) )
& ~ ( P3 @ ( cons_a @ ( sK18_X2 @ P3 ) @ ( cons_a @ ( sK19_SY341 @ P3 ) @ ( sK20_SY343 @ P3 ) ) ) ) )
| ! [Xs: list_a] : ( P3 @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(666,plain,
( ( ! [P3: list_a > list_a > $o] :
( ~ ( P3 @ nil_a @ ( sK17_X_1 @ P3 ) )
| ( ( P3 @ ( sK16_SY340 @ P3 ) @ ( sK15_SY338 @ P3 ) )
& ~ ( P3 @ ( cons_a @ ( sK14_X2 @ P3 ) @ ( sK15_SY338 @ P3 ) ) @ ( sK16_SY340 @ P3 ) ) )
| ! [A0: list_a,A1: list_a] : ( P3 @ A0 @ A1 ) ) )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(667,plain,
( ( ! [P3: list_a > list_a > $o] :
( ~ ( P3 @ nil_a @ nil_a )
| ~ ( P3 @ ( cons_a @ ( sK12_X2 @ P3 ) @ ( sK13_SY337 @ P3 ) ) @ nil_a )
| ~ ( P3 @ nil_a @ ( cons_a @ ( sK10_Y2 @ P3 ) @ ( sK11_SY336 @ P3 ) ) )
| ( ( P3 @ ( sK7_SY330 @ P3 ) @ ( sK9_SY335 @ P3 ) )
& ~ ( P3 @ ( cons_a @ ( sK6_X2 @ P3 ) @ ( sK7_SY330 @ P3 ) ) @ ( cons_a @ ( sK8_SY333 @ P3 ) @ ( sK9_SY335 @ P3 ) ) ) )
| ! [Xs: list_a,Ys2: list_a] : ( P3 @ Xs @ Ys2 ) ) )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(668,plain,
( ( ! [Xs: list_a] :
( ( Xs != nil_a )
= ( ? [Y4: a,Ys3: list_a] :
( Xs
= ( cons_a @ Y4 @ Ys3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[506]) ).
thf(669,plain,
( ( ! [P3: list_a > $o] :
( ~ ( P3 @ nil_a )
| ( ( P3 @ ( sK5_SY329 @ P3 ) )
& ~ ( P3 @ ( cons_a @ ( sK4_X1 @ P3 ) @ ( sK5_SY329 @ P3 ) ) ) )
| ! [List: list_a] : ( P3 @ List ) ) )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(670,plain,
( ( ! [Y3: list_a] :
( ( Y3 = nil_a )
| ( Y3
= ( cons_a @ ( sK2_X213 @ Y3 ) @ ( sK3_SY328 @ Y3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(671,plain,
( ( ! [List: list_a] :
( ! [X21: a,X22: list_a] :
( List
!= ( cons_a @ X21 @ X22 ) )
| ( List != nil_a ) ) )
= $true ),
inference(copy,[status(thm)],[503]) ).
thf(672,plain,
( ( ! [X21: a,X22: list_a] :
( nil_a
!= ( cons_a @ X21 @ X22 ) ) )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(673,plain,
( ( ! [X: a,Xs: list_a,Ys2: list_a] :
( ( append_a @ ( cons_a @ X @ Xs ) @ Ys2 )
= ( cons_a @ X @ ( append_a @ Xs @ Ys2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(674,plain,
( ( ! [X: a,Xs1: list_a,Ys2: list_a] :
( ( ( cons_a @ X @ Xs1 )
!= Ys2 )
| ! [Xs: list_a,Zs: list_a] :
( ( Xs
!= ( append_a @ Xs1 @ Zs ) )
| ( ( cons_a @ X @ Xs )
= ( append_a @ Ys2 @ Zs ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(675,plain,
( ( ! [A: list_a] :
( ( append_a @ nil_a @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(676,plain,
( ( ! [Ys2: list_a] :
( ( append_a @ nil_a @ Ys2 )
= Ys2 ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(677,plain,
( ( ! [Xs: list_a,Ys2: list_a] :
( ( Xs != Ys2 )
| ( Xs
= ( append_a @ nil_a @ Ys2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(678,plain,
( ( ! [X: a,Xs: list_a] :
~ ( null_a @ ( cons_a @ X @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(679,plain,
( ( ! [Xs: list_a] :
( ( Xs = nil_a )
= ( null_a @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(680,plain,
( ( null_a @ nil_a )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(681,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)],[365]) ).
thf(682,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(683,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(684,plain,
( ( ! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(685,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)],[361]) ).
thf(686,plain,
( ( ! [M: nat] :
( ( times_times_nat @ M @ zero_zero_nat )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(687,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)],[359]) ).
thf(688,plain,
( ( ! [N: nat] :
( ( N = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(689,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(690,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(691,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(692,plain,
( ( ! [M: nat,N: nat] :
( ~ ( ord_less_nat @ M @ N )
| ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[496]) ).
thf(693,plain,
( ( ! [P3: nat > $o] :
( ~ ( P3 @ zero_zero_nat )
| ( ( ord_less_nat @ zero_zero_nat @ ( sK1_N2 @ P3 ) )
& ~ ( P3 @ ( sK1_N2 @ P3 ) )
& ! [SY327: nat] :
( ~ ( ord_less_nat @ SY327 @ ( sK1_N2 @ P3 ) )
| ( P3 @ SY327 ) ) )
| ! [N: nat] : ( P3 @ N ) ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(694,plain,
( ( ! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(695,plain,
( ( ! [N: nat] :
( ( times_times_nat @ zero_zero_nat @ N )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(696,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)],[350]) ).
thf(697,plain,
( ( ( descar2095969287nges_a @ ys )
!= ( descar2095969287nges_a @ ( coeffs_a @ g ) ) )
= $true ),
inference(copy,[status(thm)],[494]) ).
thf(698,plain,
( ( ! [SX0: list_a > $o] :
( ~ ( SX0 @ nil_a )
| ~ ( SX0 @ ( cons_a @ ( sK43_X2 @ SX0 ) @ nil_a ) )
| ~ ( ~ ( ( ( sK40_X2 @ SX0 )
!= ( sK41_SY362 @ SX0 ) )
| ( SX0 @ ( cons_a @ ( sK40_X2 @ SX0 ) @ ( sK42_SY364 @ SX0 ) ) ) )
| ~ ~ ( ~ ( ( ( sK40_X2 @ SX0 )
= ( sK41_SY362 @ SX0 ) )
| ( SX0 @ ( cons_a @ ( sK41_SY362 @ SX0 ) @ ( sK42_SY364 @ SX0 ) ) ) )
| ~ ~ ( SX0 @ ( cons_a @ ( sK40_X2 @ SX0 ) @ ( cons_a @ ( sK41_SY362 @ SX0 ) @ ( sK42_SY364 @ SX0 ) ) ) ) ) )
| ! [SX1: list_a] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[659]) ).
thf(699,plain,
( ( ~ ( ~ ! [SX0: a] :
( ! [SX1: a] :
( ( times_times_a @ SX0 @ SX1 )
= zero_zero_a )
| ( SX0 != zero_zero_a ) )
| ~ ! [SX0: a,SX1: a] :
( ( ( times_times_a @ SX0 @ SX1 )
= zero_zero_a )
| ( SX1 != zero_zero_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[648]) ).
thf(700,plain,
( ( ! [SX0: list_a > $o] :
( ~ ( ~ ( ! [SX1: a,SX2: list_a] :
( ( sK25_SY345 @ SX0 )
!= ( cons_a @ SX1 @ SX2 ) )
| ( SX0 @ ( sK25_SY345 @ SX0 ) ) )
| ~ ~ ( SX0 @ ( cons_a @ ( sK24_X2 @ SX0 ) @ ( sK25_SY345 @ SX0 ) ) ) )
| ~ ( SX0 @ nil_a )
| ! [SX1: list_a] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[663]) ).
thf(701,plain,
( ( ! [SX0: list_a,SX1: list_a] :
( ( ( append_a @ SX0 @ SX1 )
= nil_a )
= ( ~ ( ( SX0 != nil_a )
| ( SX1 != nil_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[618]) ).
thf(702,plain,
( ( ! [SX0: ( a > a ) > list_a > list_a > $o,SX1: a > a] :
( ~ ( SX0 @ ( sK58_F2 @ SX1 @ SX0 ) @ nil_a @ ( sK59_SY379 @ SX1 @ SX0 ) )
| ~ ( ~ ( SX0 @ ( sK54_F2 @ SX1 @ SX0 ) @ ( sK56_SY376 @ SX1 @ SX0 ) @ ( cons_a @ ( sK54_F2 @ SX1 @ SX0 @ ( sK55_SY373 @ SX1 @ SX0 ) ) @ ( sK57_SY378 @ SX1 @ SX0 ) ) )
| ~ ~ ( SX0 @ ( sK54_F2 @ SX1 @ SX0 ) @ ( cons_a @ ( sK55_SY373 @ SX1 @ SX0 ) @ ( sK56_SY376 @ SX1 @ SX0 ) ) @ ( sK57_SY378 @ SX1 @ SX0 ) ) )
| ! [SX2: list_a,SX3: list_a] : ( SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[656]) ).
thf(703,plain,
( ( ! [SX0: list_a,SX1: a,SX2: list_a,SX3: a] :
( ( ( append_a @ SX0 @ ( cons_a @ SX1 @ nil_a ) )
= ( append_a @ SX2 @ ( cons_a @ SX3 @ nil_a ) ) )
= ( ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(704,plain,
( ( ! [SX0: ( a > a > $o ) > list_a > $o] :
( ~ ( SX0 @ ( sK39_P5 @ SX0 ) @ nil_a )
| ~ ( ~ ( SX0 @ ( sK36_P5 @ SX0 ) @ ( sK38_SY361 @ SX0 ) )
| ~ ~ ( SX0 @ ( sK36_P5 @ SX0 ) @ ( cons_a @ ( sK37_SY359 @ SX0 ) @ ( sK38_SY361 @ SX0 ) ) ) )
| ! [SX1: a > a > $o,SX2: list_a] : ( SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(705,plain,
( ( ! [SX0: nat > $o] :
( ~ ( SX0 @ zero_zero_nat )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK1_N2 @ SX0 ) )
| ~ ~ ( ~ ~ ( SX0 @ ( sK1_N2 @ SX0 ) )
| ~ ! [SX1: nat] :
( ~ ( ord_less_nat @ SX1 @ ( sK1_N2 @ SX0 ) )
| ( SX0 @ SX1 ) ) ) )
| ! [SX1: nat] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[693]) ).
thf(706,plain,
( ( ! [SX0: list_a > $o] :
( ~ ( SX0 @ nil_a )
| ~ ( ~ ( SX0 @ ( sK5_SY329 @ SX0 ) )
| ~ ~ ( SX0 @ ( cons_a @ ( sK4_X1 @ SX0 ) @ ( sK5_SY329 @ SX0 ) ) ) )
| ! [SX1: list_a] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[669]) ).
thf(707,plain,
( ( ! [SX0: list_a > $o] :
( ~ ( SX0 @ nil_a )
| ~ ( SX0 @ ( cons_a @ ( sK21_X2 @ SX0 ) @ nil_a ) )
| ~ ( ~ ( SX0 @ ( sK20_SY343 @ SX0 ) )
| ~ ~ ( ~ ( SX0 @ ( cons_a @ ( sK19_SY341 @ SX0 ) @ ( sK20_SY343 @ SX0 ) ) )
| ~ ~ ( SX0 @ ( cons_a @ ( sK18_X2 @ SX0 ) @ ( cons_a @ ( sK19_SY341 @ SX0 ) @ ( sK20_SY343 @ SX0 ) ) ) ) ) )
| ! [SX1: list_a] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[665]) ).
thf(708,plain,
( ( ! [SX0: a,SX1: list_a,SX2: a,SX3: list_a] :
( ( ( cons_a @ SX0 @ SX1 )
= ( cons_a @ SX2 @ SX3 ) )
= ( ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[590]) ).
thf(709,plain,
( ( ! [SX0: list_a > list_a > $o] :
( ~ ( SX0 @ nil_a @ ( sK17_X_1 @ SX0 ) )
| ~ ( ~ ( SX0 @ ( sK16_SY340 @ SX0 ) @ ( sK15_SY338 @ SX0 ) )
| ~ ~ ( SX0 @ ( cons_a @ ( sK14_X2 @ SX0 ) @ ( sK15_SY338 @ SX0 ) ) @ ( sK16_SY340 @ SX0 ) ) )
| ! [SX1: list_a,SX2: list_a] : ( SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[666]) ).
thf(710,plain,
( ( ! [SX0: a,SX1: poly_a] :
( ( ( pCons_a @ SX0 @ SX1 )
= zero_zero_poly_a )
= ( ~ ( ( SX0 != zero_zero_a )
| ( SX1 != zero_zero_poly_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[569]) ).
thf(711,plain,
( ( ~ ( ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( times_times_nat @ SX0 @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_nat ) )
| ~ ! [SX0: nat,SX1: nat] :
( ( ( times_times_nat @ SX0 @ SX1 )
= zero_zero_nat )
| ( SX1 != zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[650]) ).
thf(712,plain,
( ( ! [SX0: poly_a > poly_a > $o] :
( ~ ( SX0 @ zero_zero_poly_a @ zero_zero_poly_a )
| ~ ( ~ ( SX0 @ ( sK85_SY400 @ SX0 ) @ ( sK87_SY405 @ SX0 ) )
| ~ ~ ( SX0 @ ( pCons_a @ ( sK84_A2 @ SX0 ) @ ( sK85_SY400 @ SX0 ) ) @ ( pCons_a @ ( sK86_SY403 @ SX0 ) @ ( sK87_SY405 @ SX0 ) ) ) )
| ! [SX1: poly_a,SX2: poly_a] : ( SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581]) ).
thf(713,plain,
( ( ! [SX0: list_a > list_a > $o] :
( ~ ( ~ ( SX0 @ ( sK72_SY386 @ SX0 ) @ ( sK74_SY391 @ SX0 ) )
| ~ ~ ( SX0 @ ( cons_a @ ( sK71_X2 @ SX0 ) @ ( sK72_SY386 @ SX0 ) ) @ ( cons_a @ ( sK73_SY389 @ SX0 ) @ ( sK74_SY391 @ SX0 ) ) ) )
| ~ ( SX0 @ ( sK70_Xs2 @ SX0 ) @ nil_a )
| ~ ( SX0 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SX0 ) @ ( sK69_SY385 @ SX0 ) ) )
| ! [SX1: list_a,SX2: list_a] : ( SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(714,plain,
( ( ! [SX0: list_a] :
( ( SX0 = nil_a )
| ! [SX1: list_a > $o] :
( ~ ( SX1 @ ( cons_a @ ( sK53_X2 @ SX1 @ SX0 ) @ nil_a ) )
| ~ ( ~ ( ( ( sK52_SY372 @ SX1 @ SX0 )
!= nil_a ) )
| ~ ~ ( ~ ( SX1 @ ( sK52_SY372 @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( cons_a @ ( sK51_X2 @ SX1 @ SX0 ) @ ( sK52_SY372 @ SX1 @ SX0 ) ) ) ) )
| ( SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[657]) ).
thf(715,plain,
( ( ! [SX0: poly_a > $o] :
( ~ ( ~ ( ( ( sK83_SY399 @ SX0 )
= zero_zero_poly_a )
| ( SX0 @ ( sK83_SY399 @ SX0 ) ) )
| ~ ~ ( SX0 @ ( pCons_a @ ( sK82_A2 @ SX0 ) @ ( sK83_SY399 @ SX0 ) ) ) )
| ! [SX1: poly_a] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(716,plain,
( ( ! [SX0: ( a > a > $o ) > list_a > $o] :
( ~ ( SX0 @ ( sK50_P5 @ SX0 ) @ nil_a )
| ~ ( SX0 @ ( sK48_P5 @ SX0 ) @ ( cons_a @ ( sK49_SY371 @ SX0 ) @ nil_a ) )
| ~ ( ~ ( SX0 @ ( sK44_P5 @ SX0 ) @ ( cons_a @ ( sK46_SY368 @ SX0 ) @ ( sK47_SY370 @ SX0 ) ) )
| ~ ~ ( SX0 @ ( sK44_P5 @ SX0 ) @ ( cons_a @ ( sK45_SY365 @ SX0 ) @ ( cons_a @ ( sK46_SY368 @ SX0 ) @ ( sK47_SY370 @ SX0 ) ) ) ) )
| ! [SX1: a > a > $o,SX2: list_a] : ( SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[658]) ).
thf(717,plain,
( ( ! [SX0: list_a > list_a > $o] :
( ~ ( SX0 @ nil_a @ ( sK31_X_1 @ SX0 ) )
| ~ ( SX0 @ ( sK30_Xs2 @ SX0 ) @ nil_a )
| ~ ( ~ ( SX0 @ ( sK27_SY350 @ SX0 ) @ ( cons_a @ ( sK28_SY353 @ SX0 ) @ ( sK29_SY355 @ SX0 ) ) )
| ~ ~ ( ~ ( SX0 @ ( cons_a @ ( sK26_X2 @ SX0 ) @ ( sK27_SY350 @ SX0 ) ) @ ( sK29_SY355 @ SX0 ) )
| ~ ~ ( SX0 @ ( cons_a @ ( sK26_X2 @ SX0 ) @ ( sK27_SY350 @ SX0 ) ) @ ( cons_a @ ( sK28_SY353 @ SX0 ) @ ( sK29_SY355 @ SX0 ) ) ) ) )
| ! [SX1: list_a,SX2: list_a] : ( SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[662]) ).
thf(718,plain,
( ( ~ ( ~ ! [SX0: poly_a] :
( ! [SX1: poly_a] :
( ( times_times_poly_a @ SX0 @ SX1 )
= zero_zero_poly_a )
| ( SX0 != zero_zero_poly_a ) )
| ~ ! [SX0: poly_a,SX1: poly_a] :
( ( ( times_times_poly_a @ SX0 @ SX1 )
= zero_zero_poly_a )
| ( SX1 != zero_zero_poly_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[649]) ).
thf(719,plain,
( ( ! [SX0: list_a > list_a > $o] :
( ~ ( SX0 @ nil_a @ nil_a )
| ~ ( SX0 @ ( cons_a @ ( sK12_X2 @ SX0 ) @ ( sK13_SY337 @ SX0 ) ) @ nil_a )
| ~ ( SX0 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SX0 ) @ ( sK11_SY336 @ SX0 ) ) )
| ~ ( ~ ( SX0 @ ( sK7_SY330 @ SX0 ) @ ( sK9_SY335 @ SX0 ) )
| ~ ~ ( SX0 @ ( cons_a @ ( sK6_X2 @ SX0 ) @ ( sK7_SY330 @ SX0 ) ) @ ( cons_a @ ( sK8_SY333 @ SX0 ) @ ( sK9_SY335 @ SX0 ) ) ) )
| ! [SX1: list_a,SX2: list_a] : ( SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[667]) ).
thf(720,plain,
( ( ! [SX0: poly_a > $o] :
( ~ ( SX0 @ zero_zero_poly_a )
| ~ ( ~ ( ( ( sK88_A2 @ SX0 )
!= zero_zero_a )
| ( ( sK89_SY406 @ SX0 )
!= zero_zero_poly_a ) )
| ~ ~ ( ~ ( SX0 @ ( sK89_SY406 @ SX0 ) )
| ~ ~ ( SX0 @ ( pCons_a @ ( sK88_A2 @ SX0 ) @ ( sK89_SY406 @ SX0 ) ) ) ) )
| ! [SX1: poly_a] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580]) ).
thf(721,plain,
( ( ! [SX0: list_a] :
( ( SX0 != nil_a )
= ( ~ ! [SX1: a] :
~ ~ ! [SX2: list_a] :
( SX0
!= ( cons_a @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[668]) ).
thf(722,plain,
( ( ! [SX0: list_a,SX1: list_a] :
( ( nil_a
= ( append_a @ SX0 @ SX1 ) )
= ( ~ ( ( SX0 != nil_a )
| ( SX1 != nil_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619]) ).
thf(723,plain,
( ( ! [SX0: list_a > list_a > $o] :
( ~ ( SX0 @ ( sK81_Xs2 @ SX0 ) @ nil_a )
| ~ ( SX0 @ nil_a @ ( cons_a @ ( sK79_V @ SX0 ) @ ( sK80_SY398 @ SX0 ) ) )
| ~ ( ~ ( SX0 @ ( sK76_SY392 @ SX0 ) @ ( sK78_SY397 @ SX0 ) )
| ~ ~ ( SX0 @ ( cons_a @ ( sK75_X2 @ SX0 ) @ ( sK76_SY392 @ SX0 ) ) @ ( cons_a @ ( sK77_SY395 @ SX0 ) @ ( sK78_SY397 @ SX0 ) ) ) )
| ! [SX1: list_a,SX2: list_a] : ( SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[585]) ).
thf(724,plain,
( ( ! [SX0: list_a > $o] :
( ~ ( SX0 @ nil_a )
| ~ ( ~ ( SX0 @ ( sK63_SY381 @ SX0 ) )
| ~ ~ ( SX0 @ ( cons_a @ ( sK62_X2 @ SX0 ) @ ( sK63_SY381 @ SX0 ) ) ) )
| ! [SX1: list_a] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[654]) ).
thf(725,plain,
( ( ! [SV1: poly_a] :
( ( v @ SV1 )
= ( descar2095969287nges_a @ ( coeffs_a @ SV1 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[553]) ).
thf(726,plain,
( ( v
= ( ^ [F: poly_a] : ( descar2095969287nges_a @ ( coeffs_a @ F ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[553]) ).
thf(727,plain,
( ( g = zero_zero_poly_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(728,plain,
( ( ! [SV2: poly_a] :
( ( ^ [SY407: poly_a] : ( SV2 = SY407 ) )
= ( ^ [SY408: poly_a] :
( ( coeffs_a @ SV2 )
= ( coeffs_a @ SY408 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[555]) ).
thf(729,plain,
( ( ( ^ [Y: poly_a,Z: poly_a] : ( Y = Z ) )
= ( ^ [P: poly_a,Q: poly_a] :
( ( coeffs_a @ P )
= ( coeffs_a @ Q ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[555]) ).
thf(730,plain,
! [SV3: list_a] :
( ( ! [SY409: poly_a] :
( ( ( poly_a2 @ SV3 )
!= SY409 )
| ( ( descar2095969287nges_a @ SV3 )
= ( descar2095969287nges_a @ ( coeffs_a @ SY409 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(731,plain,
( ( ! [SV4: poly_a] :
( ( is_zero_a @ SV4 )
= ( null_a @ ( coeffs_a @ SV4 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[558]) ).
thf(732,plain,
( ( is_zero_a
= ( ^ [P: poly_a] : ( null_a @ ( coeffs_a @ P ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[558]) ).
thf(733,plain,
! [SV5: poly_a] :
( ( ( poly_a2 @ ( coeffs_a @ SV5 ) )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(734,plain,
! [SV6: list_a] :
( ( ( descar2095969287nges_a @ ( cons_a @ zero_zero_a @ SV6 ) )
= ( descar2095969287nges_a @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(735,plain,
! [SV7: a] :
( ( ! [SY410: list_a] :
( ( descar2095969287nges_a @ ( cons_a @ SV7 @ ( cons_a @ zero_zero_a @ SY410 ) ) )
= ( descar2095969287nges_a @ ( cons_a @ SV7 @ SY410 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(736,plain,
! [SV8: poly_a] :
( ( ( ( coeffs_a @ SV8 )
= nil_a )
= ( SV8 = zero_zero_poly_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(737,plain,
! [SV9: poly_a] :
( ( ( SV9 = zero_zero_poly_a )
| ( ( coeffs_a @ SV9 )
!= nil_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(738,plain,
! [SV10: a] :
( ( ( smult_a @ SV10 @ zero_zero_poly_a )
= zero_zero_poly_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(739,plain,
! [SV11: poly_a] :
( ( ( smult_a @ zero_zero_a @ SV11 )
= zero_zero_poly_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(740,plain,
! [SV12: a] :
( ( ! [SY411: poly_a] :
( ( ( smult_a @ SV12 @ SY411 )
= zero_zero_poly_a )
= ( ( SV12 = zero_zero_a )
| ( SY411 = zero_zero_poly_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(741,plain,
! [SV13: list_a] :
( ( ( descar1375166517sums_a @ ( cons_a @ zero_zero_a @ SV13 ) )
= ( cons_a @ zero_zero_a @ ( descar1375166517sums_a @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(742,plain,
! [SV14: a] :
( ( ( descar2095969287nges_a @ ( cons_a @ SV14 @ nil_a ) )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(743,plain,
! [SV15: list_a] :
( ( ( poly_a2 @ ( append_a @ SV15 @ ( cons_a @ zero_zero_a @ nil_a ) ) )
= ( poly_a2 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(744,plain,
! [SV16: a] :
( ( ! [SY412: list_a] :
( ( poly_a2 @ ( cons_a @ SV16 @ SY412 ) )
= ( pCons_a @ SV16 @ ( poly_a2 @ SY412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(745,plain,
! [SV17: a] :
( ( ( descar1375166517sums_a @ ( cons_a @ SV17 @ nil_a ) )
= ( cons_a @ SV17 @ nil_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(746,plain,
( ( ! [SV18: poly_a] :
( ( is_zero_a @ SV18 )
= ( SV18 = zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[579]) ).
thf(747,plain,
( ( is_zero_a
= ( ^ [P: poly_a] : ( P = zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[579]) ).
thf(748,plain,
! [SV19: poly_a] :
( ( ( times_times_poly_a @ zero_zero_poly_a @ SV19 )
= zero_zero_poly_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(749,plain,
! [SV20: poly_a] :
( ( ( times_times_poly_a @ SV20 @ zero_zero_poly_a )
= zero_zero_poly_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(750,plain,
! [SV21: list_a] :
( ( ( SV21 = nil_a )
| ( SV21
= ( cons_a @ ( sK67_X2 @ SV21 ) @ nil_a ) )
| ( SV21
= ( cons_a @ ( sK64_X2 @ SV21 ) @ ( cons_a @ ( sK65_SY382 @ SV21 ) @ ( sK66_SY384 @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(751,plain,
! [SV22: a] :
( ( ( SV22 = zero_zero_a )
| ! [SY413: poly_a] :
( ( SY413 = zero_zero_poly_a )
| ( ( descar466059845root_a @ SV22 @ SY413 )
!= zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(752,plain,
! [SV23: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV23 ) )
= ( SV23 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(753,plain,
! [SV24: a] :
( ( ! [SY414: a,SY415: a] :
( ( ( times_times_a @ SV24 @ SY414 )
= ( times_times_a @ SY415 @ SY414 ) )
= ( ( SY414 = zero_zero_a )
| ( SV24 = SY415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(754,plain,
! [SV25: poly_a] :
( ( ! [SY416: poly_a,SY417: poly_a] :
( ( ( times_times_poly_a @ SV25 @ SY416 )
= ( times_times_poly_a @ SY417 @ SY416 ) )
= ( ( SY416 = zero_zero_poly_a )
| ( SV25 = SY417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(755,plain,
! [SV26: nat] :
( ( ! [SY418: nat,SY419: nat] :
( ( ( times_times_nat @ SV26 @ SY418 )
= ( times_times_nat @ SY419 @ SY418 ) )
= ( ( SY418 = zero_zero_nat )
| ( SV26 = SY419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(756,plain,
! [SV27: a] :
( ( ! [SY420: a,SY421: a] :
( ( ( times_times_a @ SV27 @ SY420 )
= ( times_times_a @ SV27 @ SY421 ) )
= ( ( SV27 = zero_zero_a )
| ( SY420 = SY421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(757,plain,
! [SV28: poly_a] :
( ( ! [SY422: poly_a,SY423: poly_a] :
( ( ( times_times_poly_a @ SV28 @ SY422 )
= ( times_times_poly_a @ SV28 @ SY423 ) )
= ( ( SV28 = zero_zero_poly_a )
| ( SY422 = SY423 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(758,plain,
! [SV29: nat] :
( ( ! [SY424: nat,SY425: nat] :
( ( ( times_times_nat @ SV29 @ SY424 )
= ( times_times_nat @ SV29 @ SY425 ) )
= ( ( SV29 = zero_zero_nat )
| ( SY424 = SY425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(759,plain,
! [SV30: a] :
( ( ! [SY426: a] :
( ( ( times_times_a @ SV30 @ SY426 )
= zero_zero_a )
= ( ( SV30 = zero_zero_a )
| ( SY426 = zero_zero_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(760,plain,
! [SV31: poly_a] :
( ( ! [SY427: poly_a] :
( ( ( times_times_poly_a @ SV31 @ SY427 )
= zero_zero_poly_a )
= ( ( SV31 = zero_zero_poly_a )
| ( SY427 = zero_zero_poly_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(761,plain,
! [SV32: nat] :
( ( ! [SY428: nat] :
( ( ( times_times_nat @ SV32 @ SY428 )
= zero_zero_nat )
= ( ( SV32 = zero_zero_nat )
| ( SY428 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(762,plain,
! [SV33: a] :
( ( ( times_times_a @ SV33 @ zero_zero_a )
= zero_zero_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(763,plain,
! [SV34: poly_a] :
( ( ( times_times_poly_a @ SV34 @ zero_zero_poly_a )
= zero_zero_poly_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(764,plain,
! [SV35: nat] :
( ( ( times_times_nat @ SV35 @ zero_zero_nat )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(765,plain,
! [SV36: a] :
( ( ( times_times_a @ zero_zero_a @ SV36 )
= zero_zero_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(766,plain,
! [SV37: poly_a] :
( ( ( times_times_poly_a @ zero_zero_poly_a @ SV37 )
= zero_zero_poly_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(767,plain,
! [SV38: nat] :
( ( ( times_times_nat @ zero_zero_nat @ SV38 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(768,plain,
! [SV39: poly_a] :
( ( ( ( uminus_uminus_poly_a @ SV39 )
= SV39 )
= ( SV39 = zero_zero_poly_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(769,plain,
! [SV40: a] :
( ( ( ( uminus_uminus_a @ SV40 )
= SV40 )
= ( SV40 = zero_zero_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(770,plain,
! [SV41: poly_a] :
( ( ( SV41
= ( uminus_uminus_poly_a @ SV41 ) )
= ( SV41 = zero_zero_poly_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(771,plain,
! [SV42: a] :
( ( ( SV42
= ( uminus_uminus_a @ SV42 ) )
= ( SV42 = zero_zero_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(772,plain,
! [SV43: poly_a] :
( ( ( ( uminus_uminus_poly_a @ SV43 )
= zero_zero_poly_a )
= ( SV43 = zero_zero_poly_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(773,plain,
! [SV44: a] :
( ( ( ( uminus_uminus_a @ SV44 )
= zero_zero_a )
= ( SV44 = zero_zero_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(774,plain,
! [SV45: poly_a] :
( ( ( zero_zero_poly_a
= ( uminus_uminus_poly_a @ SV45 ) )
= ( zero_zero_poly_a = SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(775,plain,
! [SV46: a] :
( ( ( zero_zero_a
= ( uminus_uminus_a @ SV46 ) )
= ( zero_zero_a = SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(776,plain,
! [SV47: list_a] :
( ( ( append_a @ SV47 @ nil_a )
= SV47 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(777,plain,
! [SV48: list_a] :
( ( ! [SY429: list_a] :
( ( SV48
= ( append_a @ SY429 @ SV48 ) )
= ( SY429 = nil_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(778,plain,
! [SV49: list_a] :
( ( ! [SY430: list_a] :
( ( ( append_a @ SV49 @ SY430 )
= SY430 )
= ( SV49 = nil_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(779,plain,
! [SV50: list_a] :
( ( ! [SY431: list_a] :
( ( SV50
= ( append_a @ SV50 @ SY431 ) )
= ( SY431 = nil_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(780,plain,
! [SV51: list_a] :
( ( ! [SY432: list_a] :
( ( ( append_a @ SV51 @ SY432 )
= SV51 )
= ( SY432 = nil_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(781,plain,
! [SV52: list_a] :
( ( ( append_a @ SV52 @ nil_a )
= SV52 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(782,plain,
! [SV53: poly_a] :
( ( ( zero_zero_poly_a = SV53 )
= ( SV53 = zero_zero_poly_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(783,plain,
! [SV54: a] :
( ( ( zero_zero_a = SV54 )
= ( SV54 = zero_zero_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(784,plain,
! [SV55: nat] :
( ( ( zero_zero_nat = SV55 )
= ( SV55 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(785,plain,
! [SV56: a] :
( ( ! [SY433: list_a] :
( ( cons_a @ SV56 @ SY433 )
!= SY433 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(786,plain,
! [SV57: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV57 )
= ( SV57 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(787,plain,
! [SV58: nat] :
( ( ! [SY434: nat] :
( ~ ( ord_less_nat @ SV58 @ SY434 )
| ( SY434 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(788,plain,
! [SV59: nat] :
( ( ~ ( ord_less_nat @ SV59 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(789,plain,
! [SV60: nat] :
( ( ( SV60 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(790,plain,
( ( ord_less_nat @ zero_zero_nat @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(791,plain,
( ( ord_less_a @ zero_zero_a @ zero_zero_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(792,plain,
( ( ord_less_poly_a @ zero_zero_poly_a @ zero_zero_poly_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(793,plain,
! [SV61: a] :
( ( ( SV61 = zero_zero_a )
| ! [SY435: a,SY436: a] :
( ( ( times_times_a @ SY435 @ SV61 )
= ( times_times_a @ SY436 @ SV61 ) )
= ( SY435 = SY436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(794,plain,
! [SV62: poly_a] :
( ( ( SV62 = zero_zero_poly_a )
| ! [SY437: poly_a,SY438: poly_a] :
( ( ( times_times_poly_a @ SY437 @ SV62 )
= ( times_times_poly_a @ SY438 @ SV62 ) )
= ( SY437 = SY438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(795,plain,
! [SV63: nat] :
( ( ( SV63 = zero_zero_nat )
| ! [SY439: nat,SY440: nat] :
( ( ( times_times_nat @ SY439 @ SV63 )
= ( times_times_nat @ SY440 @ SV63 ) )
= ( SY439 = SY440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(796,plain,
! [SV64: a] :
( ( ( SV64 = zero_zero_a )
| ! [SY441: a,SY442: a] :
( ( ( times_times_a @ SV64 @ SY441 )
= ( times_times_a @ SV64 @ SY442 ) )
= ( SY441 = SY442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(797,plain,
! [SV65: poly_a] :
( ( ( SV65 = zero_zero_poly_a )
| ! [SY443: poly_a,SY444: poly_a] :
( ( ( times_times_poly_a @ SV65 @ SY443 )
= ( times_times_poly_a @ SV65 @ SY444 ) )
= ( SY443 = SY444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(798,plain,
! [SV66: nat] :
( ( ( SV66 = zero_zero_nat )
| ! [SY445: nat,SY446: nat] :
( ( ( times_times_nat @ SV66 @ SY445 )
= ( times_times_nat @ SV66 @ SY446 ) )
= ( SY445 = SY446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(799,plain,
! [SV67: a] :
( ( ( SV67 = zero_zero_a )
| ! [SY447: a] :
( ( SY447 = zero_zero_a )
| ( ( times_times_a @ SV67 @ SY447 )
!= zero_zero_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(800,plain,
! [SV68: poly_a] :
( ( ( SV68 = zero_zero_poly_a )
| ! [SY448: poly_a] :
( ( SY448 = zero_zero_poly_a )
| ( ( times_times_poly_a @ SV68 @ SY448 )
!= zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(801,plain,
! [SV69: nat] :
( ( ( SV69 = zero_zero_nat )
| ! [SY449: nat] :
( ( SY449 = zero_zero_nat )
| ( ( times_times_nat @ SV69 @ SY449 )
!= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(802,plain,
! [SV70: a] :
( ( ! [SY450: a] :
( ( ( times_times_a @ SV70 @ SY450 )
!= zero_zero_a )
| ( SV70 = zero_zero_a )
| ( SY450 = zero_zero_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(803,plain,
! [SV71: poly_a] :
( ( ! [SY451: poly_a] :
( ( ( times_times_poly_a @ SV71 @ SY451 )
!= zero_zero_poly_a )
| ( SV71 = zero_zero_poly_a )
| ( SY451 = zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(804,plain,
! [SV72: nat] :
( ( ! [SY452: nat] :
( ( ( times_times_nat @ SV72 @ SY452 )
!= zero_zero_nat )
| ( SV72 = zero_zero_nat )
| ( SY452 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(805,plain,
( ( zero_zero_poly_a = one_one_poly_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[651]) ).
thf(806,plain,
( ( zero_zero_a = one_one_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(807,plain,
( ( zero_zero_nat = one_one_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(808,plain,
! [SV73: list_a] :
( ( ( SV73 = nil_a )
| ( SV73
= ( cons_a @ ( sK60_X2 @ SV73 ) @ ( sK61_SY380 @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(809,plain,
! [SV74: list_a] :
( ( ( SV74 = nil_a )
| ( SV74
= ( cons_a @ ( sK35_X2 @ SV74 ) @ nil_a ) )
| ( SV74
= ( cons_a @ ( sK32_X2 @ SV74 ) @ ( cons_a @ ( sK33_SY356 @ SV74 ) @ ( sK34_SY358 @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(810,plain,
! [SV75: list_a] :
( ( ( SV75
= ( cons_a @ ( sK22_X2 @ SV75 ) @ ( sK23_SY344 @ SV75 ) ) )
| ( SV75 = nil_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(811,plain,
! [SV76: list_a] :
( ( ( SV76 = nil_a )
| ( SV76
= ( cons_a @ ( sK2_X213 @ SV76 ) @ ( sK3_SY328 @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(812,plain,
! [SV77: list_a] :
( ( ! [SY453: a,SY454: list_a] :
( SV77
!= ( cons_a @ SY453 @ SY454 ) )
| ( SV77 != nil_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(813,plain,
! [SV78: a] :
( ( ! [SY455: list_a] :
( nil_a
!= ( cons_a @ SV78 @ SY455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(814,plain,
! [SV79: a] :
( ( ! [SY456: list_a,SY457: list_a] :
( ( append_a @ ( cons_a @ SV79 @ SY456 ) @ SY457 )
= ( cons_a @ SV79 @ ( append_a @ SY456 @ SY457 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(815,plain,
! [SV80: a] :
( ( ! [SY458: list_a,SY459: list_a] :
( ( ( cons_a @ SV80 @ SY458 )
!= SY459 )
| ! [SY460: list_a,SY461: list_a] :
( ( SY460
!= ( append_a @ SY458 @ SY461 ) )
| ( ( cons_a @ SV80 @ SY460 )
= ( append_a @ SY459 @ SY461 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(816,plain,
! [SV81: list_a] :
( ( ( append_a @ nil_a @ SV81 )
= SV81 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(817,plain,
! [SV82: list_a] :
( ( ( append_a @ nil_a @ SV82 )
= SV82 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(818,plain,
! [SV83: list_a] :
( ( ! [SY462: list_a] :
( ( SV83 != SY462 )
| ( SV83
= ( append_a @ nil_a @ SY462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(819,plain,
! [SV84: a] :
( ( ! [SY463: list_a] :
~ ( null_a @ ( cons_a @ SV84 @ SY463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(820,plain,
! [SV85: list_a] :
( ( ( SV85 = nil_a )
= ( null_a @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(821,plain,
! [SV86: nat] :
( ( ! [SY464: nat,SY465: nat] :
( ( ( times_times_nat @ SV86 @ SY464 )
= ( times_times_nat @ SY465 @ SY464 ) )
= ( ( SV86 = SY465 )
| ( SY464 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(822,plain,
! [SV87: nat] :
( ( ( SV87 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(823,plain,
! [SV88: nat] :
( ( ~ ( ord_less_nat @ SV88 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(824,plain,
! [SV89: nat] :
( ( ( SV89 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(825,plain,
! [SV90: nat] :
( ( ! [SY466: nat] :
( ( ( times_times_nat @ SV90 @ SY466 )
= zero_zero_nat )
= ( ( SV90 = zero_zero_nat )
| ( SY466 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(826,plain,
! [SV91: nat] :
( ( ( times_times_nat @ SV91 @ zero_zero_nat )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(827,plain,
! [SV92: nat] :
( ( ! [SY467: nat,SY468: nat] :
( ( ( times_times_nat @ SV92 @ SY467 )
= ( times_times_nat @ SV92 @ SY468 ) )
= ( ( SY467 = SY468 )
| ( SV92 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(828,plain,
! [SV93: nat] :
( ( ( SV93 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(829,plain,
! [SV94: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV94 ) )
= ( SV94 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(830,plain,
! [SV95: nat] :
( ( ~ ( ord_less_nat @ SV95 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(831,plain,
! [SV96: nat] :
( ( ~ ( ord_less_nat @ SV96 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(832,plain,
! [SV97: nat] :
( ( ! [SY469: nat] :
( ~ ( ord_less_nat @ SV97 @ SY469 )
| ( SY469 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(833,plain,
! [SV98: nat] :
( ( ~ ( ord_less_nat @ SV98 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(834,plain,
! [SV99: nat] :
( ( ( times_times_nat @ zero_zero_nat @ SV99 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(835,plain,
! [SV100: nat] :
( ( ! [SY470: nat,SY471: nat] :
( ( ( times_times_nat @ SV100 @ SY470 )
= ( times_times_nat @ SV100 @ SY471 ) )
= ( ( SV100 = zero_zero_nat )
| ( SY470 = SY471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(836,plain,
( ( ( descar2095969287nges_a @ ys )
= ( descar2095969287nges_a @ ( coeffs_a @ g ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(837,plain,
! [SV101: list_a > $o] :
( ( ~ ( SV101 @ nil_a )
| ~ ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
| ~ ( ~ ( ( ( sK40_X2 @ SV101 )
!= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
| ~ ~ ( ~ ( ( ( sK40_X2 @ SV101 )
= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
| ~ ~ ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) ) ) )
| ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(838,plain,
( ( ~ ! [SX0: a] :
( ! [SX1: a] :
( ( times_times_a @ SX0 @ SX1 )
= zero_zero_a )
| ( SX0 != zero_zero_a ) )
| ~ ! [SX0: a,SX1: a] :
( ( ( times_times_a @ SX0 @ SX1 )
= zero_zero_a )
| ( SX1 != zero_zero_a ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(839,plain,
! [SV102: list_a > $o] :
( ( ~ ( ~ ( ! [SY473: a,SY474: list_a] :
( ( sK25_SY345 @ SV102 )
!= ( cons_a @ SY473 @ SY474 ) )
| ( SV102 @ ( sK25_SY345 @ SV102 ) ) )
| ~ ~ ( SV102 @ ( cons_a @ ( sK24_X2 @ SV102 ) @ ( sK25_SY345 @ SV102 ) ) ) )
| ~ ( SV102 @ nil_a )
| ! [SY475: list_a] : ( SV102 @ SY475 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(840,plain,
! [SV103: list_a] :
( ( ! [SY476: list_a] :
( ( ( append_a @ SV103 @ SY476 )
= nil_a )
= ( ~ ( ( SV103 != nil_a )
| ( SY476 != nil_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(841,plain,
! [SV104: ( a > a ) > list_a > list_a > $o] :
( ( ! [SY477: a > a] :
( ~ ( SV104 @ ( sK58_F2 @ SY477 @ SV104 ) @ nil_a @ ( sK59_SY379 @ SY477 @ SV104 ) )
| ~ ( ~ ( SV104 @ ( sK54_F2 @ SY477 @ SV104 ) @ ( sK56_SY376 @ SY477 @ SV104 ) @ ( cons_a @ ( sK54_F2 @ SY477 @ SV104 @ ( sK55_SY373 @ SY477 @ SV104 ) ) @ ( sK57_SY378 @ SY477 @ SV104 ) ) )
| ~ ~ ( SV104 @ ( sK54_F2 @ SY477 @ SV104 ) @ ( cons_a @ ( sK55_SY373 @ SY477 @ SV104 ) @ ( sK56_SY376 @ SY477 @ SV104 ) ) @ ( sK57_SY378 @ SY477 @ SV104 ) ) )
| ! [SY478: list_a,SY479: list_a] : ( SV104 @ SY477 @ SY478 @ SY479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(842,plain,
! [SV105: list_a] :
( ( ! [SY480: a,SY481: list_a,SY482: a] :
( ( ( append_a @ SV105 @ ( cons_a @ SY480 @ nil_a ) )
= ( append_a @ SY481 @ ( cons_a @ SY482 @ nil_a ) ) )
= ( ~ ( ( SV105 != SY481 )
| ( SY480 != SY482 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(843,plain,
! [SV106: ( a > a > $o ) > list_a > $o] :
( ( ~ ( SV106 @ ( sK39_P5 @ SV106 ) @ nil_a )
| ~ ( ~ ( SV106 @ ( sK36_P5 @ SV106 ) @ ( sK38_SY361 @ SV106 ) )
| ~ ~ ( SV106 @ ( sK36_P5 @ SV106 ) @ ( cons_a @ ( sK37_SY359 @ SV106 ) @ ( sK38_SY361 @ SV106 ) ) ) )
| ! [SY483: a > a > $o,SY484: list_a] : ( SV106 @ SY483 @ SY484 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(844,plain,
! [SV107: nat > $o] :
( ( ~ ( SV107 @ zero_zero_nat )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK1_N2 @ SV107 ) )
| ~ ~ ( ~ ~ ( SV107 @ ( sK1_N2 @ SV107 ) )
| ~ ! [SY485: nat] :
( ~ ( ord_less_nat @ SY485 @ ( sK1_N2 @ SV107 ) )
| ( SV107 @ SY485 ) ) ) )
| ! [SY486: nat] : ( SV107 @ SY486 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(845,plain,
! [SV108: list_a > $o] :
( ( ~ ( SV108 @ nil_a )
| ~ ( ~ ( SV108 @ ( sK5_SY329 @ SV108 ) )
| ~ ~ ( SV108 @ ( cons_a @ ( sK4_X1 @ SV108 ) @ ( sK5_SY329 @ SV108 ) ) ) )
| ! [SY487: list_a] : ( SV108 @ SY487 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(846,plain,
! [SV109: list_a > $o] :
( ( ~ ( SV109 @ nil_a )
| ~ ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
| ~ ( ~ ( SV109 @ ( sK20_SY343 @ SV109 ) )
| ~ ~ ( ~ ( SV109 @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) )
| ~ ~ ( SV109 @ ( cons_a @ ( sK18_X2 @ SV109 ) @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) ) ) ) )
| ! [SY488: list_a] : ( SV109 @ SY488 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(847,plain,
! [SV110: a] :
( ( ! [SY489: list_a,SY490: a,SY491: list_a] :
( ( ( cons_a @ SV110 @ SY489 )
= ( cons_a @ SY490 @ SY491 ) )
= ( ~ ( ( SV110 != SY490 )
| ( SY489 != SY491 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(848,plain,
! [SV111: list_a > list_a > $o] :
( ( ~ ( SV111 @ nil_a @ ( sK17_X_1 @ SV111 ) )
| ~ ( ~ ( SV111 @ ( sK16_SY340 @ SV111 ) @ ( sK15_SY338 @ SV111 ) )
| ~ ~ ( SV111 @ ( cons_a @ ( sK14_X2 @ SV111 ) @ ( sK15_SY338 @ SV111 ) ) @ ( sK16_SY340 @ SV111 ) ) )
| ! [SY492: list_a,SY493: list_a] : ( SV111 @ SY492 @ SY493 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(849,plain,
! [SV112: a] :
( ( ! [SY494: poly_a] :
( ( ( pCons_a @ SV112 @ SY494 )
= zero_zero_poly_a )
= ( ~ ( ( SV112 != zero_zero_a )
| ( SY494 != zero_zero_poly_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(850,plain,
( ( ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( times_times_nat @ SX0 @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_nat ) )
| ~ ! [SX0: nat,SX1: nat] :
( ( ( times_times_nat @ SX0 @ SX1 )
= zero_zero_nat )
| ( SX1 != zero_zero_nat ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(851,plain,
! [SV113: poly_a > poly_a > $o] :
( ( ~ ( SV113 @ zero_zero_poly_a @ zero_zero_poly_a )
| ~ ( ~ ( SV113 @ ( sK85_SY400 @ SV113 ) @ ( sK87_SY405 @ SV113 ) )
| ~ ~ ( SV113 @ ( pCons_a @ ( sK84_A2 @ SV113 ) @ ( sK85_SY400 @ SV113 ) ) @ ( pCons_a @ ( sK86_SY403 @ SV113 ) @ ( sK87_SY405 @ SV113 ) ) ) )
| ! [SY495: poly_a,SY496: poly_a] : ( SV113 @ SY495 @ SY496 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(852,plain,
! [SV114: list_a > list_a > $o] :
( ( ~ ( ~ ( SV114 @ ( sK72_SY386 @ SV114 ) @ ( sK74_SY391 @ SV114 ) )
| ~ ~ ( SV114 @ ( cons_a @ ( sK71_X2 @ SV114 ) @ ( sK72_SY386 @ SV114 ) ) @ ( cons_a @ ( sK73_SY389 @ SV114 ) @ ( sK74_SY391 @ SV114 ) ) ) )
| ~ ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a )
| ~ ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) )
| ! [SY497: list_a,SY498: list_a] : ( SV114 @ SY497 @ SY498 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(853,plain,
! [SV115: list_a] :
( ( ( SV115 = nil_a )
| ! [SY499: list_a > $o] :
( ~ ( SY499 @ ( cons_a @ ( sK53_X2 @ SY499 @ SV115 ) @ nil_a ) )
| ~ ( ~ ( ( ( sK52_SY372 @ SY499 @ SV115 )
!= nil_a ) )
| ~ ~ ( ~ ( SY499 @ ( sK52_SY372 @ SY499 @ SV115 ) )
| ~ ~ ( SY499 @ ( cons_a @ ( sK51_X2 @ SY499 @ SV115 ) @ ( sK52_SY372 @ SY499 @ SV115 ) ) ) ) )
| ( SY499 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(854,plain,
! [SV116: poly_a > $o] :
( ( ~ ( ~ ( ( ( sK83_SY399 @ SV116 )
= zero_zero_poly_a )
| ( SV116 @ ( sK83_SY399 @ SV116 ) ) )
| ~ ~ ( SV116 @ ( pCons_a @ ( sK82_A2 @ SV116 ) @ ( sK83_SY399 @ SV116 ) ) ) )
| ! [SY500: poly_a] : ( SV116 @ SY500 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(855,plain,
! [SV117: ( a > a > $o ) > list_a > $o] :
( ( ~ ( SV117 @ ( sK50_P5 @ SV117 ) @ nil_a )
| ~ ( SV117 @ ( sK48_P5 @ SV117 ) @ ( cons_a @ ( sK49_SY371 @ SV117 ) @ nil_a ) )
| ~ ( ~ ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) )
| ~ ~ ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK45_SY365 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) ) ) )
| ! [SY501: a > a > $o,SY502: list_a] : ( SV117 @ SY501 @ SY502 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(856,plain,
! [SV118: list_a > list_a > $o] :
( ( ~ ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
| ~ ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
| ~ ( ~ ( SV118 @ ( sK27_SY350 @ SV118 ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) )
| ~ ~ ( ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( sK29_SY355 @ SV118 ) )
| ~ ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) ) ) )
| ! [SY503: list_a,SY504: list_a] : ( SV118 @ SY503 @ SY504 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(857,plain,
( ( ~ ! [SX0: poly_a] :
( ! [SX1: poly_a] :
( ( times_times_poly_a @ SX0 @ SX1 )
= zero_zero_poly_a )
| ( SX0 != zero_zero_poly_a ) )
| ~ ! [SX0: poly_a,SX1: poly_a] :
( ( ( times_times_poly_a @ SX0 @ SX1 )
= zero_zero_poly_a )
| ( SX1 != zero_zero_poly_a ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(858,plain,
! [SV119: list_a > list_a > $o] :
( ( ~ ( SV119 @ nil_a @ nil_a )
| ~ ( SV119 @ ( cons_a @ ( sK12_X2 @ SV119 ) @ ( sK13_SY337 @ SV119 ) ) @ nil_a )
| ~ ( SV119 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SV119 ) @ ( sK11_SY336 @ SV119 ) ) )
| ~ ( ~ ( SV119 @ ( sK7_SY330 @ SV119 ) @ ( sK9_SY335 @ SV119 ) )
| ~ ~ ( SV119 @ ( cons_a @ ( sK6_X2 @ SV119 ) @ ( sK7_SY330 @ SV119 ) ) @ ( cons_a @ ( sK8_SY333 @ SV119 ) @ ( sK9_SY335 @ SV119 ) ) ) )
| ! [SY505: list_a,SY506: list_a] : ( SV119 @ SY505 @ SY506 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(859,plain,
! [SV120: poly_a > $o] :
( ( ~ ( SV120 @ zero_zero_poly_a )
| ~ ( ~ ( ( ( sK88_A2 @ SV120 )
!= zero_zero_a )
| ( ( sK89_SY406 @ SV120 )
!= zero_zero_poly_a ) )
| ~ ~ ( ~ ( SV120 @ ( sK89_SY406 @ SV120 ) )
| ~ ~ ( SV120 @ ( pCons_a @ ( sK88_A2 @ SV120 ) @ ( sK89_SY406 @ SV120 ) ) ) ) )
| ! [SY507: poly_a] : ( SV120 @ SY507 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(860,plain,
! [SV121: list_a] :
( ( ( SV121 != nil_a )
= ( ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(861,plain,
! [SV122: list_a] :
( ( ! [SY510: list_a] :
( ( nil_a
= ( append_a @ SV122 @ SY510 ) )
= ( ~ ( ( SV122 != nil_a )
| ( SY510 != nil_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(862,plain,
! [SV123: list_a > list_a > $o] :
( ( ~ ( SV123 @ ( sK81_Xs2 @ SV123 ) @ nil_a )
| ~ ( SV123 @ nil_a @ ( cons_a @ ( sK79_V @ SV123 ) @ ( sK80_SY398 @ SV123 ) ) )
| ~ ( ~ ( SV123 @ ( sK76_SY392 @ SV123 ) @ ( sK78_SY397 @ SV123 ) )
| ~ ~ ( SV123 @ ( cons_a @ ( sK75_X2 @ SV123 ) @ ( sK76_SY392 @ SV123 ) ) @ ( cons_a @ ( sK77_SY395 @ SV123 ) @ ( sK78_SY397 @ SV123 ) ) ) )
| ! [SY511: list_a,SY512: list_a] : ( SV123 @ SY511 @ SY512 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(863,plain,
! [SV124: list_a > $o] :
( ( ~ ( SV124 @ nil_a )
| ~ ( ~ ( SV124 @ ( sK63_SY381 @ SV124 ) )
| ~ ~ ( SV124 @ ( cons_a @ ( sK62_X2 @ SV124 ) @ ( sK63_SY381 @ SV124 ) ) ) )
| ! [SY513: list_a] : ( SV124 @ SY513 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(864,plain,
! [SV125: poly_a] :
( ( ( v @ SV125 )
= ( descar2095969287nges_a @ ( coeffs_a @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(865,plain,
! [SV126: poly_a] :
( ( ( ^ [SY514: poly_a] : ( SV126 = SY514 ) )
= ( ^ [SY515: poly_a] :
( ( coeffs_a @ SV126 )
= ( coeffs_a @ SY515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(866,plain,
! [SV127: poly_a,SV3: list_a] :
( ( ( ( poly_a2 @ SV3 )
!= SV127 )
| ( ( descar2095969287nges_a @ SV3 )
= ( descar2095969287nges_a @ ( coeffs_a @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(867,plain,
! [SV128: poly_a] :
( ( ( is_zero_a @ SV128 )
= ( null_a @ ( coeffs_a @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(868,plain,
! [SV129: list_a,SV7: a] :
( ( ( descar2095969287nges_a @ ( cons_a @ SV7 @ ( cons_a @ zero_zero_a @ SV129 ) ) )
= ( descar2095969287nges_a @ ( cons_a @ SV7 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(869,plain,
! [SV8: poly_a] :
( ( ~ ( ( ( coeffs_a @ SV8 )
= nil_a )
| ( SV8 = zero_zero_poly_a ) )
| ~ ( ( ( coeffs_a @ SV8 )
!= nil_a )
| ( SV8 != zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[736]) ).
thf(870,plain,
! [SV8: poly_a] :
( ( ( ( coeffs_a @ SV8 )
= nil_a )
= ( SV8 = zero_zero_poly_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[736]) ).
thf(871,plain,
! [SV9: poly_a] :
( ( ( SV9 = zero_zero_poly_a )
= $true )
| ( ( ( coeffs_a @ SV9 )
!= nil_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(872,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ( smult_a @ SV12 @ SV130 )
= zero_zero_poly_a )
= ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(873,plain,
! [SV131: list_a,SV16: a] :
( ( ( poly_a2 @ ( cons_a @ SV16 @ SV131 ) )
= ( pCons_a @ SV16 @ ( poly_a2 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(874,plain,
! [SV132: poly_a] :
( ( ( is_zero_a @ SV132 )
= ( SV132 = zero_zero_poly_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(875,plain,
! [SV21: list_a] :
( ( ( SV21 = nil_a )
= $true )
| ( ( ( SV21
= ( cons_a @ ( sK67_X2 @ SV21 ) @ nil_a ) )
| ( SV21
= ( cons_a @ ( sK64_X2 @ SV21 ) @ ( cons_a @ ( sK65_SY382 @ SV21 ) @ ( sK66_SY384 @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(876,plain,
! [SV22: a] :
( ( ( SV22 = zero_zero_a )
= $true )
| ( ( ! [SY413: poly_a] :
( ( SY413 = zero_zero_poly_a )
| ( ( descar466059845root_a @ SV22 @ SY413 )
!= zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(877,plain,
! [SV23: nat] :
( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV23 )
| ( SV23 = zero_zero_nat ) )
| ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV23 )
| ( SV23 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[752]) ).
thf(878,plain,
! [SV23: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV23 ) )
= ( SV23 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[752]) ).
thf(879,plain,
! [SV133: a,SV24: a] :
( ( ! [SY516: a] :
( ( ( times_times_a @ SV24 @ SV133 )
= ( times_times_a @ SY516 @ SV133 ) )
= ( ( SV133 = zero_zero_a )
| ( SV24 = SY516 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(880,plain,
! [SV134: poly_a,SV25: poly_a] :
( ( ! [SY517: poly_a] :
( ( ( times_times_poly_a @ SV25 @ SV134 )
= ( times_times_poly_a @ SY517 @ SV134 ) )
= ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SY517 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(881,plain,
! [SV135: nat,SV26: nat] :
( ( ! [SY518: nat] :
( ( ( times_times_nat @ SV26 @ SV135 )
= ( times_times_nat @ SY518 @ SV135 ) )
= ( ( SV135 = zero_zero_nat )
| ( SV26 = SY518 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(882,plain,
! [SV136: a,SV27: a] :
( ( ! [SY519: a] :
( ( ( times_times_a @ SV27 @ SV136 )
= ( times_times_a @ SV27 @ SY519 ) )
= ( ( SV27 = zero_zero_a )
| ( SV136 = SY519 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(883,plain,
! [SV137: poly_a,SV28: poly_a] :
( ( ! [SY520: poly_a] :
( ( ( times_times_poly_a @ SV28 @ SV137 )
= ( times_times_poly_a @ SV28 @ SY520 ) )
= ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SY520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(884,plain,
! [SV138: nat,SV29: nat] :
( ( ! [SY521: nat] :
( ( ( times_times_nat @ SV29 @ SV138 )
= ( times_times_nat @ SV29 @ SY521 ) )
= ( ( SV29 = zero_zero_nat )
| ( SV138 = SY521 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(885,plain,
! [SV139: a,SV30: a] :
( ( ( ( times_times_a @ SV30 @ SV139 )
= zero_zero_a )
= ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(886,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ( times_times_poly_a @ SV31 @ SV140 )
= zero_zero_poly_a )
= ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(887,plain,
! [SV141: nat,SV32: nat] :
( ( ( ( times_times_nat @ SV32 @ SV141 )
= zero_zero_nat )
= ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(888,plain,
! [SV39: poly_a] :
( ( ~ ( ( ( uminus_uminus_poly_a @ SV39 )
= SV39 )
| ( SV39 = zero_zero_poly_a ) )
| ~ ( ( ( uminus_uminus_poly_a @ SV39 )
!= SV39 )
| ( SV39 != zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[768]) ).
thf(889,plain,
! [SV39: poly_a] :
( ( ( ( uminus_uminus_poly_a @ SV39 )
= SV39 )
= ( SV39 = zero_zero_poly_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[768]) ).
thf(890,plain,
! [SV40: a] :
( ( ~ ( ( ( uminus_uminus_a @ SV40 )
= SV40 )
| ( SV40 = zero_zero_a ) )
| ~ ( ( ( uminus_uminus_a @ SV40 )
!= SV40 )
| ( SV40 != zero_zero_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[769]) ).
thf(891,plain,
! [SV40: a] :
( ( ( ( uminus_uminus_a @ SV40 )
= SV40 )
= ( SV40 = zero_zero_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[769]) ).
thf(892,plain,
! [SV41: poly_a] :
( ( ~ ( ( SV41
= ( uminus_uminus_poly_a @ SV41 ) )
| ( SV41 = zero_zero_poly_a ) )
| ~ ( ( SV41
!= ( uminus_uminus_poly_a @ SV41 ) )
| ( SV41 != zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[770]) ).
thf(893,plain,
! [SV41: poly_a] :
( ( ( SV41
= ( uminus_uminus_poly_a @ SV41 ) )
= ( SV41 = zero_zero_poly_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[770]) ).
thf(894,plain,
! [SV42: a] :
( ( ~ ( ( SV42
= ( uminus_uminus_a @ SV42 ) )
| ( SV42 = zero_zero_a ) )
| ~ ( ( SV42
!= ( uminus_uminus_a @ SV42 ) )
| ( SV42 != zero_zero_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[771]) ).
thf(895,plain,
! [SV42: a] :
( ( ( SV42
= ( uminus_uminus_a @ SV42 ) )
= ( SV42 = zero_zero_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[771]) ).
thf(896,plain,
! [SV43: poly_a] :
( ( ~ ( ( ( uminus_uminus_poly_a @ SV43 )
= zero_zero_poly_a )
| ( SV43 = zero_zero_poly_a ) )
| ~ ( ( ( uminus_uminus_poly_a @ SV43 )
!= zero_zero_poly_a )
| ( SV43 != zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[772]) ).
thf(897,plain,
! [SV43: poly_a] :
( ( ( ( uminus_uminus_poly_a @ SV43 )
= zero_zero_poly_a )
= ( SV43 = zero_zero_poly_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[772]) ).
thf(898,plain,
! [SV44: a] :
( ( ~ ( ( ( uminus_uminus_a @ SV44 )
= zero_zero_a )
| ( SV44 = zero_zero_a ) )
| ~ ( ( ( uminus_uminus_a @ SV44 )
!= zero_zero_a )
| ( SV44 != zero_zero_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[773]) ).
thf(899,plain,
! [SV44: a] :
( ( ( ( uminus_uminus_a @ SV44 )
= zero_zero_a )
= ( SV44 = zero_zero_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[773]) ).
thf(900,plain,
! [SV45: poly_a] :
( ( ~ ( ( zero_zero_poly_a
= ( uminus_uminus_poly_a @ SV45 ) )
| ( zero_zero_poly_a = SV45 ) )
| ~ ( ( zero_zero_poly_a
!= ( uminus_uminus_poly_a @ SV45 ) )
| ( zero_zero_poly_a != SV45 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[774]) ).
thf(901,plain,
! [SV45: poly_a] :
( ( ( zero_zero_poly_a
= ( uminus_uminus_poly_a @ SV45 ) )
= ( zero_zero_poly_a = SV45 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[774]) ).
thf(902,plain,
! [SV46: a] :
( ( ~ ( ( zero_zero_a
= ( uminus_uminus_a @ SV46 ) )
| ( zero_zero_a = SV46 ) )
| ~ ( ( zero_zero_a
!= ( uminus_uminus_a @ SV46 ) )
| ( zero_zero_a != SV46 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[775]) ).
thf(903,plain,
! [SV46: a] :
( ( ( zero_zero_a
= ( uminus_uminus_a @ SV46 ) )
= ( zero_zero_a = SV46 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[775]) ).
thf(904,plain,
! [SV142: list_a,SV48: list_a] :
( ( ( SV48
= ( append_a @ SV142 @ SV48 ) )
= ( SV142 = nil_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(905,plain,
! [SV143: list_a,SV49: list_a] :
( ( ( ( append_a @ SV49 @ SV143 )
= SV143 )
= ( SV49 = nil_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(906,plain,
! [SV144: list_a,SV50: list_a] :
( ( ( SV50
= ( append_a @ SV50 @ SV144 ) )
= ( SV144 = nil_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(907,plain,
! [SV145: list_a,SV51: list_a] :
( ( ( ( append_a @ SV51 @ SV145 )
= SV51 )
= ( SV145 = nil_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(908,plain,
! [SV53: poly_a] :
( ( ~ ( ( zero_zero_poly_a = SV53 )
| ( SV53 = zero_zero_poly_a ) )
| ~ ( ( zero_zero_poly_a != SV53 )
| ( SV53 != zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[782]) ).
thf(909,plain,
! [SV53: poly_a] :
( ( ( zero_zero_poly_a = SV53 )
= ( SV53 = zero_zero_poly_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[782]) ).
thf(910,plain,
! [SV54: a] :
( ( ~ ( ( zero_zero_a = SV54 )
| ( SV54 = zero_zero_a ) )
| ~ ( ( zero_zero_a != SV54 )
| ( SV54 != zero_zero_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[783]) ).
thf(911,plain,
! [SV54: a] :
( ( ( zero_zero_a = SV54 )
= ( SV54 = zero_zero_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[783]) ).
thf(912,plain,
! [SV55: nat] :
( ( ~ ( ( zero_zero_nat = SV55 )
| ( SV55 = zero_zero_nat ) )
| ~ ( ( zero_zero_nat != SV55 )
| ( SV55 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[784]) ).
thf(913,plain,
! [SV55: nat] :
( ( ( zero_zero_nat = SV55 )
= ( SV55 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[784]) ).
thf(914,plain,
! [SV146: list_a,SV56: a] :
( ( ( cons_a @ SV56 @ SV146 )
!= SV146 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(915,plain,
! [SV57: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV57 )
| ( SV57 != zero_zero_nat ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV57 )
| ~ ( ( SV57 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[786]) ).
thf(916,plain,
! [SV57: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV57 )
= ( SV57 != zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[786]) ).
thf(917,plain,
! [SV147: nat,SV58: nat] :
( ( ~ ( ord_less_nat @ SV58 @ SV147 )
| ( SV147 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(918,plain,
! [SV59: nat] :
( ( ord_less_nat @ SV59 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(919,plain,
! [SV60: nat] :
( ( ( SV60 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(920,plain,
! [SV61: a] :
( ( ( SV61 = zero_zero_a )
= $true )
| ( ( ! [SY435: a,SY436: a] :
( ( ( times_times_a @ SY435 @ SV61 )
= ( times_times_a @ SY436 @ SV61 ) )
= ( SY435 = SY436 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[793]) ).
thf(921,plain,
! [SV62: poly_a] :
( ( ( SV62 = zero_zero_poly_a )
= $true )
| ( ( ! [SY437: poly_a,SY438: poly_a] :
( ( ( times_times_poly_a @ SY437 @ SV62 )
= ( times_times_poly_a @ SY438 @ SV62 ) )
= ( SY437 = SY438 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[794]) ).
thf(922,plain,
! [SV63: nat] :
( ( ( SV63 = zero_zero_nat )
= $true )
| ( ( ! [SY439: nat,SY440: nat] :
( ( ( times_times_nat @ SY439 @ SV63 )
= ( times_times_nat @ SY440 @ SV63 ) )
= ( SY439 = SY440 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[795]) ).
thf(923,plain,
! [SV64: a] :
( ( ( SV64 = zero_zero_a )
= $true )
| ( ( ! [SY441: a,SY442: a] :
( ( ( times_times_a @ SV64 @ SY441 )
= ( times_times_a @ SV64 @ SY442 ) )
= ( SY441 = SY442 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(924,plain,
! [SV65: poly_a] :
( ( ( SV65 = zero_zero_poly_a )
= $true )
| ( ( ! [SY443: poly_a,SY444: poly_a] :
( ( ( times_times_poly_a @ SV65 @ SY443 )
= ( times_times_poly_a @ SV65 @ SY444 ) )
= ( SY443 = SY444 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[797]) ).
thf(925,plain,
! [SV66: nat] :
( ( ( SV66 = zero_zero_nat )
= $true )
| ( ( ! [SY445: nat,SY446: nat] :
( ( ( times_times_nat @ SV66 @ SY445 )
= ( times_times_nat @ SV66 @ SY446 ) )
= ( SY445 = SY446 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(926,plain,
! [SV67: a] :
( ( ( SV67 = zero_zero_a )
= $true )
| ( ( ! [SY447: a] :
( ( SY447 = zero_zero_a )
| ( ( times_times_a @ SV67 @ SY447 )
!= zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(927,plain,
! [SV68: poly_a] :
( ( ( SV68 = zero_zero_poly_a )
= $true )
| ( ( ! [SY448: poly_a] :
( ( SY448 = zero_zero_poly_a )
| ( ( times_times_poly_a @ SV68 @ SY448 )
!= zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[800]) ).
thf(928,plain,
! [SV69: nat] :
( ( ( SV69 = zero_zero_nat )
= $true )
| ( ( ! [SY449: nat] :
( ( SY449 = zero_zero_nat )
| ( ( times_times_nat @ SV69 @ SY449 )
!= zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[801]) ).
thf(929,plain,
! [SV148: a,SV70: a] :
( ( ( ( times_times_a @ SV70 @ SV148 )
!= zero_zero_a )
| ( SV70 = zero_zero_a )
| ( SV148 = zero_zero_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(930,plain,
! [SV149: poly_a,SV71: poly_a] :
( ( ( ( times_times_poly_a @ SV71 @ SV149 )
!= zero_zero_poly_a )
| ( SV71 = zero_zero_poly_a )
| ( SV149 = zero_zero_poly_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(931,plain,
! [SV150: nat,SV72: nat] :
( ( ( ( times_times_nat @ SV72 @ SV150 )
!= zero_zero_nat )
| ( SV72 = zero_zero_nat )
| ( SV150 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(932,plain,
! [SV73: list_a] :
( ( ( SV73 = nil_a )
= $true )
| ( ( SV73
= ( cons_a @ ( sK60_X2 @ SV73 ) @ ( sK61_SY380 @ SV73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[808]) ).
thf(933,plain,
! [SV74: list_a] :
( ( ( SV74 = nil_a )
= $true )
| ( ( ( SV74
= ( cons_a @ ( sK35_X2 @ SV74 ) @ nil_a ) )
| ( SV74
= ( cons_a @ ( sK32_X2 @ SV74 ) @ ( cons_a @ ( sK33_SY356 @ SV74 ) @ ( sK34_SY358 @ SV74 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[809]) ).
thf(934,plain,
! [SV75: list_a] :
( ( ( SV75
= ( cons_a @ ( sK22_X2 @ SV75 ) @ ( sK23_SY344 @ SV75 ) ) )
= $true )
| ( ( SV75 = nil_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[810]) ).
thf(935,plain,
! [SV76: list_a] :
( ( ( SV76 = nil_a )
= $true )
| ( ( SV76
= ( cons_a @ ( sK2_X213 @ SV76 ) @ ( sK3_SY328 @ SV76 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[811]) ).
thf(936,plain,
! [SV77: list_a] :
( ( ( ! [SY453: a,SY454: list_a] :
( SV77
!= ( cons_a @ SY453 @ SY454 ) ) )
= $true )
| ( ( SV77 != nil_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[812]) ).
thf(937,plain,
! [SV151: list_a,SV78: a] :
( ( nil_a
!= ( cons_a @ SV78 @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(938,plain,
! [SV152: list_a,SV79: a] :
( ( ! [SY522: list_a] :
( ( append_a @ ( cons_a @ SV79 @ SV152 ) @ SY522 )
= ( cons_a @ SV79 @ ( append_a @ SV152 @ SY522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(939,plain,
! [SV153: list_a,SV80: a] :
( ( ! [SY523: list_a] :
( ( ( cons_a @ SV80 @ SV153 )
!= SY523 )
| ! [SY524: list_a,SY525: list_a] :
( ( SY524
!= ( append_a @ SV153 @ SY525 ) )
| ( ( cons_a @ SV80 @ SY524 )
= ( append_a @ SY523 @ SY525 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(940,plain,
! [SV154: list_a,SV83: list_a] :
( ( ( SV83 != SV154 )
| ( SV83
= ( append_a @ nil_a @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(941,plain,
! [SV155: list_a,SV84: a] :
( ( ~ ( null_a @ ( cons_a @ SV84 @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(942,plain,
! [SV85: list_a] :
( ( ~ ( ( SV85 = nil_a )
| ( null_a @ SV85 ) )
| ~ ( ( SV85 != nil_a )
| ~ ( null_a @ SV85 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[820]) ).
thf(943,plain,
! [SV85: list_a] :
( ( ( SV85 = nil_a )
= ( null_a @ SV85 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[820]) ).
thf(944,plain,
! [SV156: nat,SV86: nat] :
( ( ! [SY526: nat] :
( ( ( times_times_nat @ SV86 @ SV156 )
= ( times_times_nat @ SY526 @ SV156 ) )
= ( ( SV86 = SY526 )
| ( SV156 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(945,plain,
! [SV87: nat] :
( ( ~ ( ( SV87 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV87 ) )
| ~ ( ~ ( ( SV87 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV87 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[822]) ).
thf(946,plain,
! [SV87: nat] :
( ( ( SV87 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV87 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[822]) ).
thf(947,plain,
! [SV88: nat] :
( ( ord_less_nat @ SV88 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(948,plain,
! [SV89: nat] :
( ( ~ ( ( SV89 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV89 ) )
| ~ ( ~ ( ( SV89 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV89 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[824]) ).
thf(949,plain,
! [SV89: nat] :
( ( ( SV89 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV89 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[824]) ).
thf(950,plain,
! [SV157: nat,SV90: nat] :
( ( ( ( times_times_nat @ SV90 @ SV157 )
= zero_zero_nat )
= ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(951,plain,
! [SV158: nat,SV92: nat] :
( ( ! [SY527: nat] :
( ( ( times_times_nat @ SV92 @ SV158 )
= ( times_times_nat @ SV92 @ SY527 ) )
= ( ( SV158 = SY527 )
| ( SV92 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(952,plain,
! [SV93: nat] :
( ( ( SV93 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[828]) ).
thf(953,plain,
! [SV94: nat] :
( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV94 )
| ( SV94 = zero_zero_nat ) )
| ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV94 )
| ( SV94 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[829]) ).
thf(954,plain,
! [SV94: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV94 ) )
= ( SV94 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[829]) ).
thf(955,plain,
! [SV95: nat] :
( ( ord_less_nat @ SV95 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(956,plain,
! [SV96: nat] :
( ( ord_less_nat @ SV96 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(957,plain,
! [SV159: nat,SV97: nat] :
( ( ~ ( ord_less_nat @ SV97 @ SV159 )
| ( SV159 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(958,plain,
! [SV98: nat] :
( ( ord_less_nat @ SV98 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(959,plain,
! [SV160: nat,SV100: nat] :
( ( ! [SY528: nat] :
( ( ( times_times_nat @ SV100 @ SV160 )
= ( times_times_nat @ SV100 @ SY528 ) )
= ( ( SV100 = zero_zero_nat )
| ( SV160 = SY528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(960,plain,
! [SV101: list_a > $o] :
( ( ( ~ ( SV101 @ nil_a ) )
= $true )
| ( ( ~ ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
| ~ ( ~ ( ( ( sK40_X2 @ SV101 )
!= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
| ~ ~ ( ~ ( ( ( sK40_X2 @ SV101 )
= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
| ~ ~ ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) ) ) )
| ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(961,plain,
( ( ~ ! [SX0: a] :
( ! [SX1: a] :
( ( times_times_a @ SX0 @ SX1 )
= zero_zero_a )
| ( SX0 != zero_zero_a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[838]) ).
thf(962,plain,
( ( ~ ! [SX0: a,SX1: a] :
( ( ( times_times_a @ SX0 @ SX1 )
= zero_zero_a )
| ( SX1 != zero_zero_a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[838]) ).
thf(963,plain,
! [SV102: list_a > $o] :
( ( ( ~ ( ~ ( ! [SY473: a,SY474: list_a] :
( ( sK25_SY345 @ SV102 )
!= ( cons_a @ SY473 @ SY474 ) )
| ( SV102 @ ( sK25_SY345 @ SV102 ) ) )
| ~ ~ ( SV102 @ ( cons_a @ ( sK24_X2 @ SV102 ) @ ( sK25_SY345 @ SV102 ) ) ) ) )
= $true )
| ( ( ~ ( SV102 @ nil_a )
| ! [SY475: list_a] : ( SV102 @ SY475 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(964,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ( append_a @ SV103 @ SV161 )
= nil_a )
= ( ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(965,plain,
! [SV162: a > a,SV104: ( a > a ) > list_a > list_a > $o] :
( ( ~ ( SV104 @ ( sK58_F2 @ SV162 @ SV104 ) @ nil_a @ ( sK59_SY379 @ SV162 @ SV104 ) )
| ~ ( ~ ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) @ ( cons_a @ ( sK54_F2 @ SV162 @ SV104 @ ( sK55_SY373 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) ) )
| ~ ~ ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( cons_a @ ( sK55_SY373 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) ) )
| ! [SY529: list_a,SY530: list_a] : ( SV104 @ SV162 @ SY529 @ SY530 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(966,plain,
! [SV163: a,SV105: list_a] :
( ( ! [SY531: list_a,SY532: a] :
( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SY531 @ ( cons_a @ SY532 @ nil_a ) ) )
= ( ~ ( ( SV105 != SY531 )
| ( SV163 != SY532 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(967,plain,
! [SV106: ( a > a > $o ) > list_a > $o] :
( ( ( ~ ( SV106 @ ( sK39_P5 @ SV106 ) @ nil_a ) )
= $true )
| ( ( ~ ( ~ ( SV106 @ ( sK36_P5 @ SV106 ) @ ( sK38_SY361 @ SV106 ) )
| ~ ~ ( SV106 @ ( sK36_P5 @ SV106 ) @ ( cons_a @ ( sK37_SY359 @ SV106 ) @ ( sK38_SY361 @ SV106 ) ) ) )
| ! [SY483: a > a > $o,SY484: list_a] : ( SV106 @ SY483 @ SY484 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(968,plain,
! [SV107: nat > $o] :
( ( ( ~ ( SV107 @ zero_zero_nat ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK1_N2 @ SV107 ) )
| ~ ~ ( ~ ~ ( SV107 @ ( sK1_N2 @ SV107 ) )
| ~ ! [SY485: nat] :
( ~ ( ord_less_nat @ SY485 @ ( sK1_N2 @ SV107 ) )
| ( SV107 @ SY485 ) ) ) )
| ! [SY486: nat] : ( SV107 @ SY486 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(969,plain,
! [SV108: list_a > $o] :
( ( ( ~ ( SV108 @ nil_a ) )
= $true )
| ( ( ~ ( ~ ( SV108 @ ( sK5_SY329 @ SV108 ) )
| ~ ~ ( SV108 @ ( cons_a @ ( sK4_X1 @ SV108 ) @ ( sK5_SY329 @ SV108 ) ) ) )
| ! [SY487: list_a] : ( SV108 @ SY487 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[845]) ).
thf(970,plain,
! [SV109: list_a > $o] :
( ( ( ~ ( SV109 @ nil_a ) )
= $true )
| ( ( ~ ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
| ~ ( ~ ( SV109 @ ( sK20_SY343 @ SV109 ) )
| ~ ~ ( ~ ( SV109 @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) )
| ~ ~ ( SV109 @ ( cons_a @ ( sK18_X2 @ SV109 ) @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) ) ) ) )
| ! [SY488: list_a] : ( SV109 @ SY488 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[846]) ).
thf(971,plain,
! [SV164: list_a,SV110: a] :
( ( ! [SY533: a,SY534: list_a] :
( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SY533 @ SY534 ) )
= ( ~ ( ( SV110 != SY533 )
| ( SV164 != SY534 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(972,plain,
! [SV111: list_a > list_a > $o] :
( ( ( ~ ( SV111 @ nil_a @ ( sK17_X_1 @ SV111 ) ) )
= $true )
| ( ( ~ ( ~ ( SV111 @ ( sK16_SY340 @ SV111 ) @ ( sK15_SY338 @ SV111 ) )
| ~ ~ ( SV111 @ ( cons_a @ ( sK14_X2 @ SV111 ) @ ( sK15_SY338 @ SV111 ) ) @ ( sK16_SY340 @ SV111 ) ) )
| ! [SY492: list_a,SY493: list_a] : ( SV111 @ SY492 @ SY493 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(973,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ( pCons_a @ SV112 @ SV165 )
= zero_zero_poly_a )
= ( ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(974,plain,
( ( ~ ! [SX0: nat] :
( ! [SX1: nat] :
( ( times_times_nat @ SX0 @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[850]) ).
thf(975,plain,
( ( ~ ! [SX0: nat,SX1: nat] :
( ( ( times_times_nat @ SX0 @ SX1 )
= zero_zero_nat )
| ( SX1 != zero_zero_nat ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[850]) ).
thf(976,plain,
! [SV113: poly_a > poly_a > $o] :
( ( ( ~ ( SV113 @ zero_zero_poly_a @ zero_zero_poly_a ) )
= $true )
| ( ( ~ ( ~ ( SV113 @ ( sK85_SY400 @ SV113 ) @ ( sK87_SY405 @ SV113 ) )
| ~ ~ ( SV113 @ ( pCons_a @ ( sK84_A2 @ SV113 ) @ ( sK85_SY400 @ SV113 ) ) @ ( pCons_a @ ( sK86_SY403 @ SV113 ) @ ( sK87_SY405 @ SV113 ) ) ) )
| ! [SY495: poly_a,SY496: poly_a] : ( SV113 @ SY495 @ SY496 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(977,plain,
! [SV114: list_a > list_a > $o] :
( ( ( ~ ( ~ ( SV114 @ ( sK72_SY386 @ SV114 ) @ ( sK74_SY391 @ SV114 ) )
| ~ ~ ( SV114 @ ( cons_a @ ( sK71_X2 @ SV114 ) @ ( sK72_SY386 @ SV114 ) ) @ ( cons_a @ ( sK73_SY389 @ SV114 ) @ ( sK74_SY391 @ SV114 ) ) ) ) )
= $true )
| ( ( ~ ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a )
| ~ ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) )
| ! [SY497: list_a,SY498: list_a] : ( SV114 @ SY497 @ SY498 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(978,plain,
! [SV115: list_a] :
( ( ( SV115 = nil_a )
= $true )
| ( ( ! [SY499: list_a > $o] :
( ~ ( SY499 @ ( cons_a @ ( sK53_X2 @ SY499 @ SV115 ) @ nil_a ) )
| ~ ( ~ ( ( ( sK52_SY372 @ SY499 @ SV115 )
!= nil_a ) )
| ~ ~ ( ~ ( SY499 @ ( sK52_SY372 @ SY499 @ SV115 ) )
| ~ ~ ( SY499 @ ( cons_a @ ( sK51_X2 @ SY499 @ SV115 ) @ ( sK52_SY372 @ SY499 @ SV115 ) ) ) ) )
| ( SY499 @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[853]) ).
thf(979,plain,
! [SV116: poly_a > $o] :
( ( ( ~ ( ~ ( ( ( sK83_SY399 @ SV116 )
= zero_zero_poly_a )
| ( SV116 @ ( sK83_SY399 @ SV116 ) ) )
| ~ ~ ( SV116 @ ( pCons_a @ ( sK82_A2 @ SV116 ) @ ( sK83_SY399 @ SV116 ) ) ) ) )
= $true )
| ( ( ! [SY500: poly_a] : ( SV116 @ SY500 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[854]) ).
thf(980,plain,
! [SV117: ( a > a > $o ) > list_a > $o] :
( ( ( ~ ( SV117 @ ( sK50_P5 @ SV117 ) @ nil_a ) )
= $true )
| ( ( ~ ( SV117 @ ( sK48_P5 @ SV117 ) @ ( cons_a @ ( sK49_SY371 @ SV117 ) @ nil_a ) )
| ~ ( ~ ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) )
| ~ ~ ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK45_SY365 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) ) ) )
| ! [SY501: a > a > $o,SY502: list_a] : ( SV117 @ SY501 @ SY502 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[855]) ).
thf(981,plain,
! [SV118: list_a > list_a > $o] :
( ( ( ~ ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) ) )
= $true )
| ( ( ~ ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
| ~ ( ~ ( SV118 @ ( sK27_SY350 @ SV118 ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) )
| ~ ~ ( ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( sK29_SY355 @ SV118 ) )
| ~ ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) ) ) )
| ! [SY503: list_a,SY504: list_a] : ( SV118 @ SY503 @ SY504 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[856]) ).
thf(982,plain,
( ( ~ ! [SX0: poly_a] :
( ! [SX1: poly_a] :
( ( times_times_poly_a @ SX0 @ SX1 )
= zero_zero_poly_a )
| ( SX0 != zero_zero_poly_a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(983,plain,
( ( ~ ! [SX0: poly_a,SX1: poly_a] :
( ( ( times_times_poly_a @ SX0 @ SX1 )
= zero_zero_poly_a )
| ( SX1 != zero_zero_poly_a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(984,plain,
! [SV119: list_a > list_a > $o] :
( ( ( ~ ( SV119 @ nil_a @ nil_a ) )
= $true )
| ( ( ~ ( SV119 @ ( cons_a @ ( sK12_X2 @ SV119 ) @ ( sK13_SY337 @ SV119 ) ) @ nil_a )
| ~ ( SV119 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SV119 ) @ ( sK11_SY336 @ SV119 ) ) )
| ~ ( ~ ( SV119 @ ( sK7_SY330 @ SV119 ) @ ( sK9_SY335 @ SV119 ) )
| ~ ~ ( SV119 @ ( cons_a @ ( sK6_X2 @ SV119 ) @ ( sK7_SY330 @ SV119 ) ) @ ( cons_a @ ( sK8_SY333 @ SV119 ) @ ( sK9_SY335 @ SV119 ) ) ) )
| ! [SY505: list_a,SY506: list_a] : ( SV119 @ SY505 @ SY506 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[858]) ).
thf(985,plain,
! [SV120: poly_a > $o] :
( ( ( ~ ( SV120 @ zero_zero_poly_a ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK88_A2 @ SV120 )
!= zero_zero_a )
| ( ( sK89_SY406 @ SV120 )
!= zero_zero_poly_a ) )
| ~ ~ ( ~ ( SV120 @ ( sK89_SY406 @ SV120 ) )
| ~ ~ ( SV120 @ ( pCons_a @ ( sK88_A2 @ SV120 ) @ ( sK89_SY406 @ SV120 ) ) ) ) )
| ! [SY507: poly_a] : ( SV120 @ SY507 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(986,plain,
! [SV121: list_a] :
( ( ~ ( ( SV121 != nil_a )
| ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) )
| ~ ( ~ ( ( SV121 != nil_a ) )
| ~ ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[860]) ).
thf(987,plain,
! [SV121: list_a] :
( ( ( SV121 != nil_a )
= ( ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[860]) ).
thf(988,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( nil_a
= ( append_a @ SV122 @ SV166 ) )
= ( ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(989,plain,
! [SV123: list_a > list_a > $o] :
( ( ( ~ ( SV123 @ ( sK81_Xs2 @ SV123 ) @ nil_a ) )
= $true )
| ( ( ~ ( SV123 @ nil_a @ ( cons_a @ ( sK79_V @ SV123 ) @ ( sK80_SY398 @ SV123 ) ) )
| ~ ( ~ ( SV123 @ ( sK76_SY392 @ SV123 ) @ ( sK78_SY397 @ SV123 ) )
| ~ ~ ( SV123 @ ( cons_a @ ( sK75_X2 @ SV123 ) @ ( sK76_SY392 @ SV123 ) ) @ ( cons_a @ ( sK77_SY395 @ SV123 ) @ ( sK78_SY397 @ SV123 ) ) ) )
| ! [SY511: list_a,SY512: list_a] : ( SV123 @ SY511 @ SY512 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(990,plain,
! [SV124: list_a > $o] :
( ( ( ~ ( SV124 @ nil_a ) )
= $true )
| ( ( ~ ( ~ ( SV124 @ ( sK63_SY381 @ SV124 ) )
| ~ ~ ( SV124 @ ( cons_a @ ( sK62_X2 @ SV124 ) @ ( sK63_SY381 @ SV124 ) ) ) )
| ! [SY513: list_a] : ( SV124 @ SY513 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(991,plain,
! [SV126: poly_a] :
( ( ! [SV167: poly_a] :
( ( SV126 = SV167 )
= ( ( coeffs_a @ SV126 )
= ( coeffs_a @ SV167 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[865]) ).
thf(992,plain,
! [SV126: poly_a] :
( ( ( ^ [SY514: poly_a] : ( SV126 = SY514 ) )
= ( ^ [SY515: poly_a] :
( ( coeffs_a @ SV126 )
= ( coeffs_a @ SY515 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[865]) ).
thf(993,plain,
! [SV127: poly_a,SV3: list_a] :
( ( ( ( poly_a2 @ SV3 )
!= SV127 )
= $true )
| ( ( ( descar2095969287nges_a @ SV3 )
= ( descar2095969287nges_a @ ( coeffs_a @ SV127 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(994,plain,
! [SV128: poly_a] :
( ( ~ ( ( is_zero_a @ SV128 )
| ( null_a @ ( coeffs_a @ SV128 ) ) )
| ~ ( ~ ( is_zero_a @ SV128 )
| ~ ( null_a @ ( coeffs_a @ SV128 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[867]) ).
thf(995,plain,
! [SV128: poly_a] :
( ( ( is_zero_a @ SV128 )
= ( null_a @ ( coeffs_a @ SV128 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[867]) ).
thf(996,plain,
! [SV8: poly_a] :
( ( ( ~ ( ( ( coeffs_a @ SV8 )
= nil_a )
| ( SV8 = zero_zero_poly_a ) ) )
= $true )
| ( ( ~ ( ( ( coeffs_a @ SV8 )
!= nil_a )
| ( SV8 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[869]) ).
thf(997,plain,
! [SV9: poly_a] :
( ( ( ( coeffs_a @ SV9 )
= nil_a )
= $false )
| ( ( SV9 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(998,plain,
! [SV130: poly_a,SV12: a] :
( ( ~ ( ( ( smult_a @ SV12 @ SV130 )
= zero_zero_poly_a )
| ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) )
| ~ ( ( ( smult_a @ SV12 @ SV130 )
!= zero_zero_poly_a )
| ~ ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[872]) ).
thf(999,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ( smult_a @ SV12 @ SV130 )
= zero_zero_poly_a )
= ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[872]) ).
thf(1000,plain,
! [SV132: poly_a] :
( ( ~ ( ( is_zero_a @ SV132 )
| ( SV132 = zero_zero_poly_a ) )
| ~ ( ~ ( is_zero_a @ SV132 )
| ( SV132 != zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[874]) ).
thf(1001,plain,
! [SV132: poly_a] :
( ( ( is_zero_a @ SV132 )
= ( SV132 = zero_zero_poly_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[874]) ).
thf(1002,plain,
! [SV21: list_a] :
( ( ( SV21
= ( cons_a @ ( sK67_X2 @ SV21 ) @ nil_a ) )
= $true )
| ( ( SV21
= ( cons_a @ ( sK64_X2 @ SV21 ) @ ( cons_a @ ( sK65_SY382 @ SV21 ) @ ( sK66_SY384 @ SV21 ) ) ) )
= $true )
| ( ( SV21 = nil_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(1003,plain,
! [SV22: a,SV168: poly_a] :
( ( ( ( SV168 = zero_zero_poly_a )
| ( ( descar466059845root_a @ SV22 @ SV168 )
!= zero_zero_poly_a ) )
= $true )
| ( ( SV22 = zero_zero_a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1004,plain,
! [SV23: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV23 )
| ( SV23 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV23 )
| ( SV23 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(1005,plain,
! [SV169: a,SV133: a,SV24: a] :
( ( ( ( times_times_a @ SV24 @ SV133 )
= ( times_times_a @ SV169 @ SV133 ) )
= ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1006,plain,
! [SV170: poly_a,SV134: poly_a,SV25: poly_a] :
( ( ( ( times_times_poly_a @ SV25 @ SV134 )
= ( times_times_poly_a @ SV170 @ SV134 ) )
= ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1007,plain,
! [SV171: nat,SV135: nat,SV26: nat] :
( ( ( ( times_times_nat @ SV26 @ SV135 )
= ( times_times_nat @ SV171 @ SV135 ) )
= ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1008,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ( times_times_a @ SV27 @ SV136 )
= ( times_times_a @ SV27 @ SV172 ) )
= ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1009,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ( times_times_poly_a @ SV28 @ SV137 )
= ( times_times_poly_a @ SV28 @ SV173 ) )
= ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1010,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ( times_times_nat @ SV29 @ SV138 )
= ( times_times_nat @ SV29 @ SV174 ) )
= ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1011,plain,
! [SV139: a,SV30: a] :
( ( ~ ( ( ( times_times_a @ SV30 @ SV139 )
= zero_zero_a )
| ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) )
| ~ ( ( ( times_times_a @ SV30 @ SV139 )
!= zero_zero_a )
| ~ ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[885]) ).
thf(1012,plain,
! [SV139: a,SV30: a] :
( ( ( ( times_times_a @ SV30 @ SV139 )
= zero_zero_a )
= ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[885]) ).
thf(1013,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ~ ( ( ( times_times_poly_a @ SV31 @ SV140 )
= zero_zero_poly_a )
| ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) )
| ~ ( ( ( times_times_poly_a @ SV31 @ SV140 )
!= zero_zero_poly_a )
| ~ ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[886]) ).
thf(1014,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ( times_times_poly_a @ SV31 @ SV140 )
= zero_zero_poly_a )
= ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[886]) ).
thf(1015,plain,
! [SV141: nat,SV32: nat] :
( ( ~ ( ( ( times_times_nat @ SV32 @ SV141 )
= zero_zero_nat )
| ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) )
| ~ ( ( ( times_times_nat @ SV32 @ SV141 )
!= zero_zero_nat )
| ~ ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[887]) ).
thf(1016,plain,
! [SV141: nat,SV32: nat] :
( ( ( ( times_times_nat @ SV32 @ SV141 )
= zero_zero_nat )
= ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[887]) ).
thf(1017,plain,
! [SV39: poly_a] :
( ( ( ~ ( ( ( uminus_uminus_poly_a @ SV39 )
= SV39 )
| ( SV39 = zero_zero_poly_a ) ) )
= $true )
| ( ( ~ ( ( ( uminus_uminus_poly_a @ SV39 )
!= SV39 )
| ( SV39 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(1018,plain,
! [SV40: a] :
( ( ( ~ ( ( ( uminus_uminus_a @ SV40 )
= SV40 )
| ( SV40 = zero_zero_a ) ) )
= $true )
| ( ( ~ ( ( ( uminus_uminus_a @ SV40 )
!= SV40 )
| ( SV40 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(1019,plain,
! [SV41: poly_a] :
( ( ( ~ ( ( SV41
= ( uminus_uminus_poly_a @ SV41 ) )
| ( SV41 = zero_zero_poly_a ) ) )
= $true )
| ( ( ~ ( ( SV41
!= ( uminus_uminus_poly_a @ SV41 ) )
| ( SV41 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(1020,plain,
! [SV42: a] :
( ( ( ~ ( ( SV42
= ( uminus_uminus_a @ SV42 ) )
| ( SV42 = zero_zero_a ) ) )
= $true )
| ( ( ~ ( ( SV42
!= ( uminus_uminus_a @ SV42 ) )
| ( SV42 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[894]) ).
thf(1021,plain,
! [SV43: poly_a] :
( ( ( ~ ( ( ( uminus_uminus_poly_a @ SV43 )
= zero_zero_poly_a )
| ( SV43 = zero_zero_poly_a ) ) )
= $true )
| ( ( ~ ( ( ( uminus_uminus_poly_a @ SV43 )
!= zero_zero_poly_a )
| ( SV43 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[896]) ).
thf(1022,plain,
! [SV44: a] :
( ( ( ~ ( ( ( uminus_uminus_a @ SV44 )
= zero_zero_a )
| ( SV44 = zero_zero_a ) ) )
= $true )
| ( ( ~ ( ( ( uminus_uminus_a @ SV44 )
!= zero_zero_a )
| ( SV44 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[898]) ).
thf(1023,plain,
! [SV45: poly_a] :
( ( ( ~ ( ( zero_zero_poly_a
= ( uminus_uminus_poly_a @ SV45 ) )
| ( zero_zero_poly_a = SV45 ) ) )
= $true )
| ( ( ~ ( ( zero_zero_poly_a
!= ( uminus_uminus_poly_a @ SV45 ) )
| ( zero_zero_poly_a != SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[900]) ).
thf(1024,plain,
! [SV46: a] :
( ( ( ~ ( ( zero_zero_a
= ( uminus_uminus_a @ SV46 ) )
| ( zero_zero_a = SV46 ) ) )
= $true )
| ( ( ~ ( ( zero_zero_a
!= ( uminus_uminus_a @ SV46 ) )
| ( zero_zero_a != SV46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[902]) ).
thf(1025,plain,
! [SV142: list_a,SV48: list_a] :
( ( ~ ( ( SV48
= ( append_a @ SV142 @ SV48 ) )
| ( SV142 = nil_a ) )
| ~ ( ( SV48
!= ( append_a @ SV142 @ SV48 ) )
| ( SV142 != nil_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[904]) ).
thf(1026,plain,
! [SV142: list_a,SV48: list_a] :
( ( ( SV48
= ( append_a @ SV142 @ SV48 ) )
= ( SV142 = nil_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[904]) ).
thf(1027,plain,
! [SV143: list_a,SV49: list_a] :
( ( ~ ( ( ( append_a @ SV49 @ SV143 )
= SV143 )
| ( SV49 = nil_a ) )
| ~ ( ( ( append_a @ SV49 @ SV143 )
!= SV143 )
| ( SV49 != nil_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[905]) ).
thf(1028,plain,
! [SV143: list_a,SV49: list_a] :
( ( ( ( append_a @ SV49 @ SV143 )
= SV143 )
= ( SV49 = nil_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[905]) ).
thf(1029,plain,
! [SV144: list_a,SV50: list_a] :
( ( ~ ( ( SV50
= ( append_a @ SV50 @ SV144 ) )
| ( SV144 = nil_a ) )
| ~ ( ( SV50
!= ( append_a @ SV50 @ SV144 ) )
| ( SV144 != nil_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[906]) ).
thf(1030,plain,
! [SV144: list_a,SV50: list_a] :
( ( ( SV50
= ( append_a @ SV50 @ SV144 ) )
= ( SV144 = nil_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[906]) ).
thf(1031,plain,
! [SV145: list_a,SV51: list_a] :
( ( ~ ( ( ( append_a @ SV51 @ SV145 )
= SV51 )
| ( SV145 = nil_a ) )
| ~ ( ( ( append_a @ SV51 @ SV145 )
!= SV51 )
| ( SV145 != nil_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[907]) ).
thf(1032,plain,
! [SV145: list_a,SV51: list_a] :
( ( ( ( append_a @ SV51 @ SV145 )
= SV51 )
= ( SV145 = nil_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[907]) ).
thf(1033,plain,
! [SV53: poly_a] :
( ( ( ~ ( ( zero_zero_poly_a = SV53 )
| ( SV53 = zero_zero_poly_a ) ) )
= $true )
| ( ( ~ ( ( zero_zero_poly_a != SV53 )
| ( SV53 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(1034,plain,
! [SV54: a] :
( ( ( ~ ( ( zero_zero_a = SV54 )
| ( SV54 = zero_zero_a ) ) )
= $true )
| ( ( ~ ( ( zero_zero_a != SV54 )
| ( SV54 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(1035,plain,
! [SV55: nat] :
( ( ( ~ ( ( zero_zero_nat = SV55 )
| ( SV55 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( zero_zero_nat != SV55 )
| ( SV55 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(1036,plain,
! [SV146: list_a,SV56: a] :
( ( ( cons_a @ SV56 @ SV146 )
= SV146 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(1037,plain,
! [SV57: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV57 )
| ( SV57 != zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV57 )
| ~ ( ( SV57 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(1038,plain,
! [SV147: nat,SV58: nat] :
( ( ( ~ ( ord_less_nat @ SV58 @ SV147 ) )
= $true )
| ( ( SV147 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(1039,plain,
! [SV61: a,SV175: a] :
( ( ( ! [SY535: a] :
( ( ( times_times_a @ SV175 @ SV61 )
= ( times_times_a @ SY535 @ SV61 ) )
= ( SV175 = SY535 ) ) )
= $true )
| ( ( SV61 = zero_zero_a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1040,plain,
! [SV62: poly_a,SV176: poly_a] :
( ( ( ! [SY536: poly_a] :
( ( ( times_times_poly_a @ SV176 @ SV62 )
= ( times_times_poly_a @ SY536 @ SV62 ) )
= ( SV176 = SY536 ) ) )
= $true )
| ( ( SV62 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1041,plain,
! [SV63: nat,SV177: nat] :
( ( ( ! [SY537: nat] :
( ( ( times_times_nat @ SV177 @ SV63 )
= ( times_times_nat @ SY537 @ SV63 ) )
= ( SV177 = SY537 ) ) )
= $true )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1042,plain,
! [SV178: a,SV64: a] :
( ( ( ! [SY538: a] :
( ( ( times_times_a @ SV64 @ SV178 )
= ( times_times_a @ SV64 @ SY538 ) )
= ( SV178 = SY538 ) ) )
= $true )
| ( ( SV64 = zero_zero_a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1043,plain,
! [SV179: poly_a,SV65: poly_a] :
( ( ( ! [SY539: poly_a] :
( ( ( times_times_poly_a @ SV65 @ SV179 )
= ( times_times_poly_a @ SV65 @ SY539 ) )
= ( SV179 = SY539 ) ) )
= $true )
| ( ( SV65 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1044,plain,
! [SV180: nat,SV66: nat] :
( ( ( ! [SY540: nat] :
( ( ( times_times_nat @ SV66 @ SV180 )
= ( times_times_nat @ SV66 @ SY540 ) )
= ( SV180 = SY540 ) ) )
= $true )
| ( ( SV66 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1045,plain,
! [SV67: a,SV181: a] :
( ( ( ( SV181 = zero_zero_a )
| ( ( times_times_a @ SV67 @ SV181 )
!= zero_zero_a ) )
= $true )
| ( ( SV67 = zero_zero_a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1046,plain,
! [SV68: poly_a,SV182: poly_a] :
( ( ( ( SV182 = zero_zero_poly_a )
| ( ( times_times_poly_a @ SV68 @ SV182 )
!= zero_zero_poly_a ) )
= $true )
| ( ( SV68 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1047,plain,
! [SV69: nat,SV183: nat] :
( ( ( ( SV183 = zero_zero_nat )
| ( ( times_times_nat @ SV69 @ SV183 )
!= zero_zero_nat ) )
= $true )
| ( ( SV69 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1048,plain,
! [SV148: a,SV70: a] :
( ( ( ( times_times_a @ SV70 @ SV148 )
!= zero_zero_a )
= $true )
| ( ( ( SV70 = zero_zero_a )
| ( SV148 = zero_zero_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(1049,plain,
! [SV149: poly_a,SV71: poly_a] :
( ( ( ( times_times_poly_a @ SV71 @ SV149 )
!= zero_zero_poly_a )
= $true )
| ( ( ( SV71 = zero_zero_poly_a )
| ( SV149 = zero_zero_poly_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(1050,plain,
! [SV150: nat,SV72: nat] :
( ( ( ( times_times_nat @ SV72 @ SV150 )
!= zero_zero_nat )
= $true )
| ( ( ( SV72 = zero_zero_nat )
| ( SV150 = zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(1051,plain,
! [SV74: list_a] :
( ( ( SV74
= ( cons_a @ ( sK35_X2 @ SV74 ) @ nil_a ) )
= $true )
| ( ( SV74
= ( cons_a @ ( sK32_X2 @ SV74 ) @ ( cons_a @ ( sK33_SY356 @ SV74 ) @ ( sK34_SY358 @ SV74 ) ) ) )
= $true )
| ( ( SV74 = nil_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(1052,plain,
! [SV184: a,SV77: list_a] :
( ( ( ! [SY541: list_a] :
( SV77
!= ( cons_a @ SV184 @ SY541 ) ) )
= $true )
| ( ( SV77 != nil_a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1053,plain,
! [SV151: list_a,SV78: a] :
( ( nil_a
= ( cons_a @ SV78 @ SV151 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(1054,plain,
! [SV185: list_a,SV152: list_a,SV79: a] :
( ( ( append_a @ ( cons_a @ SV79 @ SV152 ) @ SV185 )
= ( cons_a @ SV79 @ ( append_a @ SV152 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1055,plain,
! [SV186: list_a,SV153: list_a,SV80: a] :
( ( ( ( cons_a @ SV80 @ SV153 )
!= SV186 )
| ! [SY542: list_a,SY543: list_a] :
( ( SY542
!= ( append_a @ SV153 @ SY543 ) )
| ( ( cons_a @ SV80 @ SY542 )
= ( append_a @ SV186 @ SY543 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1056,plain,
! [SV154: list_a,SV83: list_a] :
( ( ( SV83 != SV154 )
= $true )
| ( ( SV83
= ( append_a @ nil_a @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(1057,plain,
! [SV155: list_a,SV84: a] :
( ( null_a @ ( cons_a @ SV84 @ SV155 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(1058,plain,
! [SV85: list_a] :
( ( ( ~ ( ( SV85 = nil_a )
| ( null_a @ SV85 ) ) )
= $true )
| ( ( ~ ( ( SV85 != nil_a )
| ~ ( null_a @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(1059,plain,
! [SV187: nat,SV156: nat,SV86: nat] :
( ( ( ( times_times_nat @ SV86 @ SV156 )
= ( times_times_nat @ SV187 @ SV156 ) )
= ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1060,plain,
! [SV87: nat] :
( ( ( ~ ( ( SV87 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV87 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV87 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[945]) ).
thf(1061,plain,
! [SV89: nat] :
( ( ( ~ ( ( SV89 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV89 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV89 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[948]) ).
thf(1062,plain,
! [SV157: nat,SV90: nat] :
( ( ~ ( ( ( times_times_nat @ SV90 @ SV157 )
= zero_zero_nat )
| ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) )
| ~ ( ( ( times_times_nat @ SV90 @ SV157 )
!= zero_zero_nat )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[950]) ).
thf(1063,plain,
! [SV157: nat,SV90: nat] :
( ( ( ( times_times_nat @ SV90 @ SV157 )
= zero_zero_nat )
= ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[950]) ).
thf(1064,plain,
! [SV188: nat,SV158: nat,SV92: nat] :
( ( ( ( times_times_nat @ SV92 @ SV158 )
= ( times_times_nat @ SV92 @ SV188 ) )
= ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1065,plain,
! [SV94: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV94 )
| ( SV94 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV94 )
| ( SV94 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[953]) ).
thf(1066,plain,
! [SV159: nat,SV97: nat] :
( ( ( ~ ( ord_less_nat @ SV97 @ SV159 ) )
= $true )
| ( ( SV159 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[957]) ).
thf(1067,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ( times_times_nat @ SV100 @ SV160 )
= ( times_times_nat @ SV100 @ SV189 ) )
= ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1068,plain,
! [SV101: list_a > $o] :
( ( ( SV101 @ nil_a )
= $false )
| ( ( ~ ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
| ~ ( ~ ( ( ( sK40_X2 @ SV101 )
!= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
| ~ ~ ( ~ ( ( ( sK40_X2 @ SV101 )
= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
| ~ ~ ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) ) ) )
| ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1069,plain,
( ( ! [SX0: a] :
( ! [SX1: a] :
( ( times_times_a @ SX0 @ SX1 )
= zero_zero_a )
| ( SX0 != zero_zero_a ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[961]) ).
thf(1070,plain,
( ( ! [SX0: a,SX1: a] :
( ( ( times_times_a @ SX0 @ SX1 )
= zero_zero_a )
| ( SX1 != zero_zero_a ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[962]) ).
thf(1071,plain,
! [SV102: list_a > $o] :
( ( ( ~ ( ! [SY473: a,SY474: list_a] :
( ( sK25_SY345 @ SV102 )
!= ( cons_a @ SY473 @ SY474 ) )
| ( SV102 @ ( sK25_SY345 @ SV102 ) ) )
| ~ ~ ( SV102 @ ( cons_a @ ( sK24_X2 @ SV102 ) @ ( sK25_SY345 @ SV102 ) ) ) )
= $false )
| ( ( ~ ( SV102 @ nil_a )
| ! [SY475: list_a] : ( SV102 @ SY475 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1072,plain,
! [SV161: list_a,SV103: list_a] :
( ( ~ ( ( ( append_a @ SV103 @ SV161 )
= nil_a )
| ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) )
| ~ ( ( ( append_a @ SV103 @ SV161 )
!= nil_a )
| ~ ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[964]) ).
thf(1073,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ( append_a @ SV103 @ SV161 )
= nil_a )
= ( ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[964]) ).
thf(1074,plain,
! [SV162: a > a,SV104: ( a > a ) > list_a > list_a > $o] :
( ( ( ~ ( SV104 @ ( sK58_F2 @ SV162 @ SV104 ) @ nil_a @ ( sK59_SY379 @ SV162 @ SV104 ) ) )
= $true )
| ( ( ~ ( ~ ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) @ ( cons_a @ ( sK54_F2 @ SV162 @ SV104 @ ( sK55_SY373 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) ) )
| ~ ~ ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( cons_a @ ( sK55_SY373 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) ) )
| ! [SY529: list_a,SY530: list_a] : ( SV104 @ SV162 @ SY529 @ SY530 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1075,plain,
! [SV190: list_a,SV163: a,SV105: list_a] :
( ( ! [SY544: a] :
( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SY544 @ nil_a ) ) )
= ( ~ ( ( SV105 != SV190 )
| ( SV163 != SY544 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1076,plain,
! [SV106: ( a > a > $o ) > list_a > $o] :
( ( ( SV106 @ ( sK39_P5 @ SV106 ) @ nil_a )
= $false )
| ( ( ~ ( ~ ( SV106 @ ( sK36_P5 @ SV106 ) @ ( sK38_SY361 @ SV106 ) )
| ~ ~ ( SV106 @ ( sK36_P5 @ SV106 ) @ ( cons_a @ ( sK37_SY359 @ SV106 ) @ ( sK38_SY361 @ SV106 ) ) ) )
| ! [SY483: a > a > $o,SY484: list_a] : ( SV106 @ SY483 @ SY484 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(1077,plain,
! [SV107: nat > $o] :
( ( ( SV107 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK1_N2 @ SV107 ) )
| ~ ~ ( ~ ~ ( SV107 @ ( sK1_N2 @ SV107 ) )
| ~ ! [SY485: nat] :
( ~ ( ord_less_nat @ SY485 @ ( sK1_N2 @ SV107 ) )
| ( SV107 @ SY485 ) ) ) )
| ! [SY486: nat] : ( SV107 @ SY486 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(1078,plain,
! [SV108: list_a > $o] :
( ( ( SV108 @ nil_a )
= $false )
| ( ( ~ ( ~ ( SV108 @ ( sK5_SY329 @ SV108 ) )
| ~ ~ ( SV108 @ ( cons_a @ ( sK4_X1 @ SV108 ) @ ( sK5_SY329 @ SV108 ) ) ) )
| ! [SY487: list_a] : ( SV108 @ SY487 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[969]) ).
thf(1079,plain,
! [SV109: list_a > $o] :
( ( ( SV109 @ nil_a )
= $false )
| ( ( ~ ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
| ~ ( ~ ( SV109 @ ( sK20_SY343 @ SV109 ) )
| ~ ~ ( ~ ( SV109 @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) )
| ~ ~ ( SV109 @ ( cons_a @ ( sK18_X2 @ SV109 ) @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) ) ) ) )
| ! [SY488: list_a] : ( SV109 @ SY488 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(1080,plain,
! [SV191: a,SV164: list_a,SV110: a] :
( ( ! [SY545: list_a] :
( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SY545 ) )
= ( ~ ( ( SV110 != SV191 )
| ( SV164 != SY545 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1081,plain,
! [SV111: list_a > list_a > $o] :
( ( ( SV111 @ nil_a @ ( sK17_X_1 @ SV111 ) )
= $false )
| ( ( ~ ( ~ ( SV111 @ ( sK16_SY340 @ SV111 ) @ ( sK15_SY338 @ SV111 ) )
| ~ ~ ( SV111 @ ( cons_a @ ( sK14_X2 @ SV111 ) @ ( sK15_SY338 @ SV111 ) ) @ ( sK16_SY340 @ SV111 ) ) )
| ! [SY492: list_a,SY493: list_a] : ( SV111 @ SY492 @ SY493 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1082,plain,
! [SV165: poly_a,SV112: a] :
( ( ~ ( ( ( pCons_a @ SV112 @ SV165 )
= zero_zero_poly_a )
| ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) )
| ~ ( ( ( pCons_a @ SV112 @ SV165 )
!= zero_zero_poly_a )
| ~ ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[973]) ).
thf(1083,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ( pCons_a @ SV112 @ SV165 )
= zero_zero_poly_a )
= ( ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[973]) ).
thf(1084,plain,
( ( ! [SX0: nat] :
( ! [SX1: nat] :
( ( times_times_nat @ SX0 @ SX1 )
= zero_zero_nat )
| ( SX0 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[974]) ).
thf(1085,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ( times_times_nat @ SX0 @ SX1 )
= zero_zero_nat )
| ( SX1 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[975]) ).
thf(1086,plain,
! [SV113: poly_a > poly_a > $o] :
( ( ( SV113 @ zero_zero_poly_a @ zero_zero_poly_a )
= $false )
| ( ( ~ ( ~ ( SV113 @ ( sK85_SY400 @ SV113 ) @ ( sK87_SY405 @ SV113 ) )
| ~ ~ ( SV113 @ ( pCons_a @ ( sK84_A2 @ SV113 ) @ ( sK85_SY400 @ SV113 ) ) @ ( pCons_a @ ( sK86_SY403 @ SV113 ) @ ( sK87_SY405 @ SV113 ) ) ) )
| ! [SY495: poly_a,SY496: poly_a] : ( SV113 @ SY495 @ SY496 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1087,plain,
! [SV114: list_a > list_a > $o] :
( ( ( ~ ( SV114 @ ( sK72_SY386 @ SV114 ) @ ( sK74_SY391 @ SV114 ) )
| ~ ~ ( SV114 @ ( cons_a @ ( sK71_X2 @ SV114 ) @ ( sK72_SY386 @ SV114 ) ) @ ( cons_a @ ( sK73_SY389 @ SV114 ) @ ( sK74_SY391 @ SV114 ) ) ) )
= $false )
| ( ( ~ ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a )
| ~ ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) )
| ! [SY497: list_a,SY498: list_a] : ( SV114 @ SY497 @ SY498 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1088,plain,
! [SV115: list_a,SV192: list_a > $o] :
( ( ( ~ ( SV192 @ ( cons_a @ ( sK53_X2 @ SV192 @ SV115 ) @ nil_a ) )
| ~ ( ~ ( ( ( sK52_SY372 @ SV192 @ SV115 )
!= nil_a ) )
| ~ ~ ( ~ ( SV192 @ ( sK52_SY372 @ SV192 @ SV115 ) )
| ~ ~ ( SV192 @ ( cons_a @ ( sK51_X2 @ SV192 @ SV115 ) @ ( sK52_SY372 @ SV192 @ SV115 ) ) ) ) )
| ( SV192 @ SV115 ) )
= $true )
| ( ( SV115 = nil_a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1089,plain,
! [SV116: poly_a > $o] :
( ( ( ~ ( ( ( sK83_SY399 @ SV116 )
= zero_zero_poly_a )
| ( SV116 @ ( sK83_SY399 @ SV116 ) ) )
| ~ ~ ( SV116 @ ( pCons_a @ ( sK82_A2 @ SV116 ) @ ( sK83_SY399 @ SV116 ) ) ) )
= $false )
| ( ( ! [SY500: poly_a] : ( SV116 @ SY500 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[979]) ).
thf(1090,plain,
! [SV117: ( a > a > $o ) > list_a > $o] :
( ( ( SV117 @ ( sK50_P5 @ SV117 ) @ nil_a )
= $false )
| ( ( ~ ( SV117 @ ( sK48_P5 @ SV117 ) @ ( cons_a @ ( sK49_SY371 @ SV117 ) @ nil_a ) )
| ~ ( ~ ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) )
| ~ ~ ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK45_SY365 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) ) ) )
| ! [SY501: a > a > $o,SY502: list_a] : ( SV117 @ SY501 @ SY502 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1091,plain,
! [SV118: list_a > list_a > $o] :
( ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false )
| ( ( ~ ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
| ~ ( ~ ( SV118 @ ( sK27_SY350 @ SV118 ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) )
| ~ ~ ( ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( sK29_SY355 @ SV118 ) )
| ~ ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) ) ) )
| ! [SY503: list_a,SY504: list_a] : ( SV118 @ SY503 @ SY504 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1092,plain,
( ( ! [SX0: poly_a] :
( ! [SX1: poly_a] :
( ( times_times_poly_a @ SX0 @ SX1 )
= zero_zero_poly_a )
| ( SX0 != zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[982]) ).
thf(1093,plain,
( ( ! [SX0: poly_a,SX1: poly_a] :
( ( ( times_times_poly_a @ SX0 @ SX1 )
= zero_zero_poly_a )
| ( SX1 != zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[983]) ).
thf(1094,plain,
! [SV119: list_a > list_a > $o] :
( ( ( SV119 @ nil_a @ nil_a )
= $false )
| ( ( ~ ( SV119 @ ( cons_a @ ( sK12_X2 @ SV119 ) @ ( sK13_SY337 @ SV119 ) ) @ nil_a )
| ~ ( SV119 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SV119 ) @ ( sK11_SY336 @ SV119 ) ) )
| ~ ( ~ ( SV119 @ ( sK7_SY330 @ SV119 ) @ ( sK9_SY335 @ SV119 ) )
| ~ ~ ( SV119 @ ( cons_a @ ( sK6_X2 @ SV119 ) @ ( sK7_SY330 @ SV119 ) ) @ ( cons_a @ ( sK8_SY333 @ SV119 ) @ ( sK9_SY335 @ SV119 ) ) ) )
| ! [SY505: list_a,SY506: list_a] : ( SV119 @ SY505 @ SY506 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(1095,plain,
! [SV120: poly_a > $o] :
( ( ( SV120 @ zero_zero_poly_a )
= $false )
| ( ( ~ ( ~ ( ( ( sK88_A2 @ SV120 )
!= zero_zero_a )
| ( ( sK89_SY406 @ SV120 )
!= zero_zero_poly_a ) )
| ~ ~ ( ~ ( SV120 @ ( sK89_SY406 @ SV120 ) )
| ~ ~ ( SV120 @ ( pCons_a @ ( sK88_A2 @ SV120 ) @ ( sK89_SY406 @ SV120 ) ) ) ) )
| ! [SY507: poly_a] : ( SV120 @ SY507 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1096,plain,
! [SV121: list_a] :
( ( ( ~ ( ( SV121 != nil_a )
| ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV121 != nil_a ) )
| ~ ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[986]) ).
thf(1097,plain,
! [SV166: list_a,SV122: list_a] :
( ( ~ ( ( nil_a
= ( append_a @ SV122 @ SV166 ) )
| ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) )
| ~ ( ( nil_a
!= ( append_a @ SV122 @ SV166 ) )
| ~ ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[988]) ).
thf(1098,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( nil_a
= ( append_a @ SV122 @ SV166 ) )
= ( ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[988]) ).
thf(1099,plain,
! [SV123: list_a > list_a > $o] :
( ( ( SV123 @ ( sK81_Xs2 @ SV123 ) @ nil_a )
= $false )
| ( ( ~ ( SV123 @ nil_a @ ( cons_a @ ( sK79_V @ SV123 ) @ ( sK80_SY398 @ SV123 ) ) )
| ~ ( ~ ( SV123 @ ( sK76_SY392 @ SV123 ) @ ( sK78_SY397 @ SV123 ) )
| ~ ~ ( SV123 @ ( cons_a @ ( sK75_X2 @ SV123 ) @ ( sK76_SY392 @ SV123 ) ) @ ( cons_a @ ( sK77_SY395 @ SV123 ) @ ( sK78_SY397 @ SV123 ) ) ) )
| ! [SY511: list_a,SY512: list_a] : ( SV123 @ SY511 @ SY512 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1100,plain,
! [SV124: list_a > $o] :
( ( ( SV124 @ nil_a )
= $false )
| ( ( ~ ( ~ ( SV124 @ ( sK63_SY381 @ SV124 ) )
| ~ ~ ( SV124 @ ( cons_a @ ( sK62_X2 @ SV124 ) @ ( sK63_SY381 @ SV124 ) ) ) )
| ! [SY513: list_a] : ( SV124 @ SY513 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1101,plain,
! [SV193: poly_a,SV126: poly_a] :
( ( ( SV126 = SV193 )
= ( ( coeffs_a @ SV126 )
= ( coeffs_a @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1102,plain,
! [SV127: poly_a,SV3: list_a] :
( ( ( ( poly_a2 @ SV3 )
= SV127 )
= $false )
| ( ( ( descar2095969287nges_a @ SV3 )
= ( descar2095969287nges_a @ ( coeffs_a @ SV127 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1103,plain,
! [SV128: poly_a] :
( ( ( ~ ( ( is_zero_a @ SV128 )
| ( null_a @ ( coeffs_a @ SV128 ) ) ) )
= $true )
| ( ( ~ ( ~ ( is_zero_a @ SV128 )
| ~ ( null_a @ ( coeffs_a @ SV128 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1104,plain,
! [SV8: poly_a] :
( ( ( ( ( coeffs_a @ SV8 )
= nil_a )
| ( SV8 = zero_zero_poly_a ) )
= $false )
| ( ( ~ ( ( ( coeffs_a @ SV8 )
!= nil_a )
| ( SV8 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1105,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ~ ( ( ( smult_a @ SV12 @ SV130 )
= zero_zero_poly_a )
| ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) ) )
= $true )
| ( ( ~ ( ( ( smult_a @ SV12 @ SV130 )
!= zero_zero_poly_a )
| ~ ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1106,plain,
! [SV132: poly_a] :
( ( ( ~ ( ( is_zero_a @ SV132 )
| ( SV132 = zero_zero_poly_a ) ) )
= $true )
| ( ( ~ ( ~ ( is_zero_a @ SV132 )
| ( SV132 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1107,plain,
! [SV22: a,SV168: poly_a] :
( ( ( SV168 = zero_zero_poly_a )
= $true )
| ( ( ( descar466059845root_a @ SV22 @ SV168 )
!= zero_zero_poly_a )
= $true )
| ( ( SV22 = zero_zero_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1108,plain,
! [SV23: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV23 )
| ( SV23 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV23 )
| ( SV23 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1109,plain,
! [SV169: a,SV133: a,SV24: a] :
( ( ~ ( ( ( times_times_a @ SV24 @ SV133 )
= ( times_times_a @ SV169 @ SV133 ) )
| ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) )
| ~ ( ( ( times_times_a @ SV24 @ SV133 )
!= ( times_times_a @ SV169 @ SV133 ) )
| ~ ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1005]) ).
thf(1110,plain,
! [SV169: a,SV133: a,SV24: a] :
( ( ( ( times_times_a @ SV24 @ SV133 )
= ( times_times_a @ SV169 @ SV133 ) )
= ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1005]) ).
thf(1111,plain,
! [SV170: poly_a,SV134: poly_a,SV25: poly_a] :
( ( ~ ( ( ( times_times_poly_a @ SV25 @ SV134 )
= ( times_times_poly_a @ SV170 @ SV134 ) )
| ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) )
| ~ ( ( ( times_times_poly_a @ SV25 @ SV134 )
!= ( times_times_poly_a @ SV170 @ SV134 ) )
| ~ ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1006]) ).
thf(1112,plain,
! [SV170: poly_a,SV134: poly_a,SV25: poly_a] :
( ( ( ( times_times_poly_a @ SV25 @ SV134 )
= ( times_times_poly_a @ SV170 @ SV134 ) )
= ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1006]) ).
thf(1113,plain,
! [SV171: nat,SV135: nat,SV26: nat] :
( ( ~ ( ( ( times_times_nat @ SV26 @ SV135 )
= ( times_times_nat @ SV171 @ SV135 ) )
| ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) )
| ~ ( ( ( times_times_nat @ SV26 @ SV135 )
!= ( times_times_nat @ SV171 @ SV135 ) )
| ~ ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1007]) ).
thf(1114,plain,
! [SV171: nat,SV135: nat,SV26: nat] :
( ( ( ( times_times_nat @ SV26 @ SV135 )
= ( times_times_nat @ SV171 @ SV135 ) )
= ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1007]) ).
thf(1115,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ~ ( ( ( times_times_a @ SV27 @ SV136 )
= ( times_times_a @ SV27 @ SV172 ) )
| ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) )
| ~ ( ( ( times_times_a @ SV27 @ SV136 )
!= ( times_times_a @ SV27 @ SV172 ) )
| ~ ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1008]) ).
thf(1116,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ( times_times_a @ SV27 @ SV136 )
= ( times_times_a @ SV27 @ SV172 ) )
= ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1008]) ).
thf(1117,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ~ ( ( ( times_times_poly_a @ SV28 @ SV137 )
= ( times_times_poly_a @ SV28 @ SV173 ) )
| ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) )
| ~ ( ( ( times_times_poly_a @ SV28 @ SV137 )
!= ( times_times_poly_a @ SV28 @ SV173 ) )
| ~ ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1009]) ).
thf(1118,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ( times_times_poly_a @ SV28 @ SV137 )
= ( times_times_poly_a @ SV28 @ SV173 ) )
= ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1009]) ).
thf(1119,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ~ ( ( ( times_times_nat @ SV29 @ SV138 )
= ( times_times_nat @ SV29 @ SV174 ) )
| ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) )
| ~ ( ( ( times_times_nat @ SV29 @ SV138 )
!= ( times_times_nat @ SV29 @ SV174 ) )
| ~ ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1010]) ).
thf(1120,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ( times_times_nat @ SV29 @ SV138 )
= ( times_times_nat @ SV29 @ SV174 ) )
= ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1010]) ).
thf(1121,plain,
! [SV139: a,SV30: a] :
( ( ( ~ ( ( ( times_times_a @ SV30 @ SV139 )
= zero_zero_a )
| ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) ) )
= $true )
| ( ( ~ ( ( ( times_times_a @ SV30 @ SV139 )
!= zero_zero_a )
| ~ ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1122,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ~ ( ( ( times_times_poly_a @ SV31 @ SV140 )
= zero_zero_poly_a )
| ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) ) )
= $true )
| ( ( ~ ( ( ( times_times_poly_a @ SV31 @ SV140 )
!= zero_zero_poly_a )
| ~ ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1123,plain,
! [SV141: nat,SV32: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV32 @ SV141 )
= zero_zero_nat )
| ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV32 @ SV141 )
!= zero_zero_nat )
| ~ ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1124,plain,
! [SV39: poly_a] :
( ( ( ( ( uminus_uminus_poly_a @ SV39 )
= SV39 )
| ( SV39 = zero_zero_poly_a ) )
= $false )
| ( ( ~ ( ( ( uminus_uminus_poly_a @ SV39 )
!= SV39 )
| ( SV39 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1125,plain,
! [SV40: a] :
( ( ( ( ( uminus_uminus_a @ SV40 )
= SV40 )
| ( SV40 = zero_zero_a ) )
= $false )
| ( ( ~ ( ( ( uminus_uminus_a @ SV40 )
!= SV40 )
| ( SV40 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1126,plain,
! [SV41: poly_a] :
( ( ( ( SV41
= ( uminus_uminus_poly_a @ SV41 ) )
| ( SV41 = zero_zero_poly_a ) )
= $false )
| ( ( ~ ( ( SV41
!= ( uminus_uminus_poly_a @ SV41 ) )
| ( SV41 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1127,plain,
! [SV42: a] :
( ( ( ( SV42
= ( uminus_uminus_a @ SV42 ) )
| ( SV42 = zero_zero_a ) )
= $false )
| ( ( ~ ( ( SV42
!= ( uminus_uminus_a @ SV42 ) )
| ( SV42 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1128,plain,
! [SV43: poly_a] :
( ( ( ( ( uminus_uminus_poly_a @ SV43 )
= zero_zero_poly_a )
| ( SV43 = zero_zero_poly_a ) )
= $false )
| ( ( ~ ( ( ( uminus_uminus_poly_a @ SV43 )
!= zero_zero_poly_a )
| ( SV43 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1129,plain,
! [SV44: a] :
( ( ( ( ( uminus_uminus_a @ SV44 )
= zero_zero_a )
| ( SV44 = zero_zero_a ) )
= $false )
| ( ( ~ ( ( ( uminus_uminus_a @ SV44 )
!= zero_zero_a )
| ( SV44 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1130,plain,
! [SV45: poly_a] :
( ( ( ( zero_zero_poly_a
= ( uminus_uminus_poly_a @ SV45 ) )
| ( zero_zero_poly_a = SV45 ) )
= $false )
| ( ( ~ ( ( zero_zero_poly_a
!= ( uminus_uminus_poly_a @ SV45 ) )
| ( zero_zero_poly_a != SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1131,plain,
! [SV46: a] :
( ( ( ( zero_zero_a
= ( uminus_uminus_a @ SV46 ) )
| ( zero_zero_a = SV46 ) )
= $false )
| ( ( ~ ( ( zero_zero_a
!= ( uminus_uminus_a @ SV46 ) )
| ( zero_zero_a != SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1132,plain,
! [SV142: list_a,SV48: list_a] :
( ( ( ~ ( ( SV48
= ( append_a @ SV142 @ SV48 ) )
| ( SV142 = nil_a ) ) )
= $true )
| ( ( ~ ( ( SV48
!= ( append_a @ SV142 @ SV48 ) )
| ( SV142 != nil_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1133,plain,
! [SV143: list_a,SV49: list_a] :
( ( ( ~ ( ( ( append_a @ SV49 @ SV143 )
= SV143 )
| ( SV49 = nil_a ) ) )
= $true )
| ( ( ~ ( ( ( append_a @ SV49 @ SV143 )
!= SV143 )
| ( SV49 != nil_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1134,plain,
! [SV144: list_a,SV50: list_a] :
( ( ( ~ ( ( SV50
= ( append_a @ SV50 @ SV144 ) )
| ( SV144 = nil_a ) ) )
= $true )
| ( ( ~ ( ( SV50
!= ( append_a @ SV50 @ SV144 ) )
| ( SV144 != nil_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1029]) ).
thf(1135,plain,
! [SV145: list_a,SV51: list_a] :
( ( ( ~ ( ( ( append_a @ SV51 @ SV145 )
= SV51 )
| ( SV145 = nil_a ) ) )
= $true )
| ( ( ~ ( ( ( append_a @ SV51 @ SV145 )
!= SV51 )
| ( SV145 != nil_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1136,plain,
! [SV53: poly_a] :
( ( ( ( zero_zero_poly_a = SV53 )
| ( SV53 = zero_zero_poly_a ) )
= $false )
| ( ( ~ ( ( zero_zero_poly_a != SV53 )
| ( SV53 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1033]) ).
thf(1137,plain,
! [SV54: a] :
( ( ( ( zero_zero_a = SV54 )
| ( SV54 = zero_zero_a ) )
= $false )
| ( ( ~ ( ( zero_zero_a != SV54 )
| ( SV54 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1138,plain,
! [SV55: nat] :
( ( ( ( zero_zero_nat = SV55 )
| ( SV55 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV55 )
| ( SV55 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1139,plain,
! [SV57: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV57 )
| ( SV57 != zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV57 )
| ~ ( ( SV57 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1140,plain,
! [SV147: nat,SV58: nat] :
( ( ( ord_less_nat @ SV58 @ SV147 )
= $false )
| ( ( SV147 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1141,plain,
! [SV194: a,SV61: a,SV175: a] :
( ( ( ( ( times_times_a @ SV175 @ SV61 )
= ( times_times_a @ SV194 @ SV61 ) )
= ( SV175 = SV194 ) )
= $true )
| ( ( SV61 = zero_zero_a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1142,plain,
! [SV195: poly_a,SV62: poly_a,SV176: poly_a] :
( ( ( ( ( times_times_poly_a @ SV176 @ SV62 )
= ( times_times_poly_a @ SV195 @ SV62 ) )
= ( SV176 = SV195 ) )
= $true )
| ( ( SV62 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1143,plain,
! [SV196: nat,SV63: nat,SV177: nat] :
( ( ( ( ( times_times_nat @ SV177 @ SV63 )
= ( times_times_nat @ SV196 @ SV63 ) )
= ( SV177 = SV196 ) )
= $true )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1144,plain,
! [SV197: a,SV178: a,SV64: a] :
( ( ( ( ( times_times_a @ SV64 @ SV178 )
= ( times_times_a @ SV64 @ SV197 ) )
= ( SV178 = SV197 ) )
= $true )
| ( ( SV64 = zero_zero_a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1145,plain,
! [SV198: poly_a,SV179: poly_a,SV65: poly_a] :
( ( ( ( ( times_times_poly_a @ SV65 @ SV179 )
= ( times_times_poly_a @ SV65 @ SV198 ) )
= ( SV179 = SV198 ) )
= $true )
| ( ( SV65 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1146,plain,
! [SV199: nat,SV180: nat,SV66: nat] :
( ( ( ( ( times_times_nat @ SV66 @ SV180 )
= ( times_times_nat @ SV66 @ SV199 ) )
= ( SV180 = SV199 ) )
= $true )
| ( ( SV66 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1147,plain,
! [SV67: a,SV181: a] :
( ( ( SV181 = zero_zero_a )
= $true )
| ( ( ( times_times_a @ SV67 @ SV181 )
!= zero_zero_a )
= $true )
| ( ( SV67 = zero_zero_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1148,plain,
! [SV68: poly_a,SV182: poly_a] :
( ( ( SV182 = zero_zero_poly_a )
= $true )
| ( ( ( times_times_poly_a @ SV68 @ SV182 )
!= zero_zero_poly_a )
= $true )
| ( ( SV68 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1046]) ).
thf(1149,plain,
! [SV69: nat,SV183: nat] :
( ( ( SV183 = zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV69 @ SV183 )
!= zero_zero_nat )
= $true )
| ( ( SV69 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1047]) ).
thf(1150,plain,
! [SV148: a,SV70: a] :
( ( ( ( times_times_a @ SV70 @ SV148 )
= zero_zero_a )
= $false )
| ( ( ( SV70 = zero_zero_a )
| ( SV148 = zero_zero_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1151,plain,
! [SV149: poly_a,SV71: poly_a] :
( ( ( ( times_times_poly_a @ SV71 @ SV149 )
= zero_zero_poly_a )
= $false )
| ( ( ( SV71 = zero_zero_poly_a )
| ( SV149 = zero_zero_poly_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1152,plain,
! [SV150: nat,SV72: nat] :
( ( ( ( times_times_nat @ SV72 @ SV150 )
= zero_zero_nat )
= $false )
| ( ( ( SV72 = zero_zero_nat )
| ( SV150 = zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1153,plain,
! [SV200: list_a,SV184: a,SV77: list_a] :
( ( ( SV77
!= ( cons_a @ SV184 @ SV200 ) )
= $true )
| ( ( SV77 != nil_a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1154,plain,
! [SV186: list_a,SV153: list_a,SV80: a] :
( ( ( ( cons_a @ SV80 @ SV153 )
!= SV186 )
= $true )
| ( ( ! [SY542: list_a,SY543: list_a] :
( ( SY542
!= ( append_a @ SV153 @ SY543 ) )
| ( ( cons_a @ SV80 @ SY542 )
= ( append_a @ SV186 @ SY543 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1155,plain,
! [SV154: list_a,SV83: list_a] :
( ( ( SV83 = SV154 )
= $false )
| ( ( SV83
= ( append_a @ nil_a @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1056]) ).
thf(1156,plain,
! [SV85: list_a] :
( ( ( ( SV85 = nil_a )
| ( null_a @ SV85 ) )
= $false )
| ( ( ~ ( ( SV85 != nil_a )
| ~ ( null_a @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1157,plain,
! [SV187: nat,SV156: nat,SV86: nat] :
( ( ~ ( ( ( times_times_nat @ SV86 @ SV156 )
= ( times_times_nat @ SV187 @ SV156 ) )
| ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) )
| ~ ( ( ( times_times_nat @ SV86 @ SV156 )
!= ( times_times_nat @ SV187 @ SV156 ) )
| ~ ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1059]) ).
thf(1158,plain,
! [SV187: nat,SV156: nat,SV86: nat] :
( ( ( ( times_times_nat @ SV86 @ SV156 )
= ( times_times_nat @ SV187 @ SV156 ) )
= ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1059]) ).
thf(1159,plain,
! [SV87: nat] :
( ( ( ( SV87 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV87 ) )
= $false )
| ( ( ~ ( ~ ( ( SV87 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1160,plain,
! [SV89: nat] :
( ( ( ( SV89 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV89 ) )
= $false )
| ( ( ~ ( ~ ( ( SV89 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1161,plain,
! [SV157: nat,SV90: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV90 @ SV157 )
= zero_zero_nat )
| ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV90 @ SV157 )
!= zero_zero_nat )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1162,plain,
! [SV188: nat,SV158: nat,SV92: nat] :
( ( ~ ( ( ( times_times_nat @ SV92 @ SV158 )
= ( times_times_nat @ SV92 @ SV188 ) )
| ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) )
| ~ ( ( ( times_times_nat @ SV92 @ SV158 )
!= ( times_times_nat @ SV92 @ SV188 ) )
| ~ ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1064]) ).
thf(1163,plain,
! [SV188: nat,SV158: nat,SV92: nat] :
( ( ( ( times_times_nat @ SV92 @ SV158 )
= ( times_times_nat @ SV92 @ SV188 ) )
= ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1064]) ).
thf(1164,plain,
! [SV94: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV94 )
| ( SV94 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV94 )
| ( SV94 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1165,plain,
! [SV159: nat,SV97: nat] :
( ( ( ord_less_nat @ SV97 @ SV159 )
= $false )
| ( ( SV159 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1166,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ~ ( ( ( times_times_nat @ SV100 @ SV160 )
= ( times_times_nat @ SV100 @ SV189 ) )
| ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) )
| ~ ( ( ( times_times_nat @ SV100 @ SV160 )
!= ( times_times_nat @ SV100 @ SV189 ) )
| ~ ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1067]) ).
thf(1167,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ( times_times_nat @ SV100 @ SV160 )
= ( times_times_nat @ SV100 @ SV189 ) )
= ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1067]) ).
thf(1168,plain,
! [SV101: list_a > $o] :
( ( ( ~ ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK40_X2 @ SV101 )
!= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
| ~ ~ ( ~ ( ( ( sK40_X2 @ SV101 )
= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
| ~ ~ ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) ) ) )
| ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1169,plain,
! [SV201: a] :
( ( ! [SY546: a] :
( ( times_times_a @ SV201 @ SY546 )
= zero_zero_a )
| ( SV201 != zero_zero_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1170,plain,
! [SV202: a] :
( ( ! [SY547: a] :
( ( ( times_times_a @ SV202 @ SY547 )
= zero_zero_a )
| ( SY547 != zero_zero_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1171,plain,
! [SV102: list_a > $o] :
( ( ( ~ ( ! [SY473: a,SY474: list_a] :
( ( sK25_SY345 @ SV102 )
!= ( cons_a @ SY473 @ SY474 ) )
| ( SV102 @ ( sK25_SY345 @ SV102 ) ) ) )
= $false )
| ( ( ~ ( SV102 @ nil_a )
| ! [SY475: list_a] : ( SV102 @ SY475 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1071]) ).
thf(1172,plain,
! [SV102: list_a > $o] :
( ( ( ~ ~ ( SV102 @ ( cons_a @ ( sK24_X2 @ SV102 ) @ ( sK25_SY345 @ SV102 ) ) ) )
= $false )
| ( ( ~ ( SV102 @ nil_a )
| ! [SY475: list_a] : ( SV102 @ SY475 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1071]) ).
thf(1173,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ~ ( ( ( append_a @ SV103 @ SV161 )
= nil_a )
| ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) ) )
= $true )
| ( ( ~ ( ( ( append_a @ SV103 @ SV161 )
!= nil_a )
| ~ ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1072]) ).
thf(1174,plain,
! [SV162: a > a,SV104: ( a > a ) > list_a > list_a > $o] :
( ( ( SV104 @ ( sK58_F2 @ SV162 @ SV104 ) @ nil_a @ ( sK59_SY379 @ SV162 @ SV104 ) )
= $false )
| ( ( ~ ( ~ ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) @ ( cons_a @ ( sK54_F2 @ SV162 @ SV104 @ ( sK55_SY373 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) ) )
| ~ ~ ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( cons_a @ ( sK55_SY373 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) ) )
| ! [SY529: list_a,SY530: list_a] : ( SV104 @ SV162 @ SY529 @ SY530 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1175,plain,
! [SV203: a,SV190: list_a,SV163: a,SV105: list_a] :
( ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
= ( ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1176,plain,
! [SV106: ( a > a > $o ) > list_a > $o] :
( ( ( ~ ( ~ ( SV106 @ ( sK36_P5 @ SV106 ) @ ( sK38_SY361 @ SV106 ) )
| ~ ~ ( SV106 @ ( sK36_P5 @ SV106 ) @ ( cons_a @ ( sK37_SY359 @ SV106 ) @ ( sK38_SY361 @ SV106 ) ) ) ) )
= $true )
| ( ( ! [SY483: a > a > $o,SY484: list_a] : ( SV106 @ SY483 @ SY484 ) )
= $true )
| ( ( SV106 @ ( sK39_P5 @ SV106 ) @ nil_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1177,plain,
! [SV107: nat > $o] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK1_N2 @ SV107 ) )
| ~ ~ ( ~ ~ ( SV107 @ ( sK1_N2 @ SV107 ) )
| ~ ! [SY485: nat] :
( ~ ( ord_less_nat @ SY485 @ ( sK1_N2 @ SV107 ) )
| ( SV107 @ SY485 ) ) ) ) )
= $true )
| ( ( ! [SY486: nat] : ( SV107 @ SY486 ) )
= $true )
| ( ( SV107 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1178,plain,
! [SV108: list_a > $o] :
( ( ( ~ ( ~ ( SV108 @ ( sK5_SY329 @ SV108 ) )
| ~ ~ ( SV108 @ ( cons_a @ ( sK4_X1 @ SV108 ) @ ( sK5_SY329 @ SV108 ) ) ) ) )
= $true )
| ( ( ! [SY487: list_a] : ( SV108 @ SY487 ) )
= $true )
| ( ( SV108 @ nil_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1179,plain,
! [SV109: list_a > $o] :
( ( ( ~ ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) ) )
= $true )
| ( ( ~ ( ~ ( SV109 @ ( sK20_SY343 @ SV109 ) )
| ~ ~ ( ~ ( SV109 @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) )
| ~ ~ ( SV109 @ ( cons_a @ ( sK18_X2 @ SV109 ) @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) ) ) ) )
| ! [SY488: list_a] : ( SV109 @ SY488 ) )
= $true )
| ( ( SV109 @ nil_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1180,plain,
! [SV204: list_a,SV191: a,SV164: list_a,SV110: a] :
( ( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SV204 ) )
= ( ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1181,plain,
! [SV111: list_a > list_a > $o] :
( ( ( ~ ( ~ ( SV111 @ ( sK16_SY340 @ SV111 ) @ ( sK15_SY338 @ SV111 ) )
| ~ ~ ( SV111 @ ( cons_a @ ( sK14_X2 @ SV111 ) @ ( sK15_SY338 @ SV111 ) ) @ ( sK16_SY340 @ SV111 ) ) ) )
= $true )
| ( ( ! [SY492: list_a,SY493: list_a] : ( SV111 @ SY492 @ SY493 ) )
= $true )
| ( ( SV111 @ nil_a @ ( sK17_X_1 @ SV111 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1081]) ).
thf(1182,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ~ ( ( ( pCons_a @ SV112 @ SV165 )
= zero_zero_poly_a )
| ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) ) )
= $true )
| ( ( ~ ( ( ( pCons_a @ SV112 @ SV165 )
!= zero_zero_poly_a )
| ~ ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1183,plain,
! [SV205: nat] :
( ( ! [SY548: nat] :
( ( times_times_nat @ SV205 @ SY548 )
= zero_zero_nat )
| ( SV205 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1184,plain,
! [SV206: nat] :
( ( ! [SY549: nat] :
( ( ( times_times_nat @ SV206 @ SY549 )
= zero_zero_nat )
| ( SY549 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1185,plain,
! [SV113: poly_a > poly_a > $o] :
( ( ( ~ ( ~ ( SV113 @ ( sK85_SY400 @ SV113 ) @ ( sK87_SY405 @ SV113 ) )
| ~ ~ ( SV113 @ ( pCons_a @ ( sK84_A2 @ SV113 ) @ ( sK85_SY400 @ SV113 ) ) @ ( pCons_a @ ( sK86_SY403 @ SV113 ) @ ( sK87_SY405 @ SV113 ) ) ) ) )
= $true )
| ( ( ! [SY495: poly_a,SY496: poly_a] : ( SV113 @ SY495 @ SY496 ) )
= $true )
| ( ( SV113 @ zero_zero_poly_a @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1086]) ).
thf(1186,plain,
! [SV114: list_a > list_a > $o] :
( ( ( ~ ( SV114 @ ( sK72_SY386 @ SV114 ) @ ( sK74_SY391 @ SV114 ) ) )
= $false )
| ( ( ~ ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a )
| ~ ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) )
| ! [SY497: list_a,SY498: list_a] : ( SV114 @ SY497 @ SY498 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1087]) ).
thf(1187,plain,
! [SV114: list_a > list_a > $o] :
( ( ( ~ ~ ( SV114 @ ( cons_a @ ( sK71_X2 @ SV114 ) @ ( sK72_SY386 @ SV114 ) ) @ ( cons_a @ ( sK73_SY389 @ SV114 ) @ ( sK74_SY391 @ SV114 ) ) ) )
= $false )
| ( ( ~ ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a )
| ~ ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) )
| ! [SY497: list_a,SY498: list_a] : ( SV114 @ SY497 @ SY498 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1087]) ).
thf(1188,plain,
! [SV115: list_a,SV192: list_a > $o] :
( ( ( ~ ( SV192 @ ( cons_a @ ( sK53_X2 @ SV192 @ SV115 ) @ nil_a ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK52_SY372 @ SV192 @ SV115 )
!= nil_a ) )
| ~ ~ ( ~ ( SV192 @ ( sK52_SY372 @ SV192 @ SV115 ) )
| ~ ~ ( SV192 @ ( cons_a @ ( sK51_X2 @ SV192 @ SV115 ) @ ( sK52_SY372 @ SV192 @ SV115 ) ) ) ) )
| ( SV192 @ SV115 ) )
= $true )
| ( ( SV115 = nil_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1189,plain,
! [SV116: poly_a > $o] :
( ( ( ~ ( ( ( sK83_SY399 @ SV116 )
= zero_zero_poly_a )
| ( SV116 @ ( sK83_SY399 @ SV116 ) ) ) )
= $false )
| ( ( ! [SY500: poly_a] : ( SV116 @ SY500 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1089]) ).
thf(1190,plain,
! [SV116: poly_a > $o] :
( ( ( ~ ~ ( SV116 @ ( pCons_a @ ( sK82_A2 @ SV116 ) @ ( sK83_SY399 @ SV116 ) ) ) )
= $false )
| ( ( ! [SY500: poly_a] : ( SV116 @ SY500 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1089]) ).
thf(1191,plain,
! [SV117: ( a > a > $o ) > list_a > $o] :
( ( ( ~ ( SV117 @ ( sK48_P5 @ SV117 ) @ ( cons_a @ ( sK49_SY371 @ SV117 ) @ nil_a ) ) )
= $true )
| ( ( ~ ( ~ ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) )
| ~ ~ ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK45_SY365 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) ) ) )
| ! [SY501: a > a > $o,SY502: list_a] : ( SV117 @ SY501 @ SY502 ) )
= $true )
| ( ( SV117 @ ( sK50_P5 @ SV117 ) @ nil_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1192,plain,
! [SV118: list_a > list_a > $o] :
( ( ( ~ ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a ) )
= $true )
| ( ( ~ ( ~ ( SV118 @ ( sK27_SY350 @ SV118 ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) )
| ~ ~ ( ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( sK29_SY355 @ SV118 ) )
| ~ ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) ) ) )
| ! [SY503: list_a,SY504: list_a] : ( SV118 @ SY503 @ SY504 ) )
= $true )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1091]) ).
thf(1193,plain,
! [SV207: poly_a] :
( ( ! [SY550: poly_a] :
( ( times_times_poly_a @ SV207 @ SY550 )
= zero_zero_poly_a )
| ( SV207 != zero_zero_poly_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1194,plain,
! [SV208: poly_a] :
( ( ! [SY551: poly_a] :
( ( ( times_times_poly_a @ SV208 @ SY551 )
= zero_zero_poly_a )
| ( SY551 != zero_zero_poly_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1195,plain,
! [SV119: list_a > list_a > $o] :
( ( ( ~ ( SV119 @ ( cons_a @ ( sK12_X2 @ SV119 ) @ ( sK13_SY337 @ SV119 ) ) @ nil_a ) )
= $true )
| ( ( ~ ( SV119 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SV119 ) @ ( sK11_SY336 @ SV119 ) ) )
| ~ ( ~ ( SV119 @ ( sK7_SY330 @ SV119 ) @ ( sK9_SY335 @ SV119 ) )
| ~ ~ ( SV119 @ ( cons_a @ ( sK6_X2 @ SV119 ) @ ( sK7_SY330 @ SV119 ) ) @ ( cons_a @ ( sK8_SY333 @ SV119 ) @ ( sK9_SY335 @ SV119 ) ) ) )
| ! [SY505: list_a,SY506: list_a] : ( SV119 @ SY505 @ SY506 ) )
= $true )
| ( ( SV119 @ nil_a @ nil_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1094]) ).
thf(1196,plain,
! [SV120: poly_a > $o] :
( ( ( ~ ( ~ ( ( ( sK88_A2 @ SV120 )
!= zero_zero_a )
| ( ( sK89_SY406 @ SV120 )
!= zero_zero_poly_a ) )
| ~ ~ ( ~ ( SV120 @ ( sK89_SY406 @ SV120 ) )
| ~ ~ ( SV120 @ ( pCons_a @ ( sK88_A2 @ SV120 ) @ ( sK89_SY406 @ SV120 ) ) ) ) ) )
= $true )
| ( ( ! [SY507: poly_a] : ( SV120 @ SY507 ) )
= $true )
| ( ( SV120 @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1095]) ).
thf(1197,plain,
! [SV121: list_a] :
( ( ( ( SV121 != nil_a )
| ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV121 != nil_a ) )
| ~ ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1198,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( ~ ( ( nil_a
= ( append_a @ SV122 @ SV166 ) )
| ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) ) )
= $true )
| ( ( ~ ( ( nil_a
!= ( append_a @ SV122 @ SV166 ) )
| ~ ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1097]) ).
thf(1199,plain,
! [SV123: list_a > list_a > $o] :
( ( ( ~ ( SV123 @ nil_a @ ( cons_a @ ( sK79_V @ SV123 ) @ ( sK80_SY398 @ SV123 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV123 @ ( sK76_SY392 @ SV123 ) @ ( sK78_SY397 @ SV123 ) )
| ~ ~ ( SV123 @ ( cons_a @ ( sK75_X2 @ SV123 ) @ ( sK76_SY392 @ SV123 ) ) @ ( cons_a @ ( sK77_SY395 @ SV123 ) @ ( sK78_SY397 @ SV123 ) ) ) )
| ! [SY511: list_a,SY512: list_a] : ( SV123 @ SY511 @ SY512 ) )
= $true )
| ( ( SV123 @ ( sK81_Xs2 @ SV123 ) @ nil_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1099]) ).
thf(1200,plain,
! [SV124: list_a > $o] :
( ( ( ~ ( ~ ( SV124 @ ( sK63_SY381 @ SV124 ) )
| ~ ~ ( SV124 @ ( cons_a @ ( sK62_X2 @ SV124 ) @ ( sK63_SY381 @ SV124 ) ) ) ) )
= $true )
| ( ( ! [SY513: list_a] : ( SV124 @ SY513 ) )
= $true )
| ( ( SV124 @ nil_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1201,plain,
! [SV193: poly_a,SV126: poly_a] :
( ( ~ ( ( SV126 = SV193 )
| ( ( coeffs_a @ SV126 )
= ( coeffs_a @ SV193 ) ) )
| ~ ( ( SV126 != SV193 )
| ( ( coeffs_a @ SV126 )
!= ( coeffs_a @ SV193 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1101]) ).
thf(1202,plain,
! [SV193: poly_a,SV126: poly_a] :
( ( ( SV126 = SV193 )
= ( ( coeffs_a @ SV126 )
= ( coeffs_a @ SV193 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1101]) ).
thf(1203,plain,
! [SV128: poly_a] :
( ( ( ( is_zero_a @ SV128 )
| ( null_a @ ( coeffs_a @ SV128 ) ) )
= $false )
| ( ( ~ ( ~ ( is_zero_a @ SV128 )
| ~ ( null_a @ ( coeffs_a @ SV128 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1103]) ).
thf(1204,plain,
! [SV8: poly_a] :
( ( ( ( coeffs_a @ SV8 )
= nil_a )
= $false )
| ( ( ~ ( ( ( coeffs_a @ SV8 )
!= nil_a )
| ( SV8 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1104]) ).
thf(1205,plain,
! [SV8: poly_a] :
( ( ( SV8 = zero_zero_poly_a )
= $false )
| ( ( ~ ( ( ( coeffs_a @ SV8 )
!= nil_a )
| ( SV8 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1104]) ).
thf(1206,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ( ( smult_a @ SV12 @ SV130 )
= zero_zero_poly_a )
| ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) )
= $false )
| ( ( ~ ( ( ( smult_a @ SV12 @ SV130 )
!= zero_zero_poly_a )
| ~ ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1207,plain,
! [SV132: poly_a] :
( ( ( ( is_zero_a @ SV132 )
| ( SV132 = zero_zero_poly_a ) )
= $false )
| ( ( ~ ( ~ ( is_zero_a @ SV132 )
| ( SV132 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1208,plain,
! [SV168: poly_a,SV22: a] :
( ( ( ( descar466059845root_a @ SV22 @ SV168 )
= zero_zero_poly_a )
= $false )
| ( ( SV168 = zero_zero_poly_a )
= $true )
| ( ( SV22 = zero_zero_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1209,plain,
! [SV23: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV23 ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV23 )
| ( SV23 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1108]) ).
thf(1210,plain,
! [SV23: nat] :
( ( ( SV23 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV23 )
| ( SV23 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1108]) ).
thf(1211,plain,
! [SV169: a,SV133: a,SV24: a] :
( ( ( ~ ( ( ( times_times_a @ SV24 @ SV133 )
= ( times_times_a @ SV169 @ SV133 ) )
| ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_a @ SV24 @ SV133 )
!= ( times_times_a @ SV169 @ SV133 ) )
| ~ ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1212,plain,
! [SV170: poly_a,SV134: poly_a,SV25: poly_a] :
( ( ( ~ ( ( ( times_times_poly_a @ SV25 @ SV134 )
= ( times_times_poly_a @ SV170 @ SV134 ) )
| ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_poly_a @ SV25 @ SV134 )
!= ( times_times_poly_a @ SV170 @ SV134 ) )
| ~ ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1111]) ).
thf(1213,plain,
! [SV171: nat,SV135: nat,SV26: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV26 @ SV135 )
= ( times_times_nat @ SV171 @ SV135 ) )
| ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV26 @ SV135 )
!= ( times_times_nat @ SV171 @ SV135 ) )
| ~ ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1113]) ).
thf(1214,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ~ ( ( ( times_times_a @ SV27 @ SV136 )
= ( times_times_a @ SV27 @ SV172 ) )
| ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_a @ SV27 @ SV136 )
!= ( times_times_a @ SV27 @ SV172 ) )
| ~ ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1115]) ).
thf(1215,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ~ ( ( ( times_times_poly_a @ SV28 @ SV137 )
= ( times_times_poly_a @ SV28 @ SV173 ) )
| ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_poly_a @ SV28 @ SV137 )
!= ( times_times_poly_a @ SV28 @ SV173 ) )
| ~ ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1117]) ).
thf(1216,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV29 @ SV138 )
= ( times_times_nat @ SV29 @ SV174 ) )
| ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV29 @ SV138 )
!= ( times_times_nat @ SV29 @ SV174 ) )
| ~ ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1217,plain,
! [SV139: a,SV30: a] :
( ( ( ( ( times_times_a @ SV30 @ SV139 )
= zero_zero_a )
| ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV30 @ SV139 )
!= zero_zero_a )
| ~ ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1218,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ( ( times_times_poly_a @ SV31 @ SV140 )
= zero_zero_poly_a )
| ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV31 @ SV140 )
!= zero_zero_poly_a )
| ~ ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1219,plain,
! [SV141: nat,SV32: nat] :
( ( ( ( ( times_times_nat @ SV32 @ SV141 )
= zero_zero_nat )
| ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV32 @ SV141 )
!= zero_zero_nat )
| ~ ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1220,plain,
! [SV39: poly_a] :
( ( ( ( uminus_uminus_poly_a @ SV39 )
= SV39 )
= $false )
| ( ( ~ ( ( ( uminus_uminus_poly_a @ SV39 )
!= SV39 )
| ( SV39 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1124]) ).
thf(1221,plain,
! [SV39: poly_a] :
( ( ( SV39 = zero_zero_poly_a )
= $false )
| ( ( ~ ( ( ( uminus_uminus_poly_a @ SV39 )
!= SV39 )
| ( SV39 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1124]) ).
thf(1222,plain,
! [SV40: a] :
( ( ( ( uminus_uminus_a @ SV40 )
= SV40 )
= $false )
| ( ( ~ ( ( ( uminus_uminus_a @ SV40 )
!= SV40 )
| ( SV40 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1125]) ).
thf(1223,plain,
! [SV40: a] :
( ( ( SV40 = zero_zero_a )
= $false )
| ( ( ~ ( ( ( uminus_uminus_a @ SV40 )
!= SV40 )
| ( SV40 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1125]) ).
thf(1224,plain,
! [SV41: poly_a] :
( ( ( SV41
= ( uminus_uminus_poly_a @ SV41 ) )
= $false )
| ( ( ~ ( ( SV41
!= ( uminus_uminus_poly_a @ SV41 ) )
| ( SV41 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1126]) ).
thf(1225,plain,
! [SV41: poly_a] :
( ( ( SV41 = zero_zero_poly_a )
= $false )
| ( ( ~ ( ( SV41
!= ( uminus_uminus_poly_a @ SV41 ) )
| ( SV41 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1126]) ).
thf(1226,plain,
! [SV42: a] :
( ( ( SV42
= ( uminus_uminus_a @ SV42 ) )
= $false )
| ( ( ~ ( ( SV42
!= ( uminus_uminus_a @ SV42 ) )
| ( SV42 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1127]) ).
thf(1227,plain,
! [SV42: a] :
( ( ( SV42 = zero_zero_a )
= $false )
| ( ( ~ ( ( SV42
!= ( uminus_uminus_a @ SV42 ) )
| ( SV42 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1127]) ).
thf(1228,plain,
! [SV43: poly_a] :
( ( ( ( uminus_uminus_poly_a @ SV43 )
= zero_zero_poly_a )
= $false )
| ( ( ~ ( ( ( uminus_uminus_poly_a @ SV43 )
!= zero_zero_poly_a )
| ( SV43 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1128]) ).
thf(1229,plain,
! [SV43: poly_a] :
( ( ( SV43 = zero_zero_poly_a )
= $false )
| ( ( ~ ( ( ( uminus_uminus_poly_a @ SV43 )
!= zero_zero_poly_a )
| ( SV43 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1128]) ).
thf(1230,plain,
! [SV44: a] :
( ( ( ( uminus_uminus_a @ SV44 )
= zero_zero_a )
= $false )
| ( ( ~ ( ( ( uminus_uminus_a @ SV44 )
!= zero_zero_a )
| ( SV44 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1129]) ).
thf(1231,plain,
! [SV44: a] :
( ( ( SV44 = zero_zero_a )
= $false )
| ( ( ~ ( ( ( uminus_uminus_a @ SV44 )
!= zero_zero_a )
| ( SV44 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1129]) ).
thf(1232,plain,
! [SV45: poly_a] :
( ( ( zero_zero_poly_a
= ( uminus_uminus_poly_a @ SV45 ) )
= $false )
| ( ( ~ ( ( zero_zero_poly_a
!= ( uminus_uminus_poly_a @ SV45 ) )
| ( zero_zero_poly_a != SV45 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1130]) ).
thf(1233,plain,
! [SV45: poly_a] :
( ( ( zero_zero_poly_a = SV45 )
= $false )
| ( ( ~ ( ( zero_zero_poly_a
!= ( uminus_uminus_poly_a @ SV45 ) )
| ( zero_zero_poly_a != SV45 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1130]) ).
thf(1234,plain,
! [SV46: a] :
( ( ( zero_zero_a
= ( uminus_uminus_a @ SV46 ) )
= $false )
| ( ( ~ ( ( zero_zero_a
!= ( uminus_uminus_a @ SV46 ) )
| ( zero_zero_a != SV46 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1235,plain,
! [SV46: a] :
( ( ( zero_zero_a = SV46 )
= $false )
| ( ( ~ ( ( zero_zero_a
!= ( uminus_uminus_a @ SV46 ) )
| ( zero_zero_a != SV46 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1236,plain,
! [SV142: list_a,SV48: list_a] :
( ( ( ( SV48
= ( append_a @ SV142 @ SV48 ) )
| ( SV142 = nil_a ) )
= $false )
| ( ( ~ ( ( SV48
!= ( append_a @ SV142 @ SV48 ) )
| ( SV142 != nil_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1237,plain,
! [SV143: list_a,SV49: list_a] :
( ( ( ( ( append_a @ SV49 @ SV143 )
= SV143 )
| ( SV49 = nil_a ) )
= $false )
| ( ( ~ ( ( ( append_a @ SV49 @ SV143 )
!= SV143 )
| ( SV49 != nil_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1238,plain,
! [SV144: list_a,SV50: list_a] :
( ( ( ( SV50
= ( append_a @ SV50 @ SV144 ) )
| ( SV144 = nil_a ) )
= $false )
| ( ( ~ ( ( SV50
!= ( append_a @ SV50 @ SV144 ) )
| ( SV144 != nil_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1239,plain,
! [SV145: list_a,SV51: list_a] :
( ( ( ( ( append_a @ SV51 @ SV145 )
= SV51 )
| ( SV145 = nil_a ) )
= $false )
| ( ( ~ ( ( ( append_a @ SV51 @ SV145 )
!= SV51 )
| ( SV145 != nil_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1240,plain,
! [SV53: poly_a] :
( ( ( zero_zero_poly_a = SV53 )
= $false )
| ( ( ~ ( ( zero_zero_poly_a != SV53 )
| ( SV53 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1136]) ).
thf(1241,plain,
! [SV53: poly_a] :
( ( ( SV53 = zero_zero_poly_a )
= $false )
| ( ( ~ ( ( zero_zero_poly_a != SV53 )
| ( SV53 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1136]) ).
thf(1242,plain,
! [SV54: a] :
( ( ( zero_zero_a = SV54 )
= $false )
| ( ( ~ ( ( zero_zero_a != SV54 )
| ( SV54 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1137]) ).
thf(1243,plain,
! [SV54: a] :
( ( ( SV54 = zero_zero_a )
= $false )
| ( ( ~ ( ( zero_zero_a != SV54 )
| ( SV54 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1137]) ).
thf(1244,plain,
! [SV55: nat] :
( ( ( zero_zero_nat = SV55 )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV55 )
| ( SV55 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1138]) ).
thf(1245,plain,
! [SV55: nat] :
( ( ( SV55 = zero_zero_nat )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV55 )
| ( SV55 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1138]) ).
thf(1246,plain,
! [SV57: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV57 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV57 )
| ~ ( ( SV57 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1139]) ).
thf(1247,plain,
! [SV57: nat] :
( ( ( SV57 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV57 )
| ~ ( ( SV57 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1139]) ).
thf(1248,plain,
! [SV58: nat,SV147: nat] :
( ( ( SV147 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV58 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1249,plain,
! [SV194: a,SV61: a,SV175: a] :
( ( ( ~ ( ( ( times_times_a @ SV175 @ SV61 )
= ( times_times_a @ SV194 @ SV61 ) )
| ( SV175 = SV194 ) )
| ~ ( ( ( times_times_a @ SV175 @ SV61 )
!= ( times_times_a @ SV194 @ SV61 ) )
| ( SV175 != SV194 ) ) )
= $true )
| ( ( SV61 = zero_zero_a )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1141]) ).
thf(1250,plain,
! [SV194: a,SV61: a,SV175: a] :
( ( ( ( ( times_times_a @ SV175 @ SV61 )
= ( times_times_a @ SV194 @ SV61 ) )
= ( SV175 = SV194 ) )
= $true )
| ( ( SV61 = zero_zero_a )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1141]) ).
thf(1251,plain,
! [SV195: poly_a,SV62: poly_a,SV176: poly_a] :
( ( ( ~ ( ( ( times_times_poly_a @ SV176 @ SV62 )
= ( times_times_poly_a @ SV195 @ SV62 ) )
| ( SV176 = SV195 ) )
| ~ ( ( ( times_times_poly_a @ SV176 @ SV62 )
!= ( times_times_poly_a @ SV195 @ SV62 ) )
| ( SV176 != SV195 ) ) )
= $true )
| ( ( SV62 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1142]) ).
thf(1252,plain,
! [SV195: poly_a,SV62: poly_a,SV176: poly_a] :
( ( ( ( ( times_times_poly_a @ SV176 @ SV62 )
= ( times_times_poly_a @ SV195 @ SV62 ) )
= ( SV176 = SV195 ) )
= $true )
| ( ( SV62 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1142]) ).
thf(1253,plain,
! [SV196: nat,SV63: nat,SV177: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV177 @ SV63 )
= ( times_times_nat @ SV196 @ SV63 ) )
| ( SV177 = SV196 ) )
| ~ ( ( ( times_times_nat @ SV177 @ SV63 )
!= ( times_times_nat @ SV196 @ SV63 ) )
| ( SV177 != SV196 ) ) )
= $true )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1143]) ).
thf(1254,plain,
! [SV196: nat,SV63: nat,SV177: nat] :
( ( ( ( ( times_times_nat @ SV177 @ SV63 )
= ( times_times_nat @ SV196 @ SV63 ) )
= ( SV177 = SV196 ) )
= $true )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1143]) ).
thf(1255,plain,
! [SV197: a,SV178: a,SV64: a] :
( ( ( ~ ( ( ( times_times_a @ SV64 @ SV178 )
= ( times_times_a @ SV64 @ SV197 ) )
| ( SV178 = SV197 ) )
| ~ ( ( ( times_times_a @ SV64 @ SV178 )
!= ( times_times_a @ SV64 @ SV197 ) )
| ( SV178 != SV197 ) ) )
= $true )
| ( ( SV64 = zero_zero_a )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1144]) ).
thf(1256,plain,
! [SV197: a,SV178: a,SV64: a] :
( ( ( ( ( times_times_a @ SV64 @ SV178 )
= ( times_times_a @ SV64 @ SV197 ) )
= ( SV178 = SV197 ) )
= $true )
| ( ( SV64 = zero_zero_a )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1144]) ).
thf(1257,plain,
! [SV198: poly_a,SV179: poly_a,SV65: poly_a] :
( ( ( ~ ( ( ( times_times_poly_a @ SV65 @ SV179 )
= ( times_times_poly_a @ SV65 @ SV198 ) )
| ( SV179 = SV198 ) )
| ~ ( ( ( times_times_poly_a @ SV65 @ SV179 )
!= ( times_times_poly_a @ SV65 @ SV198 ) )
| ( SV179 != SV198 ) ) )
= $true )
| ( ( SV65 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1145]) ).
thf(1258,plain,
! [SV198: poly_a,SV179: poly_a,SV65: poly_a] :
( ( ( ( ( times_times_poly_a @ SV65 @ SV179 )
= ( times_times_poly_a @ SV65 @ SV198 ) )
= ( SV179 = SV198 ) )
= $true )
| ( ( SV65 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1145]) ).
thf(1259,plain,
! [SV199: nat,SV180: nat,SV66: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV66 @ SV180 )
= ( times_times_nat @ SV66 @ SV199 ) )
| ( SV180 = SV199 ) )
| ~ ( ( ( times_times_nat @ SV66 @ SV180 )
!= ( times_times_nat @ SV66 @ SV199 ) )
| ( SV180 != SV199 ) ) )
= $true )
| ( ( SV66 = zero_zero_nat )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1146]) ).
thf(1260,plain,
! [SV199: nat,SV180: nat,SV66: nat] :
( ( ( ( ( times_times_nat @ SV66 @ SV180 )
= ( times_times_nat @ SV66 @ SV199 ) )
= ( SV180 = SV199 ) )
= $true )
| ( ( SV66 = zero_zero_nat )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[1146]) ).
thf(1261,plain,
! [SV181: a,SV67: a] :
( ( ( ( times_times_a @ SV67 @ SV181 )
= zero_zero_a )
= $false )
| ( ( SV181 = zero_zero_a )
= $true )
| ( ( SV67 = zero_zero_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1262,plain,
! [SV182: poly_a,SV68: poly_a] :
( ( ( ( times_times_poly_a @ SV68 @ SV182 )
= zero_zero_poly_a )
= $false )
| ( ( SV182 = zero_zero_poly_a )
= $true )
| ( ( SV68 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1263,plain,
! [SV183: nat,SV69: nat] :
( ( ( ( times_times_nat @ SV69 @ SV183 )
= zero_zero_nat )
= $false )
| ( ( SV183 = zero_zero_nat )
= $true )
| ( ( SV69 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1264,plain,
! [SV148: a,SV70: a] :
( ( ( SV70 = zero_zero_a )
= $true )
| ( ( SV148 = zero_zero_a )
= $true )
| ( ( ( times_times_a @ SV70 @ SV148 )
= zero_zero_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1265,plain,
! [SV149: poly_a,SV71: poly_a] :
( ( ( SV71 = zero_zero_poly_a )
= $true )
| ( ( SV149 = zero_zero_poly_a )
= $true )
| ( ( ( times_times_poly_a @ SV71 @ SV149 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1266,plain,
! [SV150: nat,SV72: nat] :
( ( ( SV72 = zero_zero_nat )
= $true )
| ( ( SV150 = zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV72 @ SV150 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1267,plain,
! [SV200: list_a,SV184: a,SV77: list_a] :
( ( ( SV77
= ( cons_a @ SV184 @ SV200 ) )
= $false )
| ( ( SV77 != nil_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1268,plain,
! [SV186: list_a,SV153: list_a,SV80: a] :
( ( ( ( cons_a @ SV80 @ SV153 )
= SV186 )
= $false )
| ( ( ! [SY542: list_a,SY543: list_a] :
( ( SY542
!= ( append_a @ SV153 @ SY543 ) )
| ( ( cons_a @ SV80 @ SY542 )
= ( append_a @ SV186 @ SY543 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1269,plain,
! [SV85: list_a] :
( ( ( SV85 = nil_a )
= $false )
| ( ( ~ ( ( SV85 != nil_a )
| ~ ( null_a @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1156]) ).
thf(1270,plain,
! [SV85: list_a] :
( ( ( null_a @ SV85 )
= $false )
| ( ( ~ ( ( SV85 != nil_a )
| ~ ( null_a @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1156]) ).
thf(1271,plain,
! [SV187: nat,SV156: nat,SV86: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV86 @ SV156 )
= ( times_times_nat @ SV187 @ SV156 ) )
| ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV86 @ SV156 )
!= ( times_times_nat @ SV187 @ SV156 ) )
| ~ ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1272,plain,
! [SV87: nat] :
( ( ( SV87 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ( SV87 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1159]) ).
thf(1273,plain,
! [SV87: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV87 )
= $false )
| ( ( ~ ( ~ ( ( SV87 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1159]) ).
thf(1274,plain,
! [SV89: nat] :
( ( ( SV89 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ( SV89 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV89 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1160]) ).
thf(1275,plain,
! [SV89: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV89 )
= $false )
| ( ( ~ ( ~ ( ( SV89 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV89 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1160]) ).
thf(1276,plain,
! [SV157: nat,SV90: nat] :
( ( ( ( ( times_times_nat @ SV90 @ SV157 )
= zero_zero_nat )
| ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV90 @ SV157 )
!= zero_zero_nat )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1277,plain,
! [SV188: nat,SV158: nat,SV92: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV92 @ SV158 )
= ( times_times_nat @ SV92 @ SV188 ) )
| ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV92 @ SV158 )
!= ( times_times_nat @ SV92 @ SV188 ) )
| ~ ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1162]) ).
thf(1278,plain,
! [SV94: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV94 ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV94 )
| ( SV94 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1164]) ).
thf(1279,plain,
! [SV94: nat] :
( ( ( SV94 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV94 )
| ( SV94 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1164]) ).
thf(1280,plain,
! [SV97: nat,SV159: nat] :
( ( ( SV159 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV97 @ SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1281,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV100 @ SV160 )
= ( times_times_nat @ SV100 @ SV189 ) )
| ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV100 @ SV160 )
!= ( times_times_nat @ SV100 @ SV189 ) )
| ~ ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1166]) ).
thf(1282,plain,
! [SV101: list_a > $o] :
( ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK40_X2 @ SV101 )
!= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
| ~ ~ ( ~ ( ( ( sK40_X2 @ SV101 )
= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
| ~ ~ ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) ) ) )
| ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1283,plain,
! [SV201: a] :
( ( ( ! [SY546: a] :
( ( times_times_a @ SV201 @ SY546 )
= zero_zero_a ) )
= $true )
| ( ( SV201 != zero_zero_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1284,plain,
! [SV209: a,SV202: a] :
( ( ( ( times_times_a @ SV202 @ SV209 )
= zero_zero_a )
| ( SV209 != zero_zero_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1285,plain,
! [SV102: list_a > $o] :
( ( ( ! [SY473: a,SY474: list_a] :
( ( sK25_SY345 @ SV102 )
!= ( cons_a @ SY473 @ SY474 ) )
| ( SV102 @ ( sK25_SY345 @ SV102 ) ) )
= $true )
| ( ( ~ ( SV102 @ nil_a )
| ! [SY475: list_a] : ( SV102 @ SY475 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1171]) ).
thf(1286,plain,
! [SV102: list_a > $o] :
( ( ( ~ ( SV102 @ ( cons_a @ ( sK24_X2 @ SV102 ) @ ( sK25_SY345 @ SV102 ) ) ) )
= $true )
| ( ( ~ ( SV102 @ nil_a )
| ! [SY475: list_a] : ( SV102 @ SY475 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1172]) ).
thf(1287,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ( ( append_a @ SV103 @ SV161 )
= nil_a )
| ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) )
= $false )
| ( ( ~ ( ( ( append_a @ SV103 @ SV161 )
!= nil_a )
| ~ ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1288,plain,
! [SV162: a > a,SV104: ( a > a ) > list_a > list_a > $o] :
( ( ( ~ ( ~ ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) @ ( cons_a @ ( sK54_F2 @ SV162 @ SV104 @ ( sK55_SY373 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) ) )
| ~ ~ ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( cons_a @ ( sK55_SY373 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) ) ) )
= $true )
| ( ( ! [SY529: list_a,SY530: list_a] : ( SV104 @ SV162 @ SY529 @ SY530 ) )
= $true )
| ( ( SV104 @ ( sK58_F2 @ SV162 @ SV104 ) @ nil_a @ ( sK59_SY379 @ SV162 @ SV104 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1289,plain,
! [SV203: a,SV190: list_a,SV163: a,SV105: list_a] :
( ( ~ ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
| ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) )
| ~ ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
!= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
| ~ ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1175]) ).
thf(1290,plain,
! [SV203: a,SV190: list_a,SV163: a,SV105: list_a] :
( ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
= ( ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1175]) ).
thf(1291,plain,
! [SV106: ( a > a > $o ) > list_a > $o] :
( ( ( ~ ( SV106 @ ( sK36_P5 @ SV106 ) @ ( sK38_SY361 @ SV106 ) )
| ~ ~ ( SV106 @ ( sK36_P5 @ SV106 ) @ ( cons_a @ ( sK37_SY359 @ SV106 ) @ ( sK38_SY361 @ SV106 ) ) ) )
= $false )
| ( ( ! [SY483: a > a > $o,SY484: list_a] : ( SV106 @ SY483 @ SY484 ) )
= $true )
| ( ( SV106 @ ( sK39_P5 @ SV106 ) @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1292,plain,
! [SV107: nat > $o] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK1_N2 @ SV107 ) )
| ~ ~ ( ~ ~ ( SV107 @ ( sK1_N2 @ SV107 ) )
| ~ ! [SY485: nat] :
( ~ ( ord_less_nat @ SY485 @ ( sK1_N2 @ SV107 ) )
| ( SV107 @ SY485 ) ) ) )
= $false )
| ( ( ! [SY486: nat] : ( SV107 @ SY486 ) )
= $true )
| ( ( SV107 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1293,plain,
! [SV108: list_a > $o] :
( ( ( ~ ( SV108 @ ( sK5_SY329 @ SV108 ) )
| ~ ~ ( SV108 @ ( cons_a @ ( sK4_X1 @ SV108 ) @ ( sK5_SY329 @ SV108 ) ) ) )
= $false )
| ( ( ! [SY487: list_a] : ( SV108 @ SY487 ) )
= $true )
| ( ( SV108 @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1178]) ).
thf(1294,plain,
! [SV109: list_a > $o] :
( ( ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
= $false )
| ( ( ~ ( ~ ( SV109 @ ( sK20_SY343 @ SV109 ) )
| ~ ~ ( ~ ( SV109 @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) )
| ~ ~ ( SV109 @ ( cons_a @ ( sK18_X2 @ SV109 ) @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) ) ) ) )
| ! [SY488: list_a] : ( SV109 @ SY488 ) )
= $true )
| ( ( SV109 @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1295,plain,
! [SV204: list_a,SV191: a,SV164: list_a,SV110: a] :
( ( ~ ( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SV204 ) )
| ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) )
| ~ ( ( ( cons_a @ SV110 @ SV164 )
!= ( cons_a @ SV191 @ SV204 ) )
| ~ ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1180]) ).
thf(1296,plain,
! [SV204: list_a,SV191: a,SV164: list_a,SV110: a] :
( ( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SV204 ) )
= ( ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1180]) ).
thf(1297,plain,
! [SV111: list_a > list_a > $o] :
( ( ( ~ ( SV111 @ ( sK16_SY340 @ SV111 ) @ ( sK15_SY338 @ SV111 ) )
| ~ ~ ( SV111 @ ( cons_a @ ( sK14_X2 @ SV111 ) @ ( sK15_SY338 @ SV111 ) ) @ ( sK16_SY340 @ SV111 ) ) )
= $false )
| ( ( ! [SY492: list_a,SY493: list_a] : ( SV111 @ SY492 @ SY493 ) )
= $true )
| ( ( SV111 @ nil_a @ ( sK17_X_1 @ SV111 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1298,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ( ( pCons_a @ SV112 @ SV165 )
= zero_zero_poly_a )
| ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) )
= $false )
| ( ( ~ ( ( ( pCons_a @ SV112 @ SV165 )
!= zero_zero_poly_a )
| ~ ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1299,plain,
! [SV205: nat] :
( ( ( ! [SY548: nat] :
( ( times_times_nat @ SV205 @ SY548 )
= zero_zero_nat ) )
= $true )
| ( ( SV205 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1183]) ).
thf(1300,plain,
! [SV210: nat,SV206: nat] :
( ( ( ( times_times_nat @ SV206 @ SV210 )
= zero_zero_nat )
| ( SV210 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1301,plain,
! [SV113: poly_a > poly_a > $o] :
( ( ( ~ ( SV113 @ ( sK85_SY400 @ SV113 ) @ ( sK87_SY405 @ SV113 ) )
| ~ ~ ( SV113 @ ( pCons_a @ ( sK84_A2 @ SV113 ) @ ( sK85_SY400 @ SV113 ) ) @ ( pCons_a @ ( sK86_SY403 @ SV113 ) @ ( sK87_SY405 @ SV113 ) ) ) )
= $false )
| ( ( ! [SY495: poly_a,SY496: poly_a] : ( SV113 @ SY495 @ SY496 ) )
= $true )
| ( ( SV113 @ zero_zero_poly_a @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1302,plain,
! [SV114: list_a > list_a > $o] :
( ( ( SV114 @ ( sK72_SY386 @ SV114 ) @ ( sK74_SY391 @ SV114 ) )
= $true )
| ( ( ~ ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a )
| ~ ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) )
| ! [SY497: list_a,SY498: list_a] : ( SV114 @ SY497 @ SY498 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1186]) ).
thf(1303,plain,
! [SV114: list_a > list_a > $o] :
( ( ( ~ ( SV114 @ ( cons_a @ ( sK71_X2 @ SV114 ) @ ( sK72_SY386 @ SV114 ) ) @ ( cons_a @ ( sK73_SY389 @ SV114 ) @ ( sK74_SY391 @ SV114 ) ) ) )
= $true )
| ( ( ~ ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a )
| ~ ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) )
| ! [SY497: list_a,SY498: list_a] : ( SV114 @ SY497 @ SY498 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1187]) ).
thf(1304,plain,
! [SV115: list_a,SV192: list_a > $o] :
( ( ( SV192 @ ( cons_a @ ( sK53_X2 @ SV192 @ SV115 ) @ nil_a ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK52_SY372 @ SV192 @ SV115 )
!= nil_a ) )
| ~ ~ ( ~ ( SV192 @ ( sK52_SY372 @ SV192 @ SV115 ) )
| ~ ~ ( SV192 @ ( cons_a @ ( sK51_X2 @ SV192 @ SV115 ) @ ( sK52_SY372 @ SV192 @ SV115 ) ) ) ) )
| ( SV192 @ SV115 ) )
= $true )
| ( ( SV115 = nil_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1188]) ).
thf(1305,plain,
! [SV116: poly_a > $o] :
( ( ( ( ( sK83_SY399 @ SV116 )
= zero_zero_poly_a )
| ( SV116 @ ( sK83_SY399 @ SV116 ) ) )
= $true )
| ( ( ! [SY500: poly_a] : ( SV116 @ SY500 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1189]) ).
thf(1306,plain,
! [SV116: poly_a > $o] :
( ( ( ~ ( SV116 @ ( pCons_a @ ( sK82_A2 @ SV116 ) @ ( sK83_SY399 @ SV116 ) ) ) )
= $true )
| ( ( ! [SY500: poly_a] : ( SV116 @ SY500 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1307,plain,
! [SV117: ( a > a > $o ) > list_a > $o] :
( ( ( SV117 @ ( sK48_P5 @ SV117 ) @ ( cons_a @ ( sK49_SY371 @ SV117 ) @ nil_a ) )
= $false )
| ( ( ~ ( ~ ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) )
| ~ ~ ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK45_SY365 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) ) ) )
| ! [SY501: a > a > $o,SY502: list_a] : ( SV117 @ SY501 @ SY502 ) )
= $true )
| ( ( SV117 @ ( sK50_P5 @ SV117 ) @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1308,plain,
! [SV118: list_a > list_a > $o] :
( ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( ~ ( ~ ( SV118 @ ( sK27_SY350 @ SV118 ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) )
| ~ ~ ( ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( sK29_SY355 @ SV118 ) )
| ~ ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) ) ) )
| ! [SY503: list_a,SY504: list_a] : ( SV118 @ SY503 @ SY504 ) )
= $true )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1309,plain,
! [SV207: poly_a] :
( ( ( ! [SY550: poly_a] :
( ( times_times_poly_a @ SV207 @ SY550 )
= zero_zero_poly_a ) )
= $true )
| ( ( SV207 != zero_zero_poly_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1310,plain,
! [SV211: poly_a,SV208: poly_a] :
( ( ( ( times_times_poly_a @ SV208 @ SV211 )
= zero_zero_poly_a )
| ( SV211 != zero_zero_poly_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1311,plain,
! [SV119: list_a > list_a > $o] :
( ( ( SV119 @ ( cons_a @ ( sK12_X2 @ SV119 ) @ ( sK13_SY337 @ SV119 ) ) @ nil_a )
= $false )
| ( ( ~ ( SV119 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SV119 ) @ ( sK11_SY336 @ SV119 ) ) )
| ~ ( ~ ( SV119 @ ( sK7_SY330 @ SV119 ) @ ( sK9_SY335 @ SV119 ) )
| ~ ~ ( SV119 @ ( cons_a @ ( sK6_X2 @ SV119 ) @ ( sK7_SY330 @ SV119 ) ) @ ( cons_a @ ( sK8_SY333 @ SV119 ) @ ( sK9_SY335 @ SV119 ) ) ) )
| ! [SY505: list_a,SY506: list_a] : ( SV119 @ SY505 @ SY506 ) )
= $true )
| ( ( SV119 @ nil_a @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1312,plain,
! [SV120: poly_a > $o] :
( ( ( ~ ( ( ( sK88_A2 @ SV120 )
!= zero_zero_a )
| ( ( sK89_SY406 @ SV120 )
!= zero_zero_poly_a ) )
| ~ ~ ( ~ ( SV120 @ ( sK89_SY406 @ SV120 ) )
| ~ ~ ( SV120 @ ( pCons_a @ ( sK88_A2 @ SV120 ) @ ( sK89_SY406 @ SV120 ) ) ) ) )
= $false )
| ( ( ! [SY507: poly_a] : ( SV120 @ SY507 ) )
= $true )
| ( ( SV120 @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1313,plain,
! [SV121: list_a] :
( ( ( SV121 != nil_a )
= $false )
| ( ( ~ ( ~ ( ( SV121 != nil_a ) )
| ~ ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1197]) ).
thf(1314,plain,
! [SV121: list_a] :
( ( ( ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV121 != nil_a ) )
| ~ ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1197]) ).
thf(1315,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( ( nil_a
= ( append_a @ SV122 @ SV166 ) )
| ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) )
= $false )
| ( ( ~ ( ( nil_a
!= ( append_a @ SV122 @ SV166 ) )
| ~ ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1316,plain,
! [SV123: list_a > list_a > $o] :
( ( ( SV123 @ nil_a @ ( cons_a @ ( sK79_V @ SV123 ) @ ( sK80_SY398 @ SV123 ) ) )
= $false )
| ( ( ~ ( ~ ( SV123 @ ( sK76_SY392 @ SV123 ) @ ( sK78_SY397 @ SV123 ) )
| ~ ~ ( SV123 @ ( cons_a @ ( sK75_X2 @ SV123 ) @ ( sK76_SY392 @ SV123 ) ) @ ( cons_a @ ( sK77_SY395 @ SV123 ) @ ( sK78_SY397 @ SV123 ) ) ) )
| ! [SY511: list_a,SY512: list_a] : ( SV123 @ SY511 @ SY512 ) )
= $true )
| ( ( SV123 @ ( sK81_Xs2 @ SV123 ) @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1317,plain,
! [SV124: list_a > $o] :
( ( ( ~ ( SV124 @ ( sK63_SY381 @ SV124 ) )
| ~ ~ ( SV124 @ ( cons_a @ ( sK62_X2 @ SV124 ) @ ( sK63_SY381 @ SV124 ) ) ) )
= $false )
| ( ( ! [SY513: list_a] : ( SV124 @ SY513 ) )
= $true )
| ( ( SV124 @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1318,plain,
! [SV193: poly_a,SV126: poly_a] :
( ( ( ~ ( ( SV126 = SV193 )
| ( ( coeffs_a @ SV126 )
= ( coeffs_a @ SV193 ) ) ) )
= $true )
| ( ( ~ ( ( SV126 != SV193 )
| ( ( coeffs_a @ SV126 )
!= ( coeffs_a @ SV193 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1201]) ).
thf(1319,plain,
! [SV128: poly_a] :
( ( ( is_zero_a @ SV128 )
= $false )
| ( ( ~ ( ~ ( is_zero_a @ SV128 )
| ~ ( null_a @ ( coeffs_a @ SV128 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1203]) ).
thf(1320,plain,
! [SV128: poly_a] :
( ( ( null_a @ ( coeffs_a @ SV128 ) )
= $false )
| ( ( ~ ( ~ ( is_zero_a @ SV128 )
| ~ ( null_a @ ( coeffs_a @ SV128 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1203]) ).
thf(1321,plain,
! [SV8: poly_a] :
( ( ( ( ( coeffs_a @ SV8 )
!= nil_a )
| ( SV8 != zero_zero_poly_a ) )
= $false )
| ( ( ( coeffs_a @ SV8 )
= nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1322,plain,
! [SV8: poly_a] :
( ( ( ( ( coeffs_a @ SV8 )
!= nil_a )
| ( SV8 != zero_zero_poly_a ) )
= $false )
| ( ( SV8 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1323,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ( smult_a @ SV12 @ SV130 )
= zero_zero_poly_a )
= $false )
| ( ( ~ ( ( ( smult_a @ SV12 @ SV130 )
!= zero_zero_poly_a )
| ~ ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1206]) ).
thf(1324,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) )
= $false )
| ( ( ~ ( ( ( smult_a @ SV12 @ SV130 )
!= zero_zero_poly_a )
| ~ ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1206]) ).
thf(1325,plain,
! [SV132: poly_a] :
( ( ( is_zero_a @ SV132 )
= $false )
| ( ( ~ ( ~ ( is_zero_a @ SV132 )
| ( SV132 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1207]) ).
thf(1326,plain,
! [SV132: poly_a] :
( ( ( SV132 = zero_zero_poly_a )
= $false )
| ( ( ~ ( ~ ( is_zero_a @ SV132 )
| ( SV132 != zero_zero_poly_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1207]) ).
thf(1327,plain,
! [SV23: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV23 )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV23 )
| ( SV23 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1209]) ).
thf(1328,plain,
! [SV23: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV23 )
| ( SV23 != zero_zero_nat ) )
= $false )
| ( ( SV23 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1329,plain,
! [SV169: a,SV133: a,SV24: a] :
( ( ( ( ( times_times_a @ SV24 @ SV133 )
= ( times_times_a @ SV169 @ SV133 ) )
| ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV24 @ SV133 )
!= ( times_times_a @ SV169 @ SV133 ) )
| ~ ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1330,plain,
! [SV170: poly_a,SV134: poly_a,SV25: poly_a] :
( ( ( ( ( times_times_poly_a @ SV25 @ SV134 )
= ( times_times_poly_a @ SV170 @ SV134 ) )
| ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV25 @ SV134 )
!= ( times_times_poly_a @ SV170 @ SV134 ) )
| ~ ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1331,plain,
! [SV171: nat,SV135: nat,SV26: nat] :
( ( ( ( ( times_times_nat @ SV26 @ SV135 )
= ( times_times_nat @ SV171 @ SV135 ) )
| ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV26 @ SV135 )
!= ( times_times_nat @ SV171 @ SV135 ) )
| ~ ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1332,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ( ( times_times_a @ SV27 @ SV136 )
= ( times_times_a @ SV27 @ SV172 ) )
| ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV27 @ SV136 )
!= ( times_times_a @ SV27 @ SV172 ) )
| ~ ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1333,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ( ( times_times_poly_a @ SV28 @ SV137 )
= ( times_times_poly_a @ SV28 @ SV173 ) )
| ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV28 @ SV137 )
!= ( times_times_poly_a @ SV28 @ SV173 ) )
| ~ ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1334,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ( ( times_times_nat @ SV29 @ SV138 )
= ( times_times_nat @ SV29 @ SV174 ) )
| ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV29 @ SV138 )
!= ( times_times_nat @ SV29 @ SV174 ) )
| ~ ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1335,plain,
! [SV139: a,SV30: a] :
( ( ( ( times_times_a @ SV30 @ SV139 )
= zero_zero_a )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV30 @ SV139 )
!= zero_zero_a )
| ~ ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1217]) ).
thf(1336,plain,
! [SV139: a,SV30: a] :
( ( ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV30 @ SV139 )
!= zero_zero_a )
| ~ ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1217]) ).
thf(1337,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ( times_times_poly_a @ SV31 @ SV140 )
= zero_zero_poly_a )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV31 @ SV140 )
!= zero_zero_poly_a )
| ~ ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1218]) ).
thf(1338,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV31 @ SV140 )
!= zero_zero_poly_a )
| ~ ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1218]) ).
thf(1339,plain,
! [SV141: nat,SV32: nat] :
( ( ( ( times_times_nat @ SV32 @ SV141 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV32 @ SV141 )
!= zero_zero_nat )
| ~ ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1219]) ).
thf(1340,plain,
! [SV141: nat,SV32: nat] :
( ( ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV32 @ SV141 )
!= zero_zero_nat )
| ~ ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1219]) ).
thf(1341,plain,
! [SV39: poly_a] :
( ( ( ( ( uminus_uminus_poly_a @ SV39 )
!= SV39 )
| ( SV39 != zero_zero_poly_a ) )
= $false )
| ( ( ( uminus_uminus_poly_a @ SV39 )
= SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1342,plain,
! [SV39: poly_a] :
( ( ( ( ( uminus_uminus_poly_a @ SV39 )
!= SV39 )
| ( SV39 != zero_zero_poly_a ) )
= $false )
| ( ( SV39 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1343,plain,
! [SV40: a] :
( ( ( ( ( uminus_uminus_a @ SV40 )
!= SV40 )
| ( SV40 != zero_zero_a ) )
= $false )
| ( ( ( uminus_uminus_a @ SV40 )
= SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1344,plain,
! [SV40: a] :
( ( ( ( ( uminus_uminus_a @ SV40 )
!= SV40 )
| ( SV40 != zero_zero_a ) )
= $false )
| ( ( SV40 = zero_zero_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1345,plain,
! [SV41: poly_a] :
( ( ( ( SV41
!= ( uminus_uminus_poly_a @ SV41 ) )
| ( SV41 != zero_zero_poly_a ) )
= $false )
| ( ( SV41
= ( uminus_uminus_poly_a @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1346,plain,
! [SV41: poly_a] :
( ( ( ( SV41
!= ( uminus_uminus_poly_a @ SV41 ) )
| ( SV41 != zero_zero_poly_a ) )
= $false )
| ( ( SV41 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1347,plain,
! [SV42: a] :
( ( ( ( SV42
!= ( uminus_uminus_a @ SV42 ) )
| ( SV42 != zero_zero_a ) )
= $false )
| ( ( SV42
= ( uminus_uminus_a @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1348,plain,
! [SV42: a] :
( ( ( ( SV42
!= ( uminus_uminus_a @ SV42 ) )
| ( SV42 != zero_zero_a ) )
= $false )
| ( ( SV42 = zero_zero_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1349,plain,
! [SV43: poly_a] :
( ( ( ( ( uminus_uminus_poly_a @ SV43 )
!= zero_zero_poly_a )
| ( SV43 != zero_zero_poly_a ) )
= $false )
| ( ( ( uminus_uminus_poly_a @ SV43 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1350,plain,
! [SV43: poly_a] :
( ( ( ( ( uminus_uminus_poly_a @ SV43 )
!= zero_zero_poly_a )
| ( SV43 != zero_zero_poly_a ) )
= $false )
| ( ( SV43 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1351,plain,
! [SV44: a] :
( ( ( ( ( uminus_uminus_a @ SV44 )
!= zero_zero_a )
| ( SV44 != zero_zero_a ) )
= $false )
| ( ( ( uminus_uminus_a @ SV44 )
= zero_zero_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1352,plain,
! [SV44: a] :
( ( ( ( ( uminus_uminus_a @ SV44 )
!= zero_zero_a )
| ( SV44 != zero_zero_a ) )
= $false )
| ( ( SV44 = zero_zero_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1353,plain,
! [SV45: poly_a] :
( ( ( ( zero_zero_poly_a
!= ( uminus_uminus_poly_a @ SV45 ) )
| ( zero_zero_poly_a != SV45 ) )
= $false )
| ( ( zero_zero_poly_a
= ( uminus_uminus_poly_a @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1354,plain,
! [SV45: poly_a] :
( ( ( ( zero_zero_poly_a
!= ( uminus_uminus_poly_a @ SV45 ) )
| ( zero_zero_poly_a != SV45 ) )
= $false )
| ( ( zero_zero_poly_a = SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1355,plain,
! [SV46: a] :
( ( ( ( zero_zero_a
!= ( uminus_uminus_a @ SV46 ) )
| ( zero_zero_a != SV46 ) )
= $false )
| ( ( zero_zero_a
= ( uminus_uminus_a @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1356,plain,
! [SV46: a] :
( ( ( ( zero_zero_a
!= ( uminus_uminus_a @ SV46 ) )
| ( zero_zero_a != SV46 ) )
= $false )
| ( ( zero_zero_a = SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1357,plain,
! [SV142: list_a,SV48: list_a] :
( ( ( SV48
= ( append_a @ SV142 @ SV48 ) )
= $false )
| ( ( ~ ( ( SV48
!= ( append_a @ SV142 @ SV48 ) )
| ( SV142 != nil_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1236]) ).
thf(1358,plain,
! [SV48: list_a,SV142: list_a] :
( ( ( SV142 = nil_a )
= $false )
| ( ( ~ ( ( SV48
!= ( append_a @ SV142 @ SV48 ) )
| ( SV142 != nil_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1236]) ).
thf(1359,plain,
! [SV143: list_a,SV49: list_a] :
( ( ( ( append_a @ SV49 @ SV143 )
= SV143 )
= $false )
| ( ( ~ ( ( ( append_a @ SV49 @ SV143 )
!= SV143 )
| ( SV49 != nil_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1237]) ).
thf(1360,plain,
! [SV143: list_a,SV49: list_a] :
( ( ( SV49 = nil_a )
= $false )
| ( ( ~ ( ( ( append_a @ SV49 @ SV143 )
!= SV143 )
| ( SV49 != nil_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1237]) ).
thf(1361,plain,
! [SV144: list_a,SV50: list_a] :
( ( ( SV50
= ( append_a @ SV50 @ SV144 ) )
= $false )
| ( ( ~ ( ( SV50
!= ( append_a @ SV50 @ SV144 ) )
| ( SV144 != nil_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1362,plain,
! [SV50: list_a,SV144: list_a] :
( ( ( SV144 = nil_a )
= $false )
| ( ( ~ ( ( SV50
!= ( append_a @ SV50 @ SV144 ) )
| ( SV144 != nil_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1363,plain,
! [SV145: list_a,SV51: list_a] :
( ( ( ( append_a @ SV51 @ SV145 )
= SV51 )
= $false )
| ( ( ~ ( ( ( append_a @ SV51 @ SV145 )
!= SV51 )
| ( SV145 != nil_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1239]) ).
thf(1364,plain,
! [SV51: list_a,SV145: list_a] :
( ( ( SV145 = nil_a )
= $false )
| ( ( ~ ( ( ( append_a @ SV51 @ SV145 )
!= SV51 )
| ( SV145 != nil_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1239]) ).
thf(1365,plain,
! [SV53: poly_a] :
( ( ( ( zero_zero_poly_a != SV53 )
| ( SV53 != zero_zero_poly_a ) )
= $false )
| ( ( zero_zero_poly_a = SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1366,plain,
! [SV53: poly_a] :
( ( ( ( zero_zero_poly_a != SV53 )
| ( SV53 != zero_zero_poly_a ) )
= $false )
| ( ( SV53 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1367,plain,
! [SV54: a] :
( ( ( ( zero_zero_a != SV54 )
| ( SV54 != zero_zero_a ) )
= $false )
| ( ( zero_zero_a = SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1368,plain,
! [SV54: a] :
( ( ( ( zero_zero_a != SV54 )
| ( SV54 != zero_zero_a ) )
= $false )
| ( ( SV54 = zero_zero_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1369,plain,
! [SV55: nat] :
( ( ( ( zero_zero_nat != SV55 )
| ( SV55 != zero_zero_nat ) )
= $false )
| ( ( zero_zero_nat = SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1370,plain,
! [SV55: nat] :
( ( ( ( zero_zero_nat != SV55 )
| ( SV55 != zero_zero_nat ) )
= $false )
| ( ( SV55 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1371,plain,
! [SV57: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV57 )
| ~ ( ( SV57 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1372,plain,
! [SV57: nat] :
( ( ( SV57 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV57 )
| ~ ( ( SV57 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1247]) ).
thf(1373,plain,
! [SV194: a,SV61: a,SV175: a] :
( ( ( ~ ( ( ( times_times_a @ SV175 @ SV61 )
= ( times_times_a @ SV194 @ SV61 ) )
| ( SV175 = SV194 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_a @ SV175 @ SV61 )
!= ( times_times_a @ SV194 @ SV61 ) )
| ( SV175 != SV194 ) ) )
= $true )
| ( ( SV61 = zero_zero_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1374,plain,
! [SV195: poly_a,SV62: poly_a,SV176: poly_a] :
( ( ( ~ ( ( ( times_times_poly_a @ SV176 @ SV62 )
= ( times_times_poly_a @ SV195 @ SV62 ) )
| ( SV176 = SV195 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_poly_a @ SV176 @ SV62 )
!= ( times_times_poly_a @ SV195 @ SV62 ) )
| ( SV176 != SV195 ) ) )
= $true )
| ( ( SV62 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1251]) ).
thf(1375,plain,
! [SV196: nat,SV63: nat,SV177: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV177 @ SV63 )
= ( times_times_nat @ SV196 @ SV63 ) )
| ( SV177 = SV196 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV177 @ SV63 )
!= ( times_times_nat @ SV196 @ SV63 ) )
| ( SV177 != SV196 ) ) )
= $true )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1253]) ).
thf(1376,plain,
! [SV197: a,SV178: a,SV64: a] :
( ( ( ~ ( ( ( times_times_a @ SV64 @ SV178 )
= ( times_times_a @ SV64 @ SV197 ) )
| ( SV178 = SV197 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_a @ SV64 @ SV178 )
!= ( times_times_a @ SV64 @ SV197 ) )
| ( SV178 != SV197 ) ) )
= $true )
| ( ( SV64 = zero_zero_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1255]) ).
thf(1377,plain,
! [SV198: poly_a,SV179: poly_a,SV65: poly_a] :
( ( ( ~ ( ( ( times_times_poly_a @ SV65 @ SV179 )
= ( times_times_poly_a @ SV65 @ SV198 ) )
| ( SV179 = SV198 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_poly_a @ SV65 @ SV179 )
!= ( times_times_poly_a @ SV65 @ SV198 ) )
| ( SV179 != SV198 ) ) )
= $true )
| ( ( SV65 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1378,plain,
! [SV199: nat,SV180: nat,SV66: nat] :
( ( ( ~ ( ( ( times_times_nat @ SV66 @ SV180 )
= ( times_times_nat @ SV66 @ SV199 ) )
| ( SV180 = SV199 ) ) )
= $true )
| ( ( ~ ( ( ( times_times_nat @ SV66 @ SV180 )
!= ( times_times_nat @ SV66 @ SV199 ) )
| ( SV180 != SV199 ) ) )
= $true )
| ( ( SV66 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1259]) ).
thf(1379,plain,
! [SV200: list_a,SV184: a,SV77: list_a] :
( ( ( SV77 = nil_a )
= $false )
| ( ( SV77
= ( cons_a @ SV184 @ SV200 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1267]) ).
thf(1380,plain,
! [SV186: list_a,SV80: a,SV153: list_a,SV212: list_a] :
( ( ( ! [SY552: list_a] :
( ( SV212
!= ( append_a @ SV153 @ SY552 ) )
| ( ( cons_a @ SV80 @ SV212 )
= ( append_a @ SV186 @ SY552 ) ) ) )
= $true )
| ( ( ( cons_a @ SV80 @ SV153 )
= SV186 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1381,plain,
! [SV85: list_a] :
( ( ( ( SV85 != nil_a )
| ~ ( null_a @ SV85 ) )
= $false )
| ( ( SV85 = nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1382,plain,
! [SV85: list_a] :
( ( ( ( SV85 != nil_a )
| ~ ( null_a @ SV85 ) )
= $false )
| ( ( null_a @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1383,plain,
! [SV187: nat,SV156: nat,SV86: nat] :
( ( ( ( ( times_times_nat @ SV86 @ SV156 )
= ( times_times_nat @ SV187 @ SV156 ) )
| ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV86 @ SV156 )
!= ( times_times_nat @ SV187 @ SV156 ) )
| ~ ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1384,plain,
! [SV87: nat] :
( ( ( SV87 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ( SV87 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1272]) ).
thf(1385,plain,
! [SV87: nat] :
( ( ( ~ ( ( SV87 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV87 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1273]) ).
thf(1386,plain,
! [SV89: nat] :
( ( ( SV89 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ( SV89 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV89 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1274]) ).
thf(1387,plain,
! [SV89: nat] :
( ( ( ~ ( ( SV89 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV89 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1388,plain,
! [SV157: nat,SV90: nat] :
( ( ( ( times_times_nat @ SV90 @ SV157 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV90 @ SV157 )
!= zero_zero_nat )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1276]) ).
thf(1389,plain,
! [SV157: nat,SV90: nat] :
( ( ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV90 @ SV157 )
!= zero_zero_nat )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1276]) ).
thf(1390,plain,
! [SV188: nat,SV158: nat,SV92: nat] :
( ( ( ( ( times_times_nat @ SV92 @ SV158 )
= ( times_times_nat @ SV92 @ SV188 ) )
| ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV92 @ SV158 )
!= ( times_times_nat @ SV92 @ SV188 ) )
| ~ ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1391,plain,
! [SV94: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV94 )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV94 )
| ( SV94 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1278]) ).
thf(1392,plain,
! [SV94: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV94 )
| ( SV94 != zero_zero_nat ) )
= $false )
| ( ( SV94 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1393,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ( ( times_times_nat @ SV100 @ SV160 )
= ( times_times_nat @ SV100 @ SV189 ) )
| ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV100 @ SV160 )
!= ( times_times_nat @ SV100 @ SV189 ) )
| ~ ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1394,plain,
! [SV101: list_a > $o] :
( ( ( ~ ( ~ ( ( ( sK40_X2 @ SV101 )
!= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
| ~ ~ ( ~ ( ( ( sK40_X2 @ SV101 )
= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
| ~ ~ ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) ) ) ) )
= $true )
| ( ( ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1282]) ).
thf(1395,plain,
! [SV213: a,SV201: a] :
( ( ( ( times_times_a @ SV201 @ SV213 )
= zero_zero_a )
= $true )
| ( ( SV201 != zero_zero_a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1396,plain,
! [SV209: a,SV202: a] :
( ( ( ( times_times_a @ SV202 @ SV209 )
= zero_zero_a )
= $true )
| ( ( SV209 != zero_zero_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1284]) ).
thf(1397,plain,
! [SV102: list_a > $o] :
( ( ( ! [SY473: a,SY474: list_a] :
( ( sK25_SY345 @ SV102 )
!= ( cons_a @ SY473 @ SY474 ) ) )
= $true )
| ( ( SV102 @ ( sK25_SY345 @ SV102 ) )
= $true )
| ( ( ~ ( SV102 @ nil_a )
| ! [SY475: list_a] : ( SV102 @ SY475 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1285]) ).
thf(1398,plain,
! [SV102: list_a > $o] :
( ( ( SV102 @ ( cons_a @ ( sK24_X2 @ SV102 ) @ ( sK25_SY345 @ SV102 ) ) )
= $false )
| ( ( ~ ( SV102 @ nil_a )
| ! [SY475: list_a] : ( SV102 @ SY475 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1399,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ( append_a @ SV103 @ SV161 )
= nil_a )
= $false )
| ( ( ~ ( ( ( append_a @ SV103 @ SV161 )
!= nil_a )
| ~ ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1287]) ).
thf(1400,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) )
= $false )
| ( ( ~ ( ( ( append_a @ SV103 @ SV161 )
!= nil_a )
| ~ ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1287]) ).
thf(1401,plain,
! [SV162: a > a,SV104: ( a > a ) > list_a > list_a > $o] :
( ( ( ~ ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) @ ( cons_a @ ( sK54_F2 @ SV162 @ SV104 @ ( sK55_SY373 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) ) )
| ~ ~ ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( cons_a @ ( sK55_SY373 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) ) )
= $false )
| ( ( ! [SY529: list_a,SY530: list_a] : ( SV104 @ SV162 @ SY529 @ SY530 ) )
= $true )
| ( ( SV104 @ ( sK58_F2 @ SV162 @ SV104 ) @ nil_a @ ( sK59_SY379 @ SV162 @ SV104 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1402,plain,
! [SV203: a,SV190: list_a,SV163: a,SV105: list_a] :
( ( ( ~ ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
| ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) ) )
= $true )
| ( ( ~ ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
!= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
| ~ ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1289]) ).
thf(1403,plain,
! [SV106: ( a > a > $o ) > list_a > $o] :
( ( ( ~ ( SV106 @ ( sK36_P5 @ SV106 ) @ ( sK38_SY361 @ SV106 ) ) )
= $false )
| ( ( ! [SY483: a > a > $o,SY484: list_a] : ( SV106 @ SY483 @ SY484 ) )
= $true )
| ( ( SV106 @ ( sK39_P5 @ SV106 ) @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1404,plain,
! [SV106: ( a > a > $o ) > list_a > $o] :
( ( ( ~ ~ ( SV106 @ ( sK36_P5 @ SV106 ) @ ( cons_a @ ( sK37_SY359 @ SV106 ) @ ( sK38_SY361 @ SV106 ) ) ) )
= $false )
| ( ( ! [SY483: a > a > $o,SY484: list_a] : ( SV106 @ SY483 @ SY484 ) )
= $true )
| ( ( SV106 @ ( sK39_P5 @ SV106 ) @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1405,plain,
! [SV107: nat > $o] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK1_N2 @ SV107 ) ) )
= $false )
| ( ( ! [SY486: nat] : ( SV107 @ SY486 ) )
= $true )
| ( ( SV107 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1292]) ).
thf(1406,plain,
! [SV107: nat > $o] :
( ( ( ~ ~ ( ~ ~ ( SV107 @ ( sK1_N2 @ SV107 ) )
| ~ ! [SY485: nat] :
( ~ ( ord_less_nat @ SY485 @ ( sK1_N2 @ SV107 ) )
| ( SV107 @ SY485 ) ) ) )
= $false )
| ( ( ! [SY486: nat] : ( SV107 @ SY486 ) )
= $true )
| ( ( SV107 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1292]) ).
thf(1407,plain,
! [SV108: list_a > $o] :
( ( ( ~ ( SV108 @ ( sK5_SY329 @ SV108 ) ) )
= $false )
| ( ( ! [SY487: list_a] : ( SV108 @ SY487 ) )
= $true )
| ( ( SV108 @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1293]) ).
thf(1408,plain,
! [SV108: list_a > $o] :
( ( ( ~ ~ ( SV108 @ ( cons_a @ ( sK4_X1 @ SV108 ) @ ( sK5_SY329 @ SV108 ) ) ) )
= $false )
| ( ( ! [SY487: list_a] : ( SV108 @ SY487 ) )
= $true )
| ( ( SV108 @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1293]) ).
thf(1409,plain,
! [SV109: list_a > $o] :
( ( ( ~ ( ~ ( SV109 @ ( sK20_SY343 @ SV109 ) )
| ~ ~ ( ~ ( SV109 @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) )
| ~ ~ ( SV109 @ ( cons_a @ ( sK18_X2 @ SV109 ) @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) ) ) ) ) )
= $true )
| ( ( ! [SY488: list_a] : ( SV109 @ SY488 ) )
= $true )
| ( ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
= $false )
| ( ( SV109 @ nil_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1294]) ).
thf(1410,plain,
! [SV204: list_a,SV191: a,SV164: list_a,SV110: a] :
( ( ( ~ ( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SV204 ) )
| ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) ) )
= $true )
| ( ( ~ ( ( ( cons_a @ SV110 @ SV164 )
!= ( cons_a @ SV191 @ SV204 ) )
| ~ ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1295]) ).
thf(1411,plain,
! [SV111: list_a > list_a > $o] :
( ( ( ~ ( SV111 @ ( sK16_SY340 @ SV111 ) @ ( sK15_SY338 @ SV111 ) ) )
= $false )
| ( ( ! [SY492: list_a,SY493: list_a] : ( SV111 @ SY492 @ SY493 ) )
= $true )
| ( ( SV111 @ nil_a @ ( sK17_X_1 @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1297]) ).
thf(1412,plain,
! [SV111: list_a > list_a > $o] :
( ( ( ~ ~ ( SV111 @ ( cons_a @ ( sK14_X2 @ SV111 ) @ ( sK15_SY338 @ SV111 ) ) @ ( sK16_SY340 @ SV111 ) ) )
= $false )
| ( ( ! [SY492: list_a,SY493: list_a] : ( SV111 @ SY492 @ SY493 ) )
= $true )
| ( ( SV111 @ nil_a @ ( sK17_X_1 @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1297]) ).
thf(1413,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ( pCons_a @ SV112 @ SV165 )
= zero_zero_poly_a )
= $false )
| ( ( ~ ( ( ( pCons_a @ SV112 @ SV165 )
!= zero_zero_poly_a )
| ~ ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1298]) ).
thf(1414,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) )
= $false )
| ( ( ~ ( ( ( pCons_a @ SV112 @ SV165 )
!= zero_zero_poly_a )
| ~ ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1298]) ).
thf(1415,plain,
! [SV214: nat,SV205: nat] :
( ( ( ( times_times_nat @ SV205 @ SV214 )
= zero_zero_nat )
= $true )
| ( ( SV205 != zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1416,plain,
! [SV210: nat,SV206: nat] :
( ( ( ( times_times_nat @ SV206 @ SV210 )
= zero_zero_nat )
= $true )
| ( ( SV210 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1300]) ).
thf(1417,plain,
! [SV113: poly_a > poly_a > $o] :
( ( ( ~ ( SV113 @ ( sK85_SY400 @ SV113 ) @ ( sK87_SY405 @ SV113 ) ) )
= $false )
| ( ( ! [SY495: poly_a,SY496: poly_a] : ( SV113 @ SY495 @ SY496 ) )
= $true )
| ( ( SV113 @ zero_zero_poly_a @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1301]) ).
thf(1418,plain,
! [SV113: poly_a > poly_a > $o] :
( ( ( ~ ~ ( SV113 @ ( pCons_a @ ( sK84_A2 @ SV113 ) @ ( sK85_SY400 @ SV113 ) ) @ ( pCons_a @ ( sK86_SY403 @ SV113 ) @ ( sK87_SY405 @ SV113 ) ) ) )
= $false )
| ( ( ! [SY495: poly_a,SY496: poly_a] : ( SV113 @ SY495 @ SY496 ) )
= $true )
| ( ( SV113 @ zero_zero_poly_a @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1301]) ).
thf(1419,plain,
! [SV114: list_a > list_a > $o] :
( ( ( ~ ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a ) )
= $true )
| ( ( ~ ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) )
| ! [SY497: list_a,SY498: list_a] : ( SV114 @ SY497 @ SY498 ) )
= $true )
| ( ( SV114 @ ( sK72_SY386 @ SV114 ) @ ( sK74_SY391 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1302]) ).
thf(1420,plain,
! [SV114: list_a > list_a > $o] :
( ( ( SV114 @ ( cons_a @ ( sK71_X2 @ SV114 ) @ ( sK72_SY386 @ SV114 ) ) @ ( cons_a @ ( sK73_SY389 @ SV114 ) @ ( sK74_SY391 @ SV114 ) ) )
= $false )
| ( ( ~ ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a )
| ~ ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) )
| ! [SY497: list_a,SY498: list_a] : ( SV114 @ SY497 @ SY498 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1421,plain,
! [SV115: list_a,SV192: list_a > $o] :
( ( ( ~ ( ~ ( ( ( sK52_SY372 @ SV192 @ SV115 )
!= nil_a ) )
| ~ ~ ( ~ ( SV192 @ ( sK52_SY372 @ SV192 @ SV115 ) )
| ~ ~ ( SV192 @ ( cons_a @ ( sK51_X2 @ SV192 @ SV115 ) @ ( sK52_SY372 @ SV192 @ SV115 ) ) ) ) ) )
= $true )
| ( ( SV192 @ SV115 )
= $true )
| ( ( SV192 @ ( cons_a @ ( sK53_X2 @ SV192 @ SV115 ) @ nil_a ) )
= $false )
| ( ( SV115 = nil_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1304]) ).
thf(1422,plain,
! [SV116: poly_a > $o] :
( ( ( ( sK83_SY399 @ SV116 )
= zero_zero_poly_a )
= $true )
| ( ( SV116 @ ( sK83_SY399 @ SV116 ) )
= $true )
| ( ( ! [SY500: poly_a] : ( SV116 @ SY500 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1305]) ).
thf(1423,plain,
! [SV116: poly_a > $o] :
( ( ( SV116 @ ( pCons_a @ ( sK82_A2 @ SV116 ) @ ( sK83_SY399 @ SV116 ) ) )
= $false )
| ( ( ! [SY500: poly_a] : ( SV116 @ SY500 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1424,plain,
! [SV117: ( a > a > $o ) > list_a > $o] :
( ( ( ~ ( ~ ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) )
| ~ ~ ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK45_SY365 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) ) ) ) )
= $true )
| ( ( ! [SY501: a > a > $o,SY502: list_a] : ( SV117 @ SY501 @ SY502 ) )
= $true )
| ( ( SV117 @ ( sK48_P5 @ SV117 ) @ ( cons_a @ ( sK49_SY371 @ SV117 ) @ nil_a ) )
= $false )
| ( ( SV117 @ ( sK50_P5 @ SV117 ) @ nil_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1307]) ).
thf(1425,plain,
! [SV118: list_a > list_a > $o] :
( ( ( ~ ( ~ ( SV118 @ ( sK27_SY350 @ SV118 ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) )
| ~ ~ ( ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( sK29_SY355 @ SV118 ) )
| ~ ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) ) ) ) )
= $true )
| ( ( ! [SY503: list_a,SY504: list_a] : ( SV118 @ SY503 @ SY504 ) )
= $true )
| ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1308]) ).
thf(1426,plain,
! [SV215: poly_a,SV207: poly_a] :
( ( ( ( times_times_poly_a @ SV207 @ SV215 )
= zero_zero_poly_a )
= $true )
| ( ( SV207 != zero_zero_poly_a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1427,plain,
! [SV211: poly_a,SV208: poly_a] :
( ( ( ( times_times_poly_a @ SV208 @ SV211 )
= zero_zero_poly_a )
= $true )
| ( ( SV211 != zero_zero_poly_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1310]) ).
thf(1428,plain,
! [SV119: list_a > list_a > $o] :
( ( ( ~ ( SV119 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SV119 ) @ ( sK11_SY336 @ SV119 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV119 @ ( sK7_SY330 @ SV119 ) @ ( sK9_SY335 @ SV119 ) )
| ~ ~ ( SV119 @ ( cons_a @ ( sK6_X2 @ SV119 ) @ ( sK7_SY330 @ SV119 ) ) @ ( cons_a @ ( sK8_SY333 @ SV119 ) @ ( sK9_SY335 @ SV119 ) ) ) )
| ! [SY505: list_a,SY506: list_a] : ( SV119 @ SY505 @ SY506 ) )
= $true )
| ( ( SV119 @ ( cons_a @ ( sK12_X2 @ SV119 ) @ ( sK13_SY337 @ SV119 ) ) @ nil_a )
= $false )
| ( ( SV119 @ nil_a @ nil_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1429,plain,
! [SV120: poly_a > $o] :
( ( ( ~ ( ( ( sK88_A2 @ SV120 )
!= zero_zero_a )
| ( ( sK89_SY406 @ SV120 )
!= zero_zero_poly_a ) ) )
= $false )
| ( ( ! [SY507: poly_a] : ( SV120 @ SY507 ) )
= $true )
| ( ( SV120 @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1312]) ).
thf(1430,plain,
! [SV120: poly_a > $o] :
( ( ( ~ ~ ( ~ ( SV120 @ ( sK89_SY406 @ SV120 ) )
| ~ ~ ( SV120 @ ( pCons_a @ ( sK88_A2 @ SV120 ) @ ( sK89_SY406 @ SV120 ) ) ) ) )
= $false )
| ( ( ! [SY507: poly_a] : ( SV120 @ SY507 ) )
= $true )
| ( ( SV120 @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1312]) ).
thf(1431,plain,
! [SV121: list_a] :
( ( ( SV121 = nil_a )
= $true )
| ( ( ~ ( ~ ( ( SV121 != nil_a ) )
| ~ ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1313]) ).
thf(1432,plain,
! [SV121: list_a] :
( ( ( ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV121 != nil_a ) )
| ~ ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1314]) ).
thf(1433,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( nil_a
= ( append_a @ SV122 @ SV166 ) )
= $false )
| ( ( ~ ( ( nil_a
!= ( append_a @ SV122 @ SV166 ) )
| ~ ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1315]) ).
thf(1434,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) )
= $false )
| ( ( ~ ( ( nil_a
!= ( append_a @ SV122 @ SV166 ) )
| ~ ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1315]) ).
thf(1435,plain,
! [SV123: list_a > list_a > $o] :
( ( ( ~ ( ~ ( SV123 @ ( sK76_SY392 @ SV123 ) @ ( sK78_SY397 @ SV123 ) )
| ~ ~ ( SV123 @ ( cons_a @ ( sK75_X2 @ SV123 ) @ ( sK76_SY392 @ SV123 ) ) @ ( cons_a @ ( sK77_SY395 @ SV123 ) @ ( sK78_SY397 @ SV123 ) ) ) ) )
= $true )
| ( ( ! [SY511: list_a,SY512: list_a] : ( SV123 @ SY511 @ SY512 ) )
= $true )
| ( ( SV123 @ nil_a @ ( cons_a @ ( sK79_V @ SV123 ) @ ( sK80_SY398 @ SV123 ) ) )
= $false )
| ( ( SV123 @ ( sK81_Xs2 @ SV123 ) @ nil_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1436,plain,
! [SV124: list_a > $o] :
( ( ( ~ ( SV124 @ ( sK63_SY381 @ SV124 ) ) )
= $false )
| ( ( ! [SY513: list_a] : ( SV124 @ SY513 ) )
= $true )
| ( ( SV124 @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1317]) ).
thf(1437,plain,
! [SV124: list_a > $o] :
( ( ( ~ ~ ( SV124 @ ( cons_a @ ( sK62_X2 @ SV124 ) @ ( sK63_SY381 @ SV124 ) ) ) )
= $false )
| ( ( ! [SY513: list_a] : ( SV124 @ SY513 ) )
= $true )
| ( ( SV124 @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1317]) ).
thf(1438,plain,
! [SV193: poly_a,SV126: poly_a] :
( ( ( ( SV126 = SV193 )
| ( ( coeffs_a @ SV126 )
= ( coeffs_a @ SV193 ) ) )
= $false )
| ( ( ~ ( ( SV126 != SV193 )
| ( ( coeffs_a @ SV126 )
!= ( coeffs_a @ SV193 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1439,plain,
! [SV128: poly_a] :
( ( ( ~ ( is_zero_a @ SV128 )
| ~ ( null_a @ ( coeffs_a @ SV128 ) ) )
= $false )
| ( ( is_zero_a @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1440,plain,
! [SV128: poly_a] :
( ( ( ~ ( is_zero_a @ SV128 )
| ~ ( null_a @ ( coeffs_a @ SV128 ) ) )
= $false )
| ( ( null_a @ ( coeffs_a @ SV128 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1441,plain,
! [SV8: poly_a] :
( ( ( ( coeffs_a @ SV8 )
!= nil_a )
= $false )
| ( ( ( coeffs_a @ SV8 )
= nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1321]) ).
thf(1442,plain,
! [SV8: poly_a] :
( ( ( SV8 != zero_zero_poly_a )
= $false )
| ( ( ( coeffs_a @ SV8 )
= nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1321]) ).
thf(1443,plain,
! [SV8: poly_a] :
( ( ( ( coeffs_a @ SV8 )
!= nil_a )
= $false )
| ( ( SV8 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1322]) ).
thf(1444,plain,
! [SV8: poly_a] :
( ( ( SV8 != zero_zero_poly_a )
= $false )
| ( ( SV8 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1322]) ).
thf(1445,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ( ( smult_a @ SV12 @ SV130 )
!= zero_zero_poly_a )
| ~ ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) ) )
= $false )
| ( ( ( smult_a @ SV12 @ SV130 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1446,plain,
! [SV130: poly_a,SV12: a] :
( ( ( SV12 = zero_zero_a )
= $false )
| ( ( ~ ( ( ( smult_a @ SV12 @ SV130 )
!= zero_zero_poly_a )
| ~ ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1324]) ).
thf(1447,plain,
! [SV12: a,SV130: poly_a] :
( ( ( SV130 = zero_zero_poly_a )
= $false )
| ( ( ~ ( ( ( smult_a @ SV12 @ SV130 )
!= zero_zero_poly_a )
| ~ ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1324]) ).
thf(1448,plain,
! [SV132: poly_a] :
( ( ( ~ ( is_zero_a @ SV132 )
| ( SV132 != zero_zero_poly_a ) )
= $false )
| ( ( is_zero_a @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1325]) ).
thf(1449,plain,
! [SV132: poly_a] :
( ( ( ~ ( is_zero_a @ SV132 )
| ( SV132 != zero_zero_poly_a ) )
= $false )
| ( ( SV132 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1450,plain,
! [SV23: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV23 )
| ( SV23 != zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1451,plain,
! [SV23: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV23 ) )
= $false )
| ( ( SV23 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1328]) ).
thf(1452,plain,
! [SV23: nat] :
( ( ( SV23 != zero_zero_nat )
= $false )
| ( ( SV23 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1328]) ).
thf(1453,plain,
! [SV169: a,SV133: a,SV24: a] :
( ( ( ( times_times_a @ SV24 @ SV133 )
= ( times_times_a @ SV169 @ SV133 ) )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV24 @ SV133 )
!= ( times_times_a @ SV169 @ SV133 ) )
| ~ ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1329]) ).
thf(1454,plain,
! [SV169: a,SV24: a,SV133: a] :
( ( ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV24 @ SV133 )
!= ( times_times_a @ SV169 @ SV133 ) )
| ~ ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1329]) ).
thf(1455,plain,
! [SV170: poly_a,SV134: poly_a,SV25: poly_a] :
( ( ( ( times_times_poly_a @ SV25 @ SV134 )
= ( times_times_poly_a @ SV170 @ SV134 ) )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV25 @ SV134 )
!= ( times_times_poly_a @ SV170 @ SV134 ) )
| ~ ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1330]) ).
thf(1456,plain,
! [SV170: poly_a,SV25: poly_a,SV134: poly_a] :
( ( ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV25 @ SV134 )
!= ( times_times_poly_a @ SV170 @ SV134 ) )
| ~ ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1330]) ).
thf(1457,plain,
! [SV171: nat,SV135: nat,SV26: nat] :
( ( ( ( times_times_nat @ SV26 @ SV135 )
= ( times_times_nat @ SV171 @ SV135 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV26 @ SV135 )
!= ( times_times_nat @ SV171 @ SV135 ) )
| ~ ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1331]) ).
thf(1458,plain,
! [SV171: nat,SV26: nat,SV135: nat] :
( ( ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV26 @ SV135 )
!= ( times_times_nat @ SV171 @ SV135 ) )
| ~ ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1331]) ).
thf(1459,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ( times_times_a @ SV27 @ SV136 )
= ( times_times_a @ SV27 @ SV172 ) )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV27 @ SV136 )
!= ( times_times_a @ SV27 @ SV172 ) )
| ~ ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1332]) ).
thf(1460,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV27 @ SV136 )
!= ( times_times_a @ SV27 @ SV172 ) )
| ~ ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1332]) ).
thf(1461,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ( times_times_poly_a @ SV28 @ SV137 )
= ( times_times_poly_a @ SV28 @ SV173 ) )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV28 @ SV137 )
!= ( times_times_poly_a @ SV28 @ SV173 ) )
| ~ ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1333]) ).
thf(1462,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV28 @ SV137 )
!= ( times_times_poly_a @ SV28 @ SV173 ) )
| ~ ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1333]) ).
thf(1463,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ( times_times_nat @ SV29 @ SV138 )
= ( times_times_nat @ SV29 @ SV174 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV29 @ SV138 )
!= ( times_times_nat @ SV29 @ SV174 ) )
| ~ ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1334]) ).
thf(1464,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV29 @ SV138 )
!= ( times_times_nat @ SV29 @ SV174 ) )
| ~ ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1334]) ).
thf(1465,plain,
! [SV139: a,SV30: a] :
( ( ( ( ( times_times_a @ SV30 @ SV139 )
!= zero_zero_a )
| ~ ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) ) )
= $false )
| ( ( ( times_times_a @ SV30 @ SV139 )
= zero_zero_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1466,plain,
! [SV139: a,SV30: a] :
( ( ( SV30 = zero_zero_a )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV30 @ SV139 )
!= zero_zero_a )
| ~ ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1336]) ).
thf(1467,plain,
! [SV30: a,SV139: a] :
( ( ( SV139 = zero_zero_a )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV30 @ SV139 )
!= zero_zero_a )
| ~ ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1336]) ).
thf(1468,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ( ( times_times_poly_a @ SV31 @ SV140 )
!= zero_zero_poly_a )
| ~ ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) ) )
= $false )
| ( ( ( times_times_poly_a @ SV31 @ SV140 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1469,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( SV31 = zero_zero_poly_a )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV31 @ SV140 )
!= zero_zero_poly_a )
| ~ ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1338]) ).
thf(1470,plain,
! [SV31: poly_a,SV140: poly_a] :
( ( ( SV140 = zero_zero_poly_a )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV31 @ SV140 )
!= zero_zero_poly_a )
| ~ ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1338]) ).
thf(1471,plain,
! [SV141: nat,SV32: nat] :
( ( ( ( ( times_times_nat @ SV32 @ SV141 )
!= zero_zero_nat )
| ~ ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV32 @ SV141 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1472,plain,
! [SV141: nat,SV32: nat] :
( ( ( SV32 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV32 @ SV141 )
!= zero_zero_nat )
| ~ ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1340]) ).
thf(1473,plain,
! [SV32: nat,SV141: nat] :
( ( ( SV141 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV32 @ SV141 )
!= zero_zero_nat )
| ~ ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1340]) ).
thf(1474,plain,
! [SV39: poly_a] :
( ( ( ( uminus_uminus_poly_a @ SV39 )
!= SV39 )
= $false )
| ( ( ( uminus_uminus_poly_a @ SV39 )
= SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1341]) ).
thf(1475,plain,
! [SV39: poly_a] :
( ( ( SV39 != zero_zero_poly_a )
= $false )
| ( ( ( uminus_uminus_poly_a @ SV39 )
= SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1341]) ).
thf(1476,plain,
! [SV39: poly_a] :
( ( ( ( uminus_uminus_poly_a @ SV39 )
!= SV39 )
= $false )
| ( ( SV39 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1342]) ).
thf(1477,plain,
! [SV39: poly_a] :
( ( ( SV39 != zero_zero_poly_a )
= $false )
| ( ( SV39 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1342]) ).
thf(1478,plain,
! [SV40: a] :
( ( ( ( uminus_uminus_a @ SV40 )
!= SV40 )
= $false )
| ( ( ( uminus_uminus_a @ SV40 )
= SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1343]) ).
thf(1479,plain,
! [SV40: a] :
( ( ( SV40 != zero_zero_a )
= $false )
| ( ( ( uminus_uminus_a @ SV40 )
= SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1343]) ).
thf(1480,plain,
! [SV40: a] :
( ( ( ( uminus_uminus_a @ SV40 )
!= SV40 )
= $false )
| ( ( SV40 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1481,plain,
! [SV40: a] :
( ( ( SV40 != zero_zero_a )
= $false )
| ( ( SV40 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1482,plain,
! [SV41: poly_a] :
( ( ( SV41
!= ( uminus_uminus_poly_a @ SV41 ) )
= $false )
| ( ( SV41
= ( uminus_uminus_poly_a @ SV41 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1345]) ).
thf(1483,plain,
! [SV41: poly_a] :
( ( ( SV41 != zero_zero_poly_a )
= $false )
| ( ( SV41
= ( uminus_uminus_poly_a @ SV41 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1345]) ).
thf(1484,plain,
! [SV41: poly_a] :
( ( ( SV41
!= ( uminus_uminus_poly_a @ SV41 ) )
= $false )
| ( ( SV41 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1346]) ).
thf(1485,plain,
! [SV41: poly_a] :
( ( ( SV41 != zero_zero_poly_a )
= $false )
| ( ( SV41 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1346]) ).
thf(1486,plain,
! [SV42: a] :
( ( ( SV42
!= ( uminus_uminus_a @ SV42 ) )
= $false )
| ( ( SV42
= ( uminus_uminus_a @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1347]) ).
thf(1487,plain,
! [SV42: a] :
( ( ( SV42 != zero_zero_a )
= $false )
| ( ( SV42
= ( uminus_uminus_a @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1347]) ).
thf(1488,plain,
! [SV42: a] :
( ( ( SV42
!= ( uminus_uminus_a @ SV42 ) )
= $false )
| ( ( SV42 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1348]) ).
thf(1489,plain,
! [SV42: a] :
( ( ( SV42 != zero_zero_a )
= $false )
| ( ( SV42 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1348]) ).
thf(1490,plain,
! [SV43: poly_a] :
( ( ( ( uminus_uminus_poly_a @ SV43 )
!= zero_zero_poly_a )
= $false )
| ( ( ( uminus_uminus_poly_a @ SV43 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1349]) ).
thf(1491,plain,
! [SV43: poly_a] :
( ( ( SV43 != zero_zero_poly_a )
= $false )
| ( ( ( uminus_uminus_poly_a @ SV43 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1349]) ).
thf(1492,plain,
! [SV43: poly_a] :
( ( ( ( uminus_uminus_poly_a @ SV43 )
!= zero_zero_poly_a )
= $false )
| ( ( SV43 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1350]) ).
thf(1493,plain,
! [SV43: poly_a] :
( ( ( SV43 != zero_zero_poly_a )
= $false )
| ( ( SV43 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1350]) ).
thf(1494,plain,
! [SV44: a] :
( ( ( ( uminus_uminus_a @ SV44 )
!= zero_zero_a )
= $false )
| ( ( ( uminus_uminus_a @ SV44 )
= zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1351]) ).
thf(1495,plain,
! [SV44: a] :
( ( ( SV44 != zero_zero_a )
= $false )
| ( ( ( uminus_uminus_a @ SV44 )
= zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1351]) ).
thf(1496,plain,
! [SV44: a] :
( ( ( ( uminus_uminus_a @ SV44 )
!= zero_zero_a )
= $false )
| ( ( SV44 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1352]) ).
thf(1497,plain,
! [SV44: a] :
( ( ( SV44 != zero_zero_a )
= $false )
| ( ( SV44 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1352]) ).
thf(1498,plain,
! [SV45: poly_a] :
( ( ( zero_zero_poly_a
!= ( uminus_uminus_poly_a @ SV45 ) )
= $false )
| ( ( zero_zero_poly_a
= ( uminus_uminus_poly_a @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1353]) ).
thf(1499,plain,
! [SV45: poly_a] :
( ( ( zero_zero_poly_a != SV45 )
= $false )
| ( ( zero_zero_poly_a
= ( uminus_uminus_poly_a @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1353]) ).
thf(1500,plain,
! [SV45: poly_a] :
( ( ( zero_zero_poly_a
!= ( uminus_uminus_poly_a @ SV45 ) )
= $false )
| ( ( zero_zero_poly_a = SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1354]) ).
thf(1501,plain,
! [SV45: poly_a] :
( ( ( zero_zero_poly_a != SV45 )
= $false )
| ( ( zero_zero_poly_a = SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1354]) ).
thf(1502,plain,
! [SV46: a] :
( ( ( zero_zero_a
!= ( uminus_uminus_a @ SV46 ) )
= $false )
| ( ( zero_zero_a
= ( uminus_uminus_a @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1355]) ).
thf(1503,plain,
! [SV46: a] :
( ( ( zero_zero_a != SV46 )
= $false )
| ( ( zero_zero_a
= ( uminus_uminus_a @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1355]) ).
thf(1504,plain,
! [SV46: a] :
( ( ( zero_zero_a
!= ( uminus_uminus_a @ SV46 ) )
= $false )
| ( ( zero_zero_a = SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1356]) ).
thf(1505,plain,
! [SV46: a] :
( ( ( zero_zero_a != SV46 )
= $false )
| ( ( zero_zero_a = SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1356]) ).
thf(1506,plain,
! [SV142: list_a,SV48: list_a] :
( ( ( ( SV48
!= ( append_a @ SV142 @ SV48 ) )
| ( SV142 != nil_a ) )
= $false )
| ( ( SV48
= ( append_a @ SV142 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1357]) ).
thf(1507,plain,
! [SV142: list_a,SV48: list_a] :
( ( ( ( SV48
!= ( append_a @ SV142 @ SV48 ) )
| ( SV142 != nil_a ) )
= $false )
| ( ( SV142 = nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1508,plain,
! [SV143: list_a,SV49: list_a] :
( ( ( ( ( append_a @ SV49 @ SV143 )
!= SV143 )
| ( SV49 != nil_a ) )
= $false )
| ( ( ( append_a @ SV49 @ SV143 )
= SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1509,plain,
! [SV143: list_a,SV49: list_a] :
( ( ( ( ( append_a @ SV49 @ SV143 )
!= SV143 )
| ( SV49 != nil_a ) )
= $false )
| ( ( SV49 = nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1510,plain,
! [SV144: list_a,SV50: list_a] :
( ( ( ( SV50
!= ( append_a @ SV50 @ SV144 ) )
| ( SV144 != nil_a ) )
= $false )
| ( ( SV50
= ( append_a @ SV50 @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1511,plain,
! [SV144: list_a,SV50: list_a] :
( ( ( ( SV50
!= ( append_a @ SV50 @ SV144 ) )
| ( SV144 != nil_a ) )
= $false )
| ( ( SV144 = nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1512,plain,
! [SV145: list_a,SV51: list_a] :
( ( ( ( ( append_a @ SV51 @ SV145 )
!= SV51 )
| ( SV145 != nil_a ) )
= $false )
| ( ( ( append_a @ SV51 @ SV145 )
= SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1513,plain,
! [SV145: list_a,SV51: list_a] :
( ( ( ( ( append_a @ SV51 @ SV145 )
!= SV51 )
| ( SV145 != nil_a ) )
= $false )
| ( ( SV145 = nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1514,plain,
! [SV53: poly_a] :
( ( ( zero_zero_poly_a != SV53 )
= $false )
| ( ( zero_zero_poly_a = SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1515,plain,
! [SV53: poly_a] :
( ( ( SV53 != zero_zero_poly_a )
= $false )
| ( ( zero_zero_poly_a = SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1516,plain,
! [SV53: poly_a] :
( ( ( zero_zero_poly_a != SV53 )
= $false )
| ( ( SV53 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1366]) ).
thf(1517,plain,
! [SV53: poly_a] :
( ( ( SV53 != zero_zero_poly_a )
= $false )
| ( ( SV53 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1366]) ).
thf(1518,plain,
! [SV54: a] :
( ( ( zero_zero_a != SV54 )
= $false )
| ( ( zero_zero_a = SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1367]) ).
thf(1519,plain,
! [SV54: a] :
( ( ( SV54 != zero_zero_a )
= $false )
| ( ( zero_zero_a = SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1367]) ).
thf(1520,plain,
! [SV54: a] :
( ( ( zero_zero_a != SV54 )
= $false )
| ( ( SV54 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1368]) ).
thf(1521,plain,
! [SV54: a] :
( ( ( SV54 != zero_zero_a )
= $false )
| ( ( SV54 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1368]) ).
thf(1522,plain,
! [SV55: nat] :
( ( ( zero_zero_nat != SV55 )
= $false )
| ( ( zero_zero_nat = SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1369]) ).
thf(1523,plain,
! [SV55: nat] :
( ( ( SV55 != zero_zero_nat )
= $false )
| ( ( zero_zero_nat = SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1369]) ).
thf(1524,plain,
! [SV55: nat] :
( ( ( zero_zero_nat != SV55 )
= $false )
| ( ( SV55 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1370]) ).
thf(1525,plain,
! [SV55: nat] :
( ( ( SV55 != zero_zero_nat )
= $false )
| ( ( SV55 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1370]) ).
thf(1526,plain,
! [SV57: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV57 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1371]) ).
thf(1527,plain,
! [SV57: nat] :
( ( ( ~ ( ( SV57 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1371]) ).
thf(1528,plain,
! [SV57: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV57 )
| ~ ( ( SV57 != zero_zero_nat ) ) )
= $false )
| ( ( SV57 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1529,plain,
! [SV194: a,SV61: a,SV175: a] :
( ( ( ( ( times_times_a @ SV175 @ SV61 )
= ( times_times_a @ SV194 @ SV61 ) )
| ( SV175 = SV194 ) )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV175 @ SV61 )
!= ( times_times_a @ SV194 @ SV61 ) )
| ( SV175 != SV194 ) ) )
= $true )
| ( ( SV61 = zero_zero_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1530,plain,
! [SV195: poly_a,SV62: poly_a,SV176: poly_a] :
( ( ( ( ( times_times_poly_a @ SV176 @ SV62 )
= ( times_times_poly_a @ SV195 @ SV62 ) )
| ( SV176 = SV195 ) )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV176 @ SV62 )
!= ( times_times_poly_a @ SV195 @ SV62 ) )
| ( SV176 != SV195 ) ) )
= $true )
| ( ( SV62 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1531,plain,
! [SV196: nat,SV63: nat,SV177: nat] :
( ( ( ( ( times_times_nat @ SV177 @ SV63 )
= ( times_times_nat @ SV196 @ SV63 ) )
| ( SV177 = SV196 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV177 @ SV63 )
!= ( times_times_nat @ SV196 @ SV63 ) )
| ( SV177 != SV196 ) ) )
= $true )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1375]) ).
thf(1532,plain,
! [SV197: a,SV178: a,SV64: a] :
( ( ( ( ( times_times_a @ SV64 @ SV178 )
= ( times_times_a @ SV64 @ SV197 ) )
| ( SV178 = SV197 ) )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV64 @ SV178 )
!= ( times_times_a @ SV64 @ SV197 ) )
| ( SV178 != SV197 ) ) )
= $true )
| ( ( SV64 = zero_zero_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1533,plain,
! [SV198: poly_a,SV179: poly_a,SV65: poly_a] :
( ( ( ( ( times_times_poly_a @ SV65 @ SV179 )
= ( times_times_poly_a @ SV65 @ SV198 ) )
| ( SV179 = SV198 ) )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV65 @ SV179 )
!= ( times_times_poly_a @ SV65 @ SV198 ) )
| ( SV179 != SV198 ) ) )
= $true )
| ( ( SV65 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1534,plain,
! [SV199: nat,SV180: nat,SV66: nat] :
( ( ( ( ( times_times_nat @ SV66 @ SV180 )
= ( times_times_nat @ SV66 @ SV199 ) )
| ( SV180 = SV199 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV66 @ SV180 )
!= ( times_times_nat @ SV66 @ SV199 ) )
| ( SV180 != SV199 ) ) )
= $true )
| ( ( SV66 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1535,plain,
! [SV186: list_a,SV80: a,SV216: list_a,SV153: list_a,SV212: list_a] :
( ( ( ( SV212
!= ( append_a @ SV153 @ SV216 ) )
| ( ( cons_a @ SV80 @ SV212 )
= ( append_a @ SV186 @ SV216 ) ) )
= $true )
| ( ( ( cons_a @ SV80 @ SV153 )
= SV186 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1536,plain,
! [SV85: list_a] :
( ( ( SV85 != nil_a )
= $false )
| ( ( SV85 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1381]) ).
thf(1537,plain,
! [SV85: list_a] :
( ( ( ~ ( null_a @ SV85 ) )
= $false )
| ( ( SV85 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1381]) ).
thf(1538,plain,
! [SV85: list_a] :
( ( ( SV85 != nil_a )
= $false )
| ( ( null_a @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1382]) ).
thf(1539,plain,
! [SV85: list_a] :
( ( ( ~ ( null_a @ SV85 ) )
= $false )
| ( ( null_a @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1382]) ).
thf(1540,plain,
! [SV187: nat,SV156: nat,SV86: nat] :
( ( ( ( times_times_nat @ SV86 @ SV156 )
= ( times_times_nat @ SV187 @ SV156 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV86 @ SV156 )
!= ( times_times_nat @ SV187 @ SV156 ) )
| ~ ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1383]) ).
thf(1541,plain,
! [SV156: nat,SV187: nat,SV86: nat] :
( ( ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV86 @ SV156 )
!= ( times_times_nat @ SV187 @ SV156 ) )
| ~ ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1383]) ).
thf(1542,plain,
! [SV87: nat] :
( ( ( ~ ( ( SV87 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV87 ) )
= $false )
| ( ( SV87 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1543,plain,
! [SV87: nat] :
( ( ( ~ ( ( SV87 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1385]) ).
thf(1544,plain,
! [SV87: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV87 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1385]) ).
thf(1545,plain,
! [SV89: nat] :
( ( ( ~ ( ( SV89 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV89 ) )
= $false )
| ( ( SV89 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1546,plain,
! [SV89: nat] :
( ( ( ~ ( ( SV89 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1387]) ).
thf(1547,plain,
! [SV89: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV89 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1387]) ).
thf(1548,plain,
! [SV157: nat,SV90: nat] :
( ( ( ( ( times_times_nat @ SV90 @ SV157 )
!= zero_zero_nat )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV90 @ SV157 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1549,plain,
! [SV157: nat,SV90: nat] :
( ( ( SV90 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV90 @ SV157 )
!= zero_zero_nat )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1389]) ).
thf(1550,plain,
! [SV90: nat,SV157: nat] :
( ( ( SV157 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV90 @ SV157 )
!= zero_zero_nat )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1389]) ).
thf(1551,plain,
! [SV188: nat,SV158: nat,SV92: nat] :
( ( ( ( times_times_nat @ SV92 @ SV158 )
= ( times_times_nat @ SV92 @ SV188 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV92 @ SV158 )
!= ( times_times_nat @ SV92 @ SV188 ) )
| ~ ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1390]) ).
thf(1552,plain,
! [SV92: nat,SV188: nat,SV158: nat] :
( ( ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV92 @ SV158 )
!= ( times_times_nat @ SV92 @ SV188 ) )
| ~ ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1390]) ).
thf(1553,plain,
! [SV94: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV94 )
| ( SV94 != zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1391]) ).
thf(1554,plain,
! [SV94: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV94 ) )
= $false )
| ( ( SV94 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1392]) ).
thf(1555,plain,
! [SV94: nat] :
( ( ( SV94 != zero_zero_nat )
= $false )
| ( ( SV94 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1392]) ).
thf(1556,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ( times_times_nat @ SV100 @ SV160 )
= ( times_times_nat @ SV100 @ SV189 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV100 @ SV160 )
!= ( times_times_nat @ SV100 @ SV189 ) )
| ~ ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1393]) ).
thf(1557,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV100 @ SV160 )
!= ( times_times_nat @ SV100 @ SV189 ) )
| ~ ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1393]) ).
thf(1558,plain,
! [SV101: list_a > $o] :
( ( ( ~ ( ( ( sK40_X2 @ SV101 )
!= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
| ~ ~ ( ~ ( ( ( sK40_X2 @ SV101 )
= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
| ~ ~ ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) ) ) )
= $false )
| ( ( ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1559,plain,
! [SV213: a,SV201: a] :
( ( ( SV201 = zero_zero_a )
= $false )
| ( ( ( times_times_a @ SV201 @ SV213 )
= zero_zero_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1395]) ).
thf(1560,plain,
! [SV202: a,SV209: a] :
( ( ( SV209 = zero_zero_a )
= $false )
| ( ( ( times_times_a @ SV202 @ SV209 )
= zero_zero_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1561,plain,
! [SV217: a,SV102: list_a > $o] :
( ( ( ! [SY553: list_a] :
( ( sK25_SY345 @ SV102 )
!= ( cons_a @ SV217 @ SY553 ) ) )
= $true )
| ( ( SV102 @ ( sK25_SY345 @ SV102 ) )
= $true )
| ( ( ~ ( SV102 @ nil_a )
| ! [SY475: list_a] : ( SV102 @ SY475 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1562,plain,
! [SV102: list_a > $o] :
( ( ( ~ ( SV102 @ nil_a ) )
= $true )
| ( ( ! [SY475: list_a] : ( SV102 @ SY475 ) )
= $true )
| ( ( SV102 @ ( cons_a @ ( sK24_X2 @ SV102 ) @ ( sK25_SY345 @ SV102 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1398]) ).
thf(1563,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ( ( append_a @ SV103 @ SV161 )
!= nil_a )
| ~ ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) )
= $false )
| ( ( ( append_a @ SV103 @ SV161 )
= nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1564,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ( SV103 != nil_a )
| ( SV161 != nil_a ) )
= $true )
| ( ( ~ ( ( ( append_a @ SV103 @ SV161 )
!= nil_a )
| ~ ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1400]) ).
thf(1565,plain,
! [SV162: a > a,SV104: ( a > a ) > list_a > list_a > $o] :
( ( ( ~ ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) @ ( cons_a @ ( sK54_F2 @ SV162 @ SV104 @ ( sK55_SY373 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) ) ) )
= $false )
| ( ( ! [SY529: list_a,SY530: list_a] : ( SV104 @ SV162 @ SY529 @ SY530 ) )
= $true )
| ( ( SV104 @ ( sK58_F2 @ SV162 @ SV104 ) @ nil_a @ ( sK59_SY379 @ SV162 @ SV104 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1401]) ).
thf(1566,plain,
! [SV162: a > a,SV104: ( a > a ) > list_a > list_a > $o] :
( ( ( ~ ~ ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( cons_a @ ( sK55_SY373 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) ) )
= $false )
| ( ( ! [SY529: list_a,SY530: list_a] : ( SV104 @ SV162 @ SY529 @ SY530 ) )
= $true )
| ( ( SV104 @ ( sK58_F2 @ SV162 @ SV104 ) @ nil_a @ ( sK59_SY379 @ SV162 @ SV104 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1401]) ).
thf(1567,plain,
! [SV203: a,SV190: list_a,SV163: a,SV105: list_a] :
( ( ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
| ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) )
= $false )
| ( ( ~ ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
!= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
| ~ ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1568,plain,
! [SV106: ( a > a > $o ) > list_a > $o] :
( ( ( SV106 @ ( sK36_P5 @ SV106 ) @ ( sK38_SY361 @ SV106 ) )
= $true )
| ( ( ! [SY483: a > a > $o,SY484: list_a] : ( SV106 @ SY483 @ SY484 ) )
= $true )
| ( ( SV106 @ ( sK39_P5 @ SV106 ) @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1403]) ).
thf(1569,plain,
! [SV106: ( a > a > $o ) > list_a > $o] :
( ( ( ~ ( SV106 @ ( sK36_P5 @ SV106 ) @ ( cons_a @ ( sK37_SY359 @ SV106 ) @ ( sK38_SY361 @ SV106 ) ) ) )
= $true )
| ( ( ! [SY483: a > a > $o,SY484: list_a] : ( SV106 @ SY483 @ SY484 ) )
= $true )
| ( ( SV106 @ ( sK39_P5 @ SV106 ) @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1404]) ).
thf(1570,plain,
! [SV107: nat > $o] :
( ( ( ord_less_nat @ zero_zero_nat @ ( sK1_N2 @ SV107 ) )
= $true )
| ( ( ! [SY486: nat] : ( SV107 @ SY486 ) )
= $true )
| ( ( SV107 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1405]) ).
thf(1571,plain,
! [SV107: nat > $o] :
( ( ( ~ ( ~ ~ ( SV107 @ ( sK1_N2 @ SV107 ) )
| ~ ! [SY485: nat] :
( ~ ( ord_less_nat @ SY485 @ ( sK1_N2 @ SV107 ) )
| ( SV107 @ SY485 ) ) ) )
= $true )
| ( ( ! [SY486: nat] : ( SV107 @ SY486 ) )
= $true )
| ( ( SV107 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1406]) ).
thf(1572,plain,
! [SV108: list_a > $o] :
( ( ( SV108 @ ( sK5_SY329 @ SV108 ) )
= $true )
| ( ( ! [SY487: list_a] : ( SV108 @ SY487 ) )
= $true )
| ( ( SV108 @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1407]) ).
thf(1573,plain,
! [SV108: list_a > $o] :
( ( ( ~ ( SV108 @ ( cons_a @ ( sK4_X1 @ SV108 ) @ ( sK5_SY329 @ SV108 ) ) ) )
= $true )
| ( ( ! [SY487: list_a] : ( SV108 @ SY487 ) )
= $true )
| ( ( SV108 @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1408]) ).
thf(1574,plain,
! [SV109: list_a > $o] :
( ( ( ~ ( SV109 @ ( sK20_SY343 @ SV109 ) )
| ~ ~ ( ~ ( SV109 @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) )
| ~ ~ ( SV109 @ ( cons_a @ ( sK18_X2 @ SV109 ) @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) ) ) ) )
= $false )
| ( ( ! [SY488: list_a] : ( SV109 @ SY488 ) )
= $true )
| ( ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
= $false )
| ( ( SV109 @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1409]) ).
thf(1575,plain,
! [SV204: list_a,SV191: a,SV164: list_a,SV110: a] :
( ( ( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SV204 ) )
| ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) )
= $false )
| ( ( ~ ( ( ( cons_a @ SV110 @ SV164 )
!= ( cons_a @ SV191 @ SV204 ) )
| ~ ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1576,plain,
! [SV111: list_a > list_a > $o] :
( ( ( SV111 @ ( sK16_SY340 @ SV111 ) @ ( sK15_SY338 @ SV111 ) )
= $true )
| ( ( ! [SY492: list_a,SY493: list_a] : ( SV111 @ SY492 @ SY493 ) )
= $true )
| ( ( SV111 @ nil_a @ ( sK17_X_1 @ SV111 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1411]) ).
thf(1577,plain,
! [SV111: list_a > list_a > $o] :
( ( ( ~ ( SV111 @ ( cons_a @ ( sK14_X2 @ SV111 ) @ ( sK15_SY338 @ SV111 ) ) @ ( sK16_SY340 @ SV111 ) ) )
= $true )
| ( ( ! [SY492: list_a,SY493: list_a] : ( SV111 @ SY492 @ SY493 ) )
= $true )
| ( ( SV111 @ nil_a @ ( sK17_X_1 @ SV111 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1412]) ).
thf(1578,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ( ( pCons_a @ SV112 @ SV165 )
!= zero_zero_poly_a )
| ~ ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) )
= $false )
| ( ( ( pCons_a @ SV112 @ SV165 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1413]) ).
thf(1579,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) )
= $true )
| ( ( ~ ( ( ( pCons_a @ SV112 @ SV165 )
!= zero_zero_poly_a )
| ~ ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1414]) ).
thf(1580,plain,
! [SV214: nat,SV205: nat] :
( ( ( SV205 = zero_zero_nat )
= $false )
| ( ( ( times_times_nat @ SV205 @ SV214 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1581,plain,
! [SV206: nat,SV210: nat] :
( ( ( SV210 = zero_zero_nat )
= $false )
| ( ( ( times_times_nat @ SV206 @ SV210 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1582,plain,
! [SV113: poly_a > poly_a > $o] :
( ( ( SV113 @ ( sK85_SY400 @ SV113 ) @ ( sK87_SY405 @ SV113 ) )
= $true )
| ( ( ! [SY495: poly_a,SY496: poly_a] : ( SV113 @ SY495 @ SY496 ) )
= $true )
| ( ( SV113 @ zero_zero_poly_a @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1417]) ).
thf(1583,plain,
! [SV113: poly_a > poly_a > $o] :
( ( ( ~ ( SV113 @ ( pCons_a @ ( sK84_A2 @ SV113 ) @ ( sK85_SY400 @ SV113 ) ) @ ( pCons_a @ ( sK86_SY403 @ SV113 ) @ ( sK87_SY405 @ SV113 ) ) ) )
= $true )
| ( ( ! [SY495: poly_a,SY496: poly_a] : ( SV113 @ SY495 @ SY496 ) )
= $true )
| ( ( SV113 @ zero_zero_poly_a @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1418]) ).
thf(1584,plain,
! [SV114: list_a > list_a > $o] :
( ( ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a )
= $false )
| ( ( ~ ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) )
| ! [SY497: list_a,SY498: list_a] : ( SV114 @ SY497 @ SY498 ) )
= $true )
| ( ( SV114 @ ( sK72_SY386 @ SV114 ) @ ( sK74_SY391 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1585,plain,
! [SV114: list_a > list_a > $o] :
( ( ( ~ ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a ) )
= $true )
| ( ( ~ ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) )
| ! [SY497: list_a,SY498: list_a] : ( SV114 @ SY497 @ SY498 ) )
= $true )
| ( ( SV114 @ ( cons_a @ ( sK71_X2 @ SV114 ) @ ( sK72_SY386 @ SV114 ) ) @ ( cons_a @ ( sK73_SY389 @ SV114 ) @ ( sK74_SY391 @ SV114 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1420]) ).
thf(1586,plain,
! [SV115: list_a,SV192: list_a > $o] :
( ( ( ~ ( ( ( sK52_SY372 @ SV192 @ SV115 )
!= nil_a ) )
| ~ ~ ( ~ ( SV192 @ ( sK52_SY372 @ SV192 @ SV115 ) )
| ~ ~ ( SV192 @ ( cons_a @ ( sK51_X2 @ SV192 @ SV115 ) @ ( sK52_SY372 @ SV192 @ SV115 ) ) ) ) )
= $false )
| ( ( SV192 @ SV115 )
= $true )
| ( ( SV192 @ ( cons_a @ ( sK53_X2 @ SV192 @ SV115 ) @ nil_a ) )
= $false )
| ( ( SV115 = nil_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1421]) ).
thf(1587,plain,
! [SV218: poly_a,SV116: poly_a > $o] :
( ( ( SV116 @ SV218 )
= $true )
| ( ( SV116 @ ( sK83_SY399 @ SV116 ) )
= $true )
| ( ( ( sK83_SY399 @ SV116 )
= zero_zero_poly_a )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1588,plain,
! [SV219: poly_a,SV116: poly_a > $o] :
( ( ( SV116 @ SV219 )
= $true )
| ( ( SV116 @ ( pCons_a @ ( sK82_A2 @ SV116 ) @ ( sK83_SY399 @ SV116 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1589,plain,
! [SV117: ( a > a > $o ) > list_a > $o] :
( ( ( ~ ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) )
| ~ ~ ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK45_SY365 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) ) ) )
= $false )
| ( ( ! [SY501: a > a > $o,SY502: list_a] : ( SV117 @ SY501 @ SY502 ) )
= $true )
| ( ( SV117 @ ( sK48_P5 @ SV117 ) @ ( cons_a @ ( sK49_SY371 @ SV117 ) @ nil_a ) )
= $false )
| ( ( SV117 @ ( sK50_P5 @ SV117 ) @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1590,plain,
! [SV118: list_a > list_a > $o] :
( ( ( ~ ( SV118 @ ( sK27_SY350 @ SV118 ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) )
| ~ ~ ( ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( sK29_SY355 @ SV118 ) )
| ~ ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) ) ) )
= $false )
| ( ( ! [SY503: list_a,SY504: list_a] : ( SV118 @ SY503 @ SY504 ) )
= $true )
| ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1591,plain,
! [SV215: poly_a,SV207: poly_a] :
( ( ( SV207 = zero_zero_poly_a )
= $false )
| ( ( ( times_times_poly_a @ SV207 @ SV215 )
= zero_zero_poly_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1592,plain,
! [SV208: poly_a,SV211: poly_a] :
( ( ( SV211 = zero_zero_poly_a )
= $false )
| ( ( ( times_times_poly_a @ SV208 @ SV211 )
= zero_zero_poly_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1427]) ).
thf(1593,plain,
! [SV119: list_a > list_a > $o] :
( ( ( SV119 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SV119 ) @ ( sK11_SY336 @ SV119 ) ) )
= $false )
| ( ( ~ ( ~ ( SV119 @ ( sK7_SY330 @ SV119 ) @ ( sK9_SY335 @ SV119 ) )
| ~ ~ ( SV119 @ ( cons_a @ ( sK6_X2 @ SV119 ) @ ( sK7_SY330 @ SV119 ) ) @ ( cons_a @ ( sK8_SY333 @ SV119 ) @ ( sK9_SY335 @ SV119 ) ) ) )
| ! [SY505: list_a,SY506: list_a] : ( SV119 @ SY505 @ SY506 ) )
= $true )
| ( ( SV119 @ ( cons_a @ ( sK12_X2 @ SV119 ) @ ( sK13_SY337 @ SV119 ) ) @ nil_a )
= $false )
| ( ( SV119 @ nil_a @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1428]) ).
thf(1594,plain,
! [SV120: poly_a > $o] :
( ( ( ( ( sK88_A2 @ SV120 )
!= zero_zero_a )
| ( ( sK89_SY406 @ SV120 )
!= zero_zero_poly_a ) )
= $true )
| ( ( ! [SY507: poly_a] : ( SV120 @ SY507 ) )
= $true )
| ( ( SV120 @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1429]) ).
thf(1595,plain,
! [SV120: poly_a > $o] :
( ( ( ~ ( ~ ( SV120 @ ( sK89_SY406 @ SV120 ) )
| ~ ~ ( SV120 @ ( pCons_a @ ( sK88_A2 @ SV120 ) @ ( sK89_SY406 @ SV120 ) ) ) ) )
= $true )
| ( ( ! [SY507: poly_a] : ( SV120 @ SY507 ) )
= $true )
| ( ( SV120 @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1430]) ).
thf(1596,plain,
! [SV121: list_a] :
( ( ( ~ ( ( SV121 != nil_a ) )
| ~ ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) )
= $false )
| ( ( SV121 = nil_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1597,plain,
! [SV220: a,SV121: list_a] :
( ( ( ~ ~ ! [SY554: list_a] :
( SV121
!= ( cons_a @ SV220 @ SY554 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV121 != nil_a ) )
| ~ ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1598,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( ( nil_a
!= ( append_a @ SV122 @ SV166 ) )
| ~ ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) )
= $false )
| ( ( nil_a
= ( append_a @ SV122 @ SV166 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1599,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( ( SV122 != nil_a )
| ( SV166 != nil_a ) )
= $true )
| ( ( ~ ( ( nil_a
!= ( append_a @ SV122 @ SV166 ) )
| ~ ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1434]) ).
thf(1600,plain,
! [SV123: list_a > list_a > $o] :
( ( ( ~ ( SV123 @ ( sK76_SY392 @ SV123 ) @ ( sK78_SY397 @ SV123 ) )
| ~ ~ ( SV123 @ ( cons_a @ ( sK75_X2 @ SV123 ) @ ( sK76_SY392 @ SV123 ) ) @ ( cons_a @ ( sK77_SY395 @ SV123 ) @ ( sK78_SY397 @ SV123 ) ) ) )
= $false )
| ( ( ! [SY511: list_a,SY512: list_a] : ( SV123 @ SY511 @ SY512 ) )
= $true )
| ( ( SV123 @ nil_a @ ( cons_a @ ( sK79_V @ SV123 ) @ ( sK80_SY398 @ SV123 ) ) )
= $false )
| ( ( SV123 @ ( sK81_Xs2 @ SV123 ) @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1435]) ).
thf(1601,plain,
! [SV124: list_a > $o] :
( ( ( SV124 @ ( sK63_SY381 @ SV124 ) )
= $true )
| ( ( ! [SY513: list_a] : ( SV124 @ SY513 ) )
= $true )
| ( ( SV124 @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1436]) ).
thf(1602,plain,
! [SV124: list_a > $o] :
( ( ( ~ ( SV124 @ ( cons_a @ ( sK62_X2 @ SV124 ) @ ( sK63_SY381 @ SV124 ) ) ) )
= $true )
| ( ( ! [SY513: list_a] : ( SV124 @ SY513 ) )
= $true )
| ( ( SV124 @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1437]) ).
thf(1603,plain,
! [SV193: poly_a,SV126: poly_a] :
( ( ( SV126 = SV193 )
= $false )
| ( ( ~ ( ( SV126 != SV193 )
| ( ( coeffs_a @ SV126 )
!= ( coeffs_a @ SV193 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1438]) ).
thf(1604,plain,
! [SV193: poly_a,SV126: poly_a] :
( ( ( ( coeffs_a @ SV126 )
= ( coeffs_a @ SV193 ) )
= $false )
| ( ( ~ ( ( SV126 != SV193 )
| ( ( coeffs_a @ SV126 )
!= ( coeffs_a @ SV193 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1438]) ).
thf(1605,plain,
! [SV128: poly_a] :
( ( ( ~ ( is_zero_a @ SV128 ) )
= $false )
| ( ( is_zero_a @ SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1606,plain,
! [SV128: poly_a] :
( ( ( ~ ( null_a @ ( coeffs_a @ SV128 ) ) )
= $false )
| ( ( is_zero_a @ SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1607,plain,
! [SV128: poly_a] :
( ( ( ~ ( is_zero_a @ SV128 ) )
= $false )
| ( ( null_a @ ( coeffs_a @ SV128 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1608,plain,
! [SV128: poly_a] :
( ( ( ~ ( null_a @ ( coeffs_a @ SV128 ) ) )
= $false )
| ( ( null_a @ ( coeffs_a @ SV128 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1609,plain,
! [SV8: poly_a] :
( ( ( ( coeffs_a @ SV8 )
= nil_a )
= $true )
| ( ( ( coeffs_a @ SV8 )
= nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1441]) ).
thf(1610,plain,
! [SV8: poly_a] :
( ( ( SV8 = zero_zero_poly_a )
= $true )
| ( ( ( coeffs_a @ SV8 )
= nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1442]) ).
thf(1611,plain,
! [SV8: poly_a] :
( ( ( ( coeffs_a @ SV8 )
= nil_a )
= $true )
| ( ( SV8 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1443]) ).
thf(1612,plain,
! [SV8: poly_a] :
( ( ( SV8 = zero_zero_poly_a )
= $true )
| ( ( SV8 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1444]) ).
thf(1613,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ( smult_a @ SV12 @ SV130 )
!= zero_zero_poly_a )
= $false )
| ( ( ( smult_a @ SV12 @ SV130 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1445]) ).
thf(1614,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ~ ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) ) )
= $false )
| ( ( ( smult_a @ SV12 @ SV130 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1445]) ).
thf(1615,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ( ( smult_a @ SV12 @ SV130 )
!= zero_zero_poly_a )
| ~ ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) ) )
= $false )
| ( ( SV12 = zero_zero_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1616,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ( ( smult_a @ SV12 @ SV130 )
!= zero_zero_poly_a )
| ~ ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) ) )
= $false )
| ( ( SV130 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1447]) ).
thf(1617,plain,
! [SV132: poly_a] :
( ( ( ~ ( is_zero_a @ SV132 ) )
= $false )
| ( ( is_zero_a @ SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1448]) ).
thf(1618,plain,
! [SV132: poly_a] :
( ( ( SV132 != zero_zero_poly_a )
= $false )
| ( ( is_zero_a @ SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1448]) ).
thf(1619,plain,
! [SV132: poly_a] :
( ( ( ~ ( is_zero_a @ SV132 ) )
= $false )
| ( ( SV132 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1449]) ).
thf(1620,plain,
! [SV132: poly_a] :
( ( ( SV132 != zero_zero_poly_a )
= $false )
| ( ( SV132 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1449]) ).
thf(1621,plain,
! [SV23: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV23 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1622,plain,
! [SV23: nat] :
( ( ( SV23 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1623,plain,
! [SV23: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV23 ) )
= $true )
| ( ( SV23 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1451]) ).
thf(1624,plain,
! [SV23: nat] :
( ( ( SV23 = zero_zero_nat )
= $true )
| ( ( SV23 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1452]) ).
thf(1625,plain,
! [SV169: a,SV133: a,SV24: a] :
( ( ( ( ( times_times_a @ SV24 @ SV133 )
!= ( times_times_a @ SV169 @ SV133 ) )
| ~ ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) ) )
= $false )
| ( ( ( times_times_a @ SV24 @ SV133 )
= ( times_times_a @ SV169 @ SV133 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1453]) ).
thf(1626,plain,
! [SV169: a,SV24: a,SV133: a] :
( ( ( SV133 = zero_zero_a )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV24 @ SV133 )
!= ( times_times_a @ SV169 @ SV133 ) )
| ~ ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1627,plain,
! [SV133: a,SV169: a,SV24: a] :
( ( ( SV24 = SV169 )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV24 @ SV133 )
!= ( times_times_a @ SV169 @ SV133 ) )
| ~ ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1628,plain,
! [SV170: poly_a,SV134: poly_a,SV25: poly_a] :
( ( ( ( ( times_times_poly_a @ SV25 @ SV134 )
!= ( times_times_poly_a @ SV170 @ SV134 ) )
| ~ ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) ) )
= $false )
| ( ( ( times_times_poly_a @ SV25 @ SV134 )
= ( times_times_poly_a @ SV170 @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1629,plain,
! [SV170: poly_a,SV25: poly_a,SV134: poly_a] :
( ( ( SV134 = zero_zero_poly_a )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV25 @ SV134 )
!= ( times_times_poly_a @ SV170 @ SV134 ) )
| ~ ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1456]) ).
thf(1630,plain,
! [SV134: poly_a,SV170: poly_a,SV25: poly_a] :
( ( ( SV25 = SV170 )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV25 @ SV134 )
!= ( times_times_poly_a @ SV170 @ SV134 ) )
| ~ ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1456]) ).
thf(1631,plain,
! [SV171: nat,SV135: nat,SV26: nat] :
( ( ( ( ( times_times_nat @ SV26 @ SV135 )
!= ( times_times_nat @ SV171 @ SV135 ) )
| ~ ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) ) )
= $false )
| ( ( ( times_times_nat @ SV26 @ SV135 )
= ( times_times_nat @ SV171 @ SV135 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1457]) ).
thf(1632,plain,
! [SV171: nat,SV26: nat,SV135: nat] :
( ( ( SV135 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV26 @ SV135 )
!= ( times_times_nat @ SV171 @ SV135 ) )
| ~ ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1633,plain,
! [SV135: nat,SV171: nat,SV26: nat] :
( ( ( SV26 = SV171 )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV26 @ SV135 )
!= ( times_times_nat @ SV171 @ SV135 ) )
| ~ ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1634,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ( ( times_times_a @ SV27 @ SV136 )
!= ( times_times_a @ SV27 @ SV172 ) )
| ~ ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) ) )
= $false )
| ( ( ( times_times_a @ SV27 @ SV136 )
= ( times_times_a @ SV27 @ SV172 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1459]) ).
thf(1635,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( SV27 = zero_zero_a )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV27 @ SV136 )
!= ( times_times_a @ SV27 @ SV172 ) )
| ~ ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1460]) ).
thf(1636,plain,
! [SV27: a,SV172: a,SV136: a] :
( ( ( SV136 = SV172 )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV27 @ SV136 )
!= ( times_times_a @ SV27 @ SV172 ) )
| ~ ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1460]) ).
thf(1637,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ( ( times_times_poly_a @ SV28 @ SV137 )
!= ( times_times_poly_a @ SV28 @ SV173 ) )
| ~ ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) ) )
= $false )
| ( ( ( times_times_poly_a @ SV28 @ SV137 )
= ( times_times_poly_a @ SV28 @ SV173 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1638,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( SV28 = zero_zero_poly_a )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV28 @ SV137 )
!= ( times_times_poly_a @ SV28 @ SV173 ) )
| ~ ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1462]) ).
thf(1639,plain,
! [SV28: poly_a,SV173: poly_a,SV137: poly_a] :
( ( ( SV137 = SV173 )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV28 @ SV137 )
!= ( times_times_poly_a @ SV28 @ SV173 ) )
| ~ ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1462]) ).
thf(1640,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ( ( times_times_nat @ SV29 @ SV138 )
!= ( times_times_nat @ SV29 @ SV174 ) )
| ~ ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) ) )
= $false )
| ( ( ( times_times_nat @ SV29 @ SV138 )
= ( times_times_nat @ SV29 @ SV174 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1463]) ).
thf(1641,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( SV29 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV29 @ SV138 )
!= ( times_times_nat @ SV29 @ SV174 ) )
| ~ ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1464]) ).
thf(1642,plain,
! [SV29: nat,SV174: nat,SV138: nat] :
( ( ( SV138 = SV174 )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV29 @ SV138 )
!= ( times_times_nat @ SV29 @ SV174 ) )
| ~ ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1464]) ).
thf(1643,plain,
! [SV139: a,SV30: a] :
( ( ( ( times_times_a @ SV30 @ SV139 )
!= zero_zero_a )
= $false )
| ( ( ( times_times_a @ SV30 @ SV139 )
= zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1644,plain,
! [SV139: a,SV30: a] :
( ( ( ~ ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) ) )
= $false )
| ( ( ( times_times_a @ SV30 @ SV139 )
= zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1645,plain,
! [SV139: a,SV30: a] :
( ( ( ( ( times_times_a @ SV30 @ SV139 )
!= zero_zero_a )
| ~ ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) ) )
= $false )
| ( ( SV30 = zero_zero_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1646,plain,
! [SV139: a,SV30: a] :
( ( ( ( ( times_times_a @ SV30 @ SV139 )
!= zero_zero_a )
| ~ ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) ) )
= $false )
| ( ( SV139 = zero_zero_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1647,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ( times_times_poly_a @ SV31 @ SV140 )
!= zero_zero_poly_a )
= $false )
| ( ( ( times_times_poly_a @ SV31 @ SV140 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1468]) ).
thf(1648,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ~ ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) ) )
= $false )
| ( ( ( times_times_poly_a @ SV31 @ SV140 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1468]) ).
thf(1649,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ( ( times_times_poly_a @ SV31 @ SV140 )
!= zero_zero_poly_a )
| ~ ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) ) )
= $false )
| ( ( SV31 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1469]) ).
thf(1650,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ( ( times_times_poly_a @ SV31 @ SV140 )
!= zero_zero_poly_a )
| ~ ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) ) )
= $false )
| ( ( SV140 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1651,plain,
! [SV141: nat,SV32: nat] :
( ( ( ( times_times_nat @ SV32 @ SV141 )
!= zero_zero_nat )
= $false )
| ( ( ( times_times_nat @ SV32 @ SV141 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1471]) ).
thf(1652,plain,
! [SV141: nat,SV32: nat] :
( ( ( ~ ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV32 @ SV141 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1471]) ).
thf(1653,plain,
! [SV141: nat,SV32: nat] :
( ( ( ( ( times_times_nat @ SV32 @ SV141 )
!= zero_zero_nat )
| ~ ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) ) )
= $false )
| ( ( SV32 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1654,plain,
! [SV141: nat,SV32: nat] :
( ( ( ( ( times_times_nat @ SV32 @ SV141 )
!= zero_zero_nat )
| ~ ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) ) )
= $false )
| ( ( SV141 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1655,plain,
! [SV39: poly_a] :
( ( ( ( uminus_uminus_poly_a @ SV39 )
= SV39 )
= $true )
| ( ( ( uminus_uminus_poly_a @ SV39 )
= SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1474]) ).
thf(1656,plain,
! [SV39: poly_a] :
( ( ( SV39 = zero_zero_poly_a )
= $true )
| ( ( ( uminus_uminus_poly_a @ SV39 )
= SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1475]) ).
thf(1657,plain,
! [SV39: poly_a] :
( ( ( ( uminus_uminus_poly_a @ SV39 )
= SV39 )
= $true )
| ( ( SV39 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1476]) ).
thf(1658,plain,
! [SV39: poly_a] :
( ( ( SV39 = zero_zero_poly_a )
= $true )
| ( ( SV39 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1477]) ).
thf(1659,plain,
! [SV40: a] :
( ( ( ( uminus_uminus_a @ SV40 )
= SV40 )
= $true )
| ( ( ( uminus_uminus_a @ SV40 )
= SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1478]) ).
thf(1660,plain,
! [SV40: a] :
( ( ( SV40 = zero_zero_a )
= $true )
| ( ( ( uminus_uminus_a @ SV40 )
= SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1479]) ).
thf(1661,plain,
! [SV40: a] :
( ( ( ( uminus_uminus_a @ SV40 )
= SV40 )
= $true )
| ( ( SV40 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1480]) ).
thf(1662,plain,
! [SV40: a] :
( ( ( SV40 = zero_zero_a )
= $true )
| ( ( SV40 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1481]) ).
thf(1663,plain,
! [SV41: poly_a] :
( ( ( SV41
= ( uminus_uminus_poly_a @ SV41 ) )
= $true )
| ( ( SV41
= ( uminus_uminus_poly_a @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1482]) ).
thf(1664,plain,
! [SV41: poly_a] :
( ( ( SV41 = zero_zero_poly_a )
= $true )
| ( ( SV41
= ( uminus_uminus_poly_a @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1483]) ).
thf(1665,plain,
! [SV41: poly_a] :
( ( ( SV41
= ( uminus_uminus_poly_a @ SV41 ) )
= $true )
| ( ( SV41 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1484]) ).
thf(1666,plain,
! [SV41: poly_a] :
( ( ( SV41 = zero_zero_poly_a )
= $true )
| ( ( SV41 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1485]) ).
thf(1667,plain,
! [SV42: a] :
( ( ( SV42
= ( uminus_uminus_a @ SV42 ) )
= $true )
| ( ( SV42
= ( uminus_uminus_a @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1486]) ).
thf(1668,plain,
! [SV42: a] :
( ( ( SV42 = zero_zero_a )
= $true )
| ( ( SV42
= ( uminus_uminus_a @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1487]) ).
thf(1669,plain,
! [SV42: a] :
( ( ( SV42
= ( uminus_uminus_a @ SV42 ) )
= $true )
| ( ( SV42 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1488]) ).
thf(1670,plain,
! [SV42: a] :
( ( ( SV42 = zero_zero_a )
= $true )
| ( ( SV42 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1489]) ).
thf(1671,plain,
! [SV43: poly_a] :
( ( ( ( uminus_uminus_poly_a @ SV43 )
= zero_zero_poly_a )
= $true )
| ( ( ( uminus_uminus_poly_a @ SV43 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1490]) ).
thf(1672,plain,
! [SV43: poly_a] :
( ( ( SV43 = zero_zero_poly_a )
= $true )
| ( ( ( uminus_uminus_poly_a @ SV43 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1491]) ).
thf(1673,plain,
! [SV43: poly_a] :
( ( ( ( uminus_uminus_poly_a @ SV43 )
= zero_zero_poly_a )
= $true )
| ( ( SV43 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1492]) ).
thf(1674,plain,
! [SV43: poly_a] :
( ( ( SV43 = zero_zero_poly_a )
= $true )
| ( ( SV43 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1493]) ).
thf(1675,plain,
! [SV44: a] :
( ( ( ( uminus_uminus_a @ SV44 )
= zero_zero_a )
= $true )
| ( ( ( uminus_uminus_a @ SV44 )
= zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1494]) ).
thf(1676,plain,
! [SV44: a] :
( ( ( SV44 = zero_zero_a )
= $true )
| ( ( ( uminus_uminus_a @ SV44 )
= zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1495]) ).
thf(1677,plain,
! [SV44: a] :
( ( ( ( uminus_uminus_a @ SV44 )
= zero_zero_a )
= $true )
| ( ( SV44 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1496]) ).
thf(1678,plain,
! [SV44: a] :
( ( ( SV44 = zero_zero_a )
= $true )
| ( ( SV44 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1497]) ).
thf(1679,plain,
! [SV45: poly_a] :
( ( ( zero_zero_poly_a
= ( uminus_uminus_poly_a @ SV45 ) )
= $true )
| ( ( zero_zero_poly_a
= ( uminus_uminus_poly_a @ SV45 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1498]) ).
thf(1680,plain,
! [SV45: poly_a] :
( ( ( zero_zero_poly_a = SV45 )
= $true )
| ( ( zero_zero_poly_a
= ( uminus_uminus_poly_a @ SV45 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1499]) ).
thf(1681,plain,
! [SV45: poly_a] :
( ( ( zero_zero_poly_a
= ( uminus_uminus_poly_a @ SV45 ) )
= $true )
| ( ( zero_zero_poly_a = SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1500]) ).
thf(1682,plain,
! [SV45: poly_a] :
( ( ( zero_zero_poly_a = SV45 )
= $true )
| ( ( zero_zero_poly_a = SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1501]) ).
thf(1683,plain,
! [SV46: a] :
( ( ( zero_zero_a
= ( uminus_uminus_a @ SV46 ) )
= $true )
| ( ( zero_zero_a
= ( uminus_uminus_a @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1502]) ).
thf(1684,plain,
! [SV46: a] :
( ( ( zero_zero_a = SV46 )
= $true )
| ( ( zero_zero_a
= ( uminus_uminus_a @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1503]) ).
thf(1685,plain,
! [SV46: a] :
( ( ( zero_zero_a
= ( uminus_uminus_a @ SV46 ) )
= $true )
| ( ( zero_zero_a = SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1504]) ).
thf(1686,plain,
! [SV46: a] :
( ( ( zero_zero_a = SV46 )
= $true )
| ( ( zero_zero_a = SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1505]) ).
thf(1687,plain,
! [SV142: list_a,SV48: list_a] :
( ( ( SV48
!= ( append_a @ SV142 @ SV48 ) )
= $false )
| ( ( SV48
= ( append_a @ SV142 @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1506]) ).
thf(1688,plain,
! [SV48: list_a,SV142: list_a] :
( ( ( SV142 != nil_a )
= $false )
| ( ( SV48
= ( append_a @ SV142 @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1506]) ).
thf(1689,plain,
! [SV142: list_a,SV48: list_a] :
( ( ( SV48
!= ( append_a @ SV142 @ SV48 ) )
= $false )
| ( ( SV142 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1507]) ).
thf(1690,plain,
! [SV142: list_a] :
( ( ( SV142 != nil_a )
= $false )
| ( ( SV142 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1507]) ).
thf(1691,plain,
! [SV143: list_a,SV49: list_a] :
( ( ( ( append_a @ SV49 @ SV143 )
!= SV143 )
= $false )
| ( ( ( append_a @ SV49 @ SV143 )
= SV143 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1508]) ).
thf(1692,plain,
! [SV143: list_a,SV49: list_a] :
( ( ( SV49 != nil_a )
= $false )
| ( ( ( append_a @ SV49 @ SV143 )
= SV143 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1508]) ).
thf(1693,plain,
! [SV143: list_a,SV49: list_a] :
( ( ( ( append_a @ SV49 @ SV143 )
!= SV143 )
= $false )
| ( ( SV49 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1509]) ).
thf(1694,plain,
! [SV49: list_a] :
( ( ( SV49 != nil_a )
= $false )
| ( ( SV49 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1509]) ).
thf(1695,plain,
! [SV144: list_a,SV50: list_a] :
( ( ( SV50
!= ( append_a @ SV50 @ SV144 ) )
= $false )
| ( ( SV50
= ( append_a @ SV50 @ SV144 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1510]) ).
thf(1696,plain,
! [SV50: list_a,SV144: list_a] :
( ( ( SV144 != nil_a )
= $false )
| ( ( SV50
= ( append_a @ SV50 @ SV144 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1510]) ).
thf(1697,plain,
! [SV144: list_a,SV50: list_a] :
( ( ( SV50
!= ( append_a @ SV50 @ SV144 ) )
= $false )
| ( ( SV144 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1511]) ).
thf(1698,plain,
! [SV144: list_a] :
( ( ( SV144 != nil_a )
= $false )
| ( ( SV144 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1511]) ).
thf(1699,plain,
! [SV145: list_a,SV51: list_a] :
( ( ( ( append_a @ SV51 @ SV145 )
!= SV51 )
= $false )
| ( ( ( append_a @ SV51 @ SV145 )
= SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1512]) ).
thf(1700,plain,
! [SV51: list_a,SV145: list_a] :
( ( ( SV145 != nil_a )
= $false )
| ( ( ( append_a @ SV51 @ SV145 )
= SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1512]) ).
thf(1701,plain,
! [SV145: list_a,SV51: list_a] :
( ( ( ( append_a @ SV51 @ SV145 )
!= SV51 )
= $false )
| ( ( SV145 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1513]) ).
thf(1702,plain,
! [SV145: list_a] :
( ( ( SV145 != nil_a )
= $false )
| ( ( SV145 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1513]) ).
thf(1703,plain,
! [SV53: poly_a] :
( ( ( zero_zero_poly_a = SV53 )
= $true )
| ( ( zero_zero_poly_a = SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1514]) ).
thf(1704,plain,
! [SV53: poly_a] :
( ( ( SV53 = zero_zero_poly_a )
= $true )
| ( ( zero_zero_poly_a = SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1515]) ).
thf(1705,plain,
! [SV53: poly_a] :
( ( ( zero_zero_poly_a = SV53 )
= $true )
| ( ( SV53 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1516]) ).
thf(1706,plain,
! [SV53: poly_a] :
( ( ( SV53 = zero_zero_poly_a )
= $true )
| ( ( SV53 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1517]) ).
thf(1707,plain,
! [SV54: a] :
( ( ( zero_zero_a = SV54 )
= $true )
| ( ( zero_zero_a = SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1518]) ).
thf(1708,plain,
! [SV54: a] :
( ( ( SV54 = zero_zero_a )
= $true )
| ( ( zero_zero_a = SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1519]) ).
thf(1709,plain,
! [SV54: a] :
( ( ( zero_zero_a = SV54 )
= $true )
| ( ( SV54 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1520]) ).
thf(1710,plain,
! [SV54: a] :
( ( ( SV54 = zero_zero_a )
= $true )
| ( ( SV54 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1521]) ).
thf(1711,plain,
! [SV55: nat] :
( ( ( zero_zero_nat = SV55 )
= $true )
| ( ( zero_zero_nat = SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1522]) ).
thf(1712,plain,
! [SV55: nat] :
( ( ( SV55 = zero_zero_nat )
= $true )
| ( ( zero_zero_nat = SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1523]) ).
thf(1713,plain,
! [SV55: nat] :
( ( ( zero_zero_nat = SV55 )
= $true )
| ( ( SV55 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1524]) ).
thf(1714,plain,
! [SV55: nat] :
( ( ( SV55 = zero_zero_nat )
= $true )
| ( ( SV55 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1525]) ).
thf(1715,plain,
! [SV57: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV57 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1526]) ).
thf(1716,plain,
! [SV57: nat] :
( ( ( SV57 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1527]) ).
thf(1717,plain,
! [SV57: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV57 ) )
= $false )
| ( ( SV57 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1528]) ).
thf(1718,plain,
! [SV57: nat] :
( ( ( ~ ( ( SV57 != zero_zero_nat ) ) )
= $false )
| ( ( SV57 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1528]) ).
thf(1719,plain,
! [SV194: a,SV61: a,SV175: a] :
( ( ( ( times_times_a @ SV175 @ SV61 )
= ( times_times_a @ SV194 @ SV61 ) )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV175 @ SV61 )
!= ( times_times_a @ SV194 @ SV61 ) )
| ( SV175 != SV194 ) ) )
= $true )
| ( ( SV61 = zero_zero_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1720,plain,
! [SV61: a,SV194: a,SV175: a] :
( ( ( SV175 = SV194 )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV175 @ SV61 )
!= ( times_times_a @ SV194 @ SV61 ) )
| ( SV175 != SV194 ) ) )
= $true )
| ( ( SV61 = zero_zero_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1721,plain,
! [SV195: poly_a,SV62: poly_a,SV176: poly_a] :
( ( ( ( times_times_poly_a @ SV176 @ SV62 )
= ( times_times_poly_a @ SV195 @ SV62 ) )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV176 @ SV62 )
!= ( times_times_poly_a @ SV195 @ SV62 ) )
| ( SV176 != SV195 ) ) )
= $true )
| ( ( SV62 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1530]) ).
thf(1722,plain,
! [SV62: poly_a,SV195: poly_a,SV176: poly_a] :
( ( ( SV176 = SV195 )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV176 @ SV62 )
!= ( times_times_poly_a @ SV195 @ SV62 ) )
| ( SV176 != SV195 ) ) )
= $true )
| ( ( SV62 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1530]) ).
thf(1723,plain,
! [SV196: nat,SV63: nat,SV177: nat] :
( ( ( ( times_times_nat @ SV177 @ SV63 )
= ( times_times_nat @ SV196 @ SV63 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV177 @ SV63 )
!= ( times_times_nat @ SV196 @ SV63 ) )
| ( SV177 != SV196 ) ) )
= $true )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1531]) ).
thf(1724,plain,
! [SV63: nat,SV196: nat,SV177: nat] :
( ( ( SV177 = SV196 )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV177 @ SV63 )
!= ( times_times_nat @ SV196 @ SV63 ) )
| ( SV177 != SV196 ) ) )
= $true )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1531]) ).
thf(1725,plain,
! [SV197: a,SV178: a,SV64: a] :
( ( ( ( times_times_a @ SV64 @ SV178 )
= ( times_times_a @ SV64 @ SV197 ) )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV64 @ SV178 )
!= ( times_times_a @ SV64 @ SV197 ) )
| ( SV178 != SV197 ) ) )
= $true )
| ( ( SV64 = zero_zero_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1532]) ).
thf(1726,plain,
! [SV64: a,SV197: a,SV178: a] :
( ( ( SV178 = SV197 )
= $false )
| ( ( ~ ( ( ( times_times_a @ SV64 @ SV178 )
!= ( times_times_a @ SV64 @ SV197 ) )
| ( SV178 != SV197 ) ) )
= $true )
| ( ( SV64 = zero_zero_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1532]) ).
thf(1727,plain,
! [SV198: poly_a,SV179: poly_a,SV65: poly_a] :
( ( ( ( times_times_poly_a @ SV65 @ SV179 )
= ( times_times_poly_a @ SV65 @ SV198 ) )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV65 @ SV179 )
!= ( times_times_poly_a @ SV65 @ SV198 ) )
| ( SV179 != SV198 ) ) )
= $true )
| ( ( SV65 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1533]) ).
thf(1728,plain,
! [SV65: poly_a,SV198: poly_a,SV179: poly_a] :
( ( ( SV179 = SV198 )
= $false )
| ( ( ~ ( ( ( times_times_poly_a @ SV65 @ SV179 )
!= ( times_times_poly_a @ SV65 @ SV198 ) )
| ( SV179 != SV198 ) ) )
= $true )
| ( ( SV65 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1533]) ).
thf(1729,plain,
! [SV199: nat,SV180: nat,SV66: nat] :
( ( ( ( times_times_nat @ SV66 @ SV180 )
= ( times_times_nat @ SV66 @ SV199 ) )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV66 @ SV180 )
!= ( times_times_nat @ SV66 @ SV199 ) )
| ( SV180 != SV199 ) ) )
= $true )
| ( ( SV66 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1534]) ).
thf(1730,plain,
! [SV66: nat,SV199: nat,SV180: nat] :
( ( ( SV180 = SV199 )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV66 @ SV180 )
!= ( times_times_nat @ SV66 @ SV199 ) )
| ( SV180 != SV199 ) ) )
= $true )
| ( ( SV66 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1534]) ).
thf(1731,plain,
! [SV186: list_a,SV80: a,SV216: list_a,SV153: list_a,SV212: list_a] :
( ( ( SV212
!= ( append_a @ SV153 @ SV216 ) )
= $true )
| ( ( ( cons_a @ SV80 @ SV212 )
= ( append_a @ SV186 @ SV216 ) )
= $true )
| ( ( ( cons_a @ SV80 @ SV153 )
= SV186 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1535]) ).
thf(1732,plain,
! [SV85: list_a] :
( ( ( SV85 = nil_a )
= $true )
| ( ( SV85 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1536]) ).
thf(1733,plain,
! [SV85: list_a] :
( ( ( null_a @ SV85 )
= $true )
| ( ( SV85 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1537]) ).
thf(1734,plain,
! [SV85: list_a] :
( ( ( SV85 = nil_a )
= $true )
| ( ( null_a @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1538]) ).
thf(1735,plain,
! [SV85: list_a] :
( ( ( null_a @ SV85 )
= $true )
| ( ( null_a @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1539]) ).
thf(1736,plain,
! [SV187: nat,SV156: nat,SV86: nat] :
( ( ( ( ( times_times_nat @ SV86 @ SV156 )
!= ( times_times_nat @ SV187 @ SV156 ) )
| ~ ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV86 @ SV156 )
= ( times_times_nat @ SV187 @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1737,plain,
! [SV156: nat,SV187: nat,SV86: nat] :
( ( ( SV86 = SV187 )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV86 @ SV156 )
!= ( times_times_nat @ SV187 @ SV156 ) )
| ~ ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1541]) ).
thf(1738,plain,
! [SV187: nat,SV86: nat,SV156: nat] :
( ( ( SV156 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV86 @ SV156 )
!= ( times_times_nat @ SV187 @ SV156 ) )
| ~ ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1541]) ).
thf(1739,plain,
! [SV87: nat] :
( ( ( ~ ( ( SV87 != zero_zero_nat ) ) )
= $false )
| ( ( SV87 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1542]) ).
thf(1740,plain,
! [SV87: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV87 ) )
= $false )
| ( ( SV87 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1542]) ).
thf(1741,plain,
! [SV87: nat] :
( ( ( SV87 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1543]) ).
thf(1742,plain,
! [SV87: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV87 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1544]) ).
thf(1743,plain,
! [SV89: nat] :
( ( ( ~ ( ( SV89 != zero_zero_nat ) ) )
= $false )
| ( ( SV89 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1545]) ).
thf(1744,plain,
! [SV89: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV89 ) )
= $false )
| ( ( SV89 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1545]) ).
thf(1745,plain,
! [SV89: nat] :
( ( ( SV89 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1546]) ).
thf(1746,plain,
! [SV89: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV89 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1547]) ).
thf(1747,plain,
! [SV157: nat,SV90: nat] :
( ( ( ( times_times_nat @ SV90 @ SV157 )
!= zero_zero_nat )
= $false )
| ( ( ( times_times_nat @ SV90 @ SV157 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1548]) ).
thf(1748,plain,
! [SV157: nat,SV90: nat] :
( ( ( ~ ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV90 @ SV157 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1548]) ).
thf(1749,plain,
! [SV157: nat,SV90: nat] :
( ( ( ( ( times_times_nat @ SV90 @ SV157 )
!= zero_zero_nat )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) ) )
= $false )
| ( ( SV90 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1750,plain,
! [SV157: nat,SV90: nat] :
( ( ( ( ( times_times_nat @ SV90 @ SV157 )
!= zero_zero_nat )
| ~ ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) ) )
= $false )
| ( ( SV157 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1550]) ).
thf(1751,plain,
! [SV188: nat,SV158: nat,SV92: nat] :
( ( ( ( ( times_times_nat @ SV92 @ SV158 )
!= ( times_times_nat @ SV92 @ SV188 ) )
| ~ ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV92 @ SV158 )
= ( times_times_nat @ SV92 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1551]) ).
thf(1752,plain,
! [SV92: nat,SV188: nat,SV158: nat] :
( ( ( SV158 = SV188 )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV92 @ SV158 )
!= ( times_times_nat @ SV92 @ SV188 ) )
| ~ ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1753,plain,
! [SV188: nat,SV158: nat,SV92: nat] :
( ( ( SV92 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV92 @ SV158 )
!= ( times_times_nat @ SV92 @ SV188 ) )
| ~ ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1754,plain,
! [SV94: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV94 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV94 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1553]) ).
thf(1755,plain,
! [SV94: nat] :
( ( ( SV94 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV94 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1553]) ).
thf(1756,plain,
! [SV94: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV94 ) )
= $true )
| ( ( SV94 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1554]) ).
thf(1757,plain,
! [SV94: nat] :
( ( ( SV94 = zero_zero_nat )
= $true )
| ( ( SV94 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1555]) ).
thf(1758,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ( ( times_times_nat @ SV100 @ SV160 )
!= ( times_times_nat @ SV100 @ SV189 ) )
| ~ ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) ) )
= $false )
| ( ( ( times_times_nat @ SV100 @ SV160 )
= ( times_times_nat @ SV100 @ SV189 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1556]) ).
thf(1759,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( SV100 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV100 @ SV160 )
!= ( times_times_nat @ SV100 @ SV189 ) )
| ~ ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1760,plain,
! [SV100: nat,SV189: nat,SV160: nat] :
( ( ( SV160 = SV189 )
= $false )
| ( ( ~ ( ( ( times_times_nat @ SV100 @ SV160 )
!= ( times_times_nat @ SV100 @ SV189 ) )
| ~ ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1761,plain,
! [SV101: list_a > $o] :
( ( ( ~ ( ( ( sK40_X2 @ SV101 )
!= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) ) )
= $false )
| ( ( ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1762,plain,
! [SV101: list_a > $o] :
( ( ( ~ ~ ( ~ ( ( ( sK40_X2 @ SV101 )
= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
| ~ ~ ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) ) ) )
= $false )
| ( ( ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1763,plain,
! [SV221: list_a,SV217: a,SV102: list_a > $o] :
( ( ( ( sK25_SY345 @ SV102 )
!= ( cons_a @ SV217 @ SV221 ) )
= $true )
| ( ( SV102 @ ( sK25_SY345 @ SV102 ) )
= $true )
| ( ( ~ ( SV102 @ nil_a )
| ! [SY475: list_a] : ( SV102 @ SY475 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(1764,plain,
! [SV102: list_a > $o] :
( ( ( SV102 @ nil_a )
= $false )
| ( ( ! [SY475: list_a] : ( SV102 @ SY475 ) )
= $true )
| ( ( SV102 @ ( cons_a @ ( sK24_X2 @ SV102 ) @ ( sK25_SY345 @ SV102 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1765,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ( append_a @ SV103 @ SV161 )
!= nil_a )
= $false )
| ( ( ( append_a @ SV103 @ SV161 )
= nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1563]) ).
thf(1766,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ~ ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) )
= $false )
| ( ( ( append_a @ SV103 @ SV161 )
= nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1563]) ).
thf(1767,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( SV103 != nil_a )
= $true )
| ( ( SV161 != nil_a )
= $true )
| ( ( ~ ( ( ( append_a @ SV103 @ SV161 )
!= nil_a )
| ~ ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1564]) ).
thf(1768,plain,
! [SV162: a > a,SV104: ( a > a ) > list_a > list_a > $o] :
( ( ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) @ ( cons_a @ ( sK54_F2 @ SV162 @ SV104 @ ( sK55_SY373 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) ) )
= $true )
| ( ( ! [SY529: list_a,SY530: list_a] : ( SV104 @ SV162 @ SY529 @ SY530 ) )
= $true )
| ( ( SV104 @ ( sK58_F2 @ SV162 @ SV104 ) @ nil_a @ ( sK59_SY379 @ SV162 @ SV104 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1565]) ).
thf(1769,plain,
! [SV162: a > a,SV104: ( a > a ) > list_a > list_a > $o] :
( ( ( ~ ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( cons_a @ ( sK55_SY373 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) ) )
= $true )
| ( ( ! [SY529: list_a,SY530: list_a] : ( SV104 @ SV162 @ SY529 @ SY530 ) )
= $true )
| ( ( SV104 @ ( sK58_F2 @ SV162 @ SV104 ) @ nil_a @ ( sK59_SY379 @ SV162 @ SV104 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1566]) ).
thf(1770,plain,
! [SV203: a,SV190: list_a,SV163: a,SV105: list_a] :
( ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
= $false )
| ( ( ~ ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
!= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
| ~ ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1567]) ).
thf(1771,plain,
! [SV203: a,SV163: a,SV190: list_a,SV105: list_a] :
( ( ( ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) )
= $false )
| ( ( ~ ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
!= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
| ~ ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1567]) ).
thf(1772,plain,
! [SV222: a > a > $o,SV106: ( a > a > $o ) > list_a > $o] :
( ( ( ! [SY555: list_a] : ( SV106 @ SV222 @ SY555 ) )
= $true )
| ( ( SV106 @ ( sK36_P5 @ SV106 ) @ ( sK38_SY361 @ SV106 ) )
= $true )
| ( ( SV106 @ ( sK39_P5 @ SV106 ) @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1773,plain,
! [SV106: ( a > a > $o ) > list_a > $o] :
( ( ( SV106 @ ( sK36_P5 @ SV106 ) @ ( cons_a @ ( sK37_SY359 @ SV106 ) @ ( sK38_SY361 @ SV106 ) ) )
= $false )
| ( ( ! [SY483: a > a > $o,SY484: list_a] : ( SV106 @ SY483 @ SY484 ) )
= $true )
| ( ( SV106 @ ( sK39_P5 @ SV106 ) @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1774,plain,
! [SV223: nat,SV107: nat > $o] :
( ( ( SV107 @ SV223 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( sK1_N2 @ SV107 ) )
= $true )
| ( ( SV107 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1775,plain,
! [SV107: nat > $o] :
( ( ( ~ ~ ( SV107 @ ( sK1_N2 @ SV107 ) )
| ~ ! [SY485: nat] :
( ~ ( ord_less_nat @ SY485 @ ( sK1_N2 @ SV107 ) )
| ( SV107 @ SY485 ) ) )
= $false )
| ( ( ! [SY486: nat] : ( SV107 @ SY486 ) )
= $true )
| ( ( SV107 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1776,plain,
! [SV224: list_a,SV108: list_a > $o] :
( ( ( SV108 @ SV224 )
= $true )
| ( ( SV108 @ ( sK5_SY329 @ SV108 ) )
= $true )
| ( ( SV108 @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(1777,plain,
! [SV108: list_a > $o] :
( ( ( SV108 @ ( cons_a @ ( sK4_X1 @ SV108 ) @ ( sK5_SY329 @ SV108 ) ) )
= $false )
| ( ( ! [SY487: list_a] : ( SV108 @ SY487 ) )
= $true )
| ( ( SV108 @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1573]) ).
thf(1778,plain,
! [SV109: list_a > $o] :
( ( ( ~ ( SV109 @ ( sK20_SY343 @ SV109 ) ) )
= $false )
| ( ( ! [SY488: list_a] : ( SV109 @ SY488 ) )
= $true )
| ( ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
= $false )
| ( ( SV109 @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1574]) ).
thf(1779,plain,
! [SV109: list_a > $o] :
( ( ( ~ ~ ( ~ ( SV109 @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) )
| ~ ~ ( SV109 @ ( cons_a @ ( sK18_X2 @ SV109 ) @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) ) ) ) )
= $false )
| ( ( ! [SY488: list_a] : ( SV109 @ SY488 ) )
= $true )
| ( ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
= $false )
| ( ( SV109 @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1574]) ).
thf(1780,plain,
! [SV204: list_a,SV191: a,SV164: list_a,SV110: a] :
( ( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SV204 ) )
= $false )
| ( ( ~ ( ( ( cons_a @ SV110 @ SV164 )
!= ( cons_a @ SV191 @ SV204 ) )
| ~ ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1575]) ).
thf(1781,plain,
! [SV204: list_a,SV164: list_a,SV191: a,SV110: a] :
( ( ( ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) )
= $false )
| ( ( ~ ( ( ( cons_a @ SV110 @ SV164 )
!= ( cons_a @ SV191 @ SV204 ) )
| ~ ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1575]) ).
thf(1782,plain,
! [SV225: list_a,SV111: list_a > list_a > $o] :
( ( ( ! [SY556: list_a] : ( SV111 @ SV225 @ SY556 ) )
= $true )
| ( ( SV111 @ ( sK16_SY340 @ SV111 ) @ ( sK15_SY338 @ SV111 ) )
= $true )
| ( ( SV111 @ nil_a @ ( sK17_X_1 @ SV111 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1783,plain,
! [SV111: list_a > list_a > $o] :
( ( ( SV111 @ ( cons_a @ ( sK14_X2 @ SV111 ) @ ( sK15_SY338 @ SV111 ) ) @ ( sK16_SY340 @ SV111 ) )
= $false )
| ( ( ! [SY492: list_a,SY493: list_a] : ( SV111 @ SY492 @ SY493 ) )
= $true )
| ( ( SV111 @ nil_a @ ( sK17_X_1 @ SV111 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1577]) ).
thf(1784,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ( pCons_a @ SV112 @ SV165 )
!= zero_zero_poly_a )
= $false )
| ( ( ( pCons_a @ SV112 @ SV165 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1578]) ).
thf(1785,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ~ ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) )
= $false )
| ( ( ( pCons_a @ SV112 @ SV165 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1578]) ).
thf(1786,plain,
! [SV165: poly_a,SV112: a] :
( ( ( SV112 != zero_zero_a )
= $true )
| ( ( SV165 != zero_zero_poly_a )
= $true )
| ( ( ~ ( ( ( pCons_a @ SV112 @ SV165 )
!= zero_zero_poly_a )
| ~ ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1579]) ).
thf(1787,plain,
! [SV226: poly_a,SV113: poly_a > poly_a > $o] :
( ( ( ! [SY557: poly_a] : ( SV113 @ SV226 @ SY557 ) )
= $true )
| ( ( SV113 @ ( sK85_SY400 @ SV113 ) @ ( sK87_SY405 @ SV113 ) )
= $true )
| ( ( SV113 @ zero_zero_poly_a @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1788,plain,
! [SV113: poly_a > poly_a > $o] :
( ( ( SV113 @ ( pCons_a @ ( sK84_A2 @ SV113 ) @ ( sK85_SY400 @ SV113 ) ) @ ( pCons_a @ ( sK86_SY403 @ SV113 ) @ ( sK87_SY405 @ SV113 ) ) )
= $false )
| ( ( ! [SY495: poly_a,SY496: poly_a] : ( SV113 @ SY495 @ SY496 ) )
= $true )
| ( ( SV113 @ zero_zero_poly_a @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1583]) ).
thf(1789,plain,
! [SV114: list_a > list_a > $o] :
( ( ( ~ ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) ) )
= $true )
| ( ( ! [SY497: list_a,SY498: list_a] : ( SV114 @ SY497 @ SY498 ) )
= $true )
| ( ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a )
= $false )
| ( ( SV114 @ ( sK72_SY386 @ SV114 ) @ ( sK74_SY391 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1584]) ).
thf(1790,plain,
! [SV114: list_a > list_a > $o] :
( ( ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a )
= $false )
| ( ( ~ ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) )
| ! [SY497: list_a,SY498: list_a] : ( SV114 @ SY497 @ SY498 ) )
= $true )
| ( ( SV114 @ ( cons_a @ ( sK71_X2 @ SV114 ) @ ( sK72_SY386 @ SV114 ) ) @ ( cons_a @ ( sK73_SY389 @ SV114 ) @ ( sK74_SY391 @ SV114 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1791,plain,
! [SV115: list_a,SV192: list_a > $o] :
( ( ( ~ ( ( ( sK52_SY372 @ SV192 @ SV115 )
!= nil_a ) ) )
= $false )
| ( ( SV192 @ SV115 )
= $true )
| ( ( SV192 @ ( cons_a @ ( sK53_X2 @ SV192 @ SV115 ) @ nil_a ) )
= $false )
| ( ( SV115 = nil_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1586]) ).
thf(1792,plain,
! [SV115: list_a,SV192: list_a > $o] :
( ( ( ~ ~ ( ~ ( SV192 @ ( sK52_SY372 @ SV192 @ SV115 ) )
| ~ ~ ( SV192 @ ( cons_a @ ( sK51_X2 @ SV192 @ SV115 ) @ ( sK52_SY372 @ SV192 @ SV115 ) ) ) ) )
= $false )
| ( ( SV192 @ SV115 )
= $true )
| ( ( SV192 @ ( cons_a @ ( sK53_X2 @ SV192 @ SV115 ) @ nil_a ) )
= $false )
| ( ( SV115 = nil_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1586]) ).
thf(1793,plain,
! [SV117: ( a > a > $o ) > list_a > $o] :
( ( ( ~ ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) ) )
= $false )
| ( ( ! [SY501: a > a > $o,SY502: list_a] : ( SV117 @ SY501 @ SY502 ) )
= $true )
| ( ( SV117 @ ( sK48_P5 @ SV117 ) @ ( cons_a @ ( sK49_SY371 @ SV117 ) @ nil_a ) )
= $false )
| ( ( SV117 @ ( sK50_P5 @ SV117 ) @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1589]) ).
thf(1794,plain,
! [SV117: ( a > a > $o ) > list_a > $o] :
( ( ( ~ ~ ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK45_SY365 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) ) ) )
= $false )
| ( ( ! [SY501: a > a > $o,SY502: list_a] : ( SV117 @ SY501 @ SY502 ) )
= $true )
| ( ( SV117 @ ( sK48_P5 @ SV117 ) @ ( cons_a @ ( sK49_SY371 @ SV117 ) @ nil_a ) )
= $false )
| ( ( SV117 @ ( sK50_P5 @ SV117 ) @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1589]) ).
thf(1795,plain,
! [SV118: list_a > list_a > $o] :
( ( ( ~ ( SV118 @ ( sK27_SY350 @ SV118 ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) ) )
= $false )
| ( ( ! [SY503: list_a,SY504: list_a] : ( SV118 @ SY503 @ SY504 ) )
= $true )
| ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1590]) ).
thf(1796,plain,
! [SV118: list_a > list_a > $o] :
( ( ( ~ ~ ( ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( sK29_SY355 @ SV118 ) )
| ~ ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) ) ) )
= $false )
| ( ( ! [SY503: list_a,SY504: list_a] : ( SV118 @ SY503 @ SY504 ) )
= $true )
| ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1590]) ).
thf(1797,plain,
! [SV119: list_a > list_a > $o] :
( ( ( ~ ( ~ ( SV119 @ ( sK7_SY330 @ SV119 ) @ ( sK9_SY335 @ SV119 ) )
| ~ ~ ( SV119 @ ( cons_a @ ( sK6_X2 @ SV119 ) @ ( sK7_SY330 @ SV119 ) ) @ ( cons_a @ ( sK8_SY333 @ SV119 ) @ ( sK9_SY335 @ SV119 ) ) ) ) )
= $true )
| ( ( ! [SY505: list_a,SY506: list_a] : ( SV119 @ SY505 @ SY506 ) )
= $true )
| ( ( SV119 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SV119 ) @ ( sK11_SY336 @ SV119 ) ) )
= $false )
| ( ( SV119 @ ( cons_a @ ( sK12_X2 @ SV119 ) @ ( sK13_SY337 @ SV119 ) ) @ nil_a )
= $false )
| ( ( SV119 @ nil_a @ nil_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1593]) ).
thf(1798,plain,
! [SV120: poly_a > $o] :
( ( ( ( sK88_A2 @ SV120 )
!= zero_zero_a )
= $true )
| ( ( ( sK89_SY406 @ SV120 )
!= zero_zero_poly_a )
= $true )
| ( ( ! [SY507: poly_a] : ( SV120 @ SY507 ) )
= $true )
| ( ( SV120 @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1594]) ).
thf(1799,plain,
! [SV120: poly_a > $o] :
( ( ( ~ ( SV120 @ ( sK89_SY406 @ SV120 ) )
| ~ ~ ( SV120 @ ( pCons_a @ ( sK88_A2 @ SV120 ) @ ( sK89_SY406 @ SV120 ) ) ) )
= $false )
| ( ( ! [SY507: poly_a] : ( SV120 @ SY507 ) )
= $true )
| ( ( SV120 @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1800,plain,
! [SV121: list_a] :
( ( ( ~ ( ( SV121 != nil_a ) ) )
= $false )
| ( ( SV121 = nil_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1596]) ).
thf(1801,plain,
! [SV121: list_a] :
( ( ( ~ ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) )
= $false )
| ( ( SV121 = nil_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1596]) ).
thf(1802,plain,
! [SV220: a,SV121: list_a] :
( ( ( ~ ! [SY554: list_a] :
( SV121
!= ( cons_a @ SV220 @ SY554 ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV121 != nil_a ) )
| ~ ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1803,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( nil_a
!= ( append_a @ SV122 @ SV166 ) )
= $false )
| ( ( nil_a
= ( append_a @ SV122 @ SV166 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1598]) ).
thf(1804,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( ~ ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) )
= $false )
| ( ( nil_a
= ( append_a @ SV122 @ SV166 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1598]) ).
thf(1805,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( SV122 != nil_a )
= $true )
| ( ( SV166 != nil_a )
= $true )
| ( ( ~ ( ( nil_a
!= ( append_a @ SV122 @ SV166 ) )
| ~ ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1599]) ).
thf(1806,plain,
! [SV123: list_a > list_a > $o] :
( ( ( ~ ( SV123 @ ( sK76_SY392 @ SV123 ) @ ( sK78_SY397 @ SV123 ) ) )
= $false )
| ( ( ! [SY511: list_a,SY512: list_a] : ( SV123 @ SY511 @ SY512 ) )
= $true )
| ( ( SV123 @ nil_a @ ( cons_a @ ( sK79_V @ SV123 ) @ ( sK80_SY398 @ SV123 ) ) )
= $false )
| ( ( SV123 @ ( sK81_Xs2 @ SV123 ) @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1600]) ).
thf(1807,plain,
! [SV123: list_a > list_a > $o] :
( ( ( ~ ~ ( SV123 @ ( cons_a @ ( sK75_X2 @ SV123 ) @ ( sK76_SY392 @ SV123 ) ) @ ( cons_a @ ( sK77_SY395 @ SV123 ) @ ( sK78_SY397 @ SV123 ) ) ) )
= $false )
| ( ( ! [SY511: list_a,SY512: list_a] : ( SV123 @ SY511 @ SY512 ) )
= $true )
| ( ( SV123 @ nil_a @ ( cons_a @ ( sK79_V @ SV123 ) @ ( sK80_SY398 @ SV123 ) ) )
= $false )
| ( ( SV123 @ ( sK81_Xs2 @ SV123 ) @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1600]) ).
thf(1808,plain,
! [SV227: list_a,SV124: list_a > $o] :
( ( ( SV124 @ SV227 )
= $true )
| ( ( SV124 @ ( sK63_SY381 @ SV124 ) )
= $true )
| ( ( SV124 @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(1809,plain,
! [SV124: list_a > $o] :
( ( ( SV124 @ ( cons_a @ ( sK62_X2 @ SV124 ) @ ( sK63_SY381 @ SV124 ) ) )
= $false )
| ( ( ! [SY513: list_a] : ( SV124 @ SY513 ) )
= $true )
| ( ( SV124 @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1810,plain,
! [SV193: poly_a,SV126: poly_a] :
( ( ( ( SV126 != SV193 )
| ( ( coeffs_a @ SV126 )
!= ( coeffs_a @ SV193 ) ) )
= $false )
| ( ( SV126 = SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1811,plain,
! [SV193: poly_a,SV126: poly_a] :
( ( ( ( SV126 != SV193 )
| ( ( coeffs_a @ SV126 )
!= ( coeffs_a @ SV193 ) ) )
= $false )
| ( ( ( coeffs_a @ SV126 )
= ( coeffs_a @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1604]) ).
thf(1812,plain,
! [SV128: poly_a] :
( ( ( is_zero_a @ SV128 )
= $true )
| ( ( is_zero_a @ SV128 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1605]) ).
thf(1813,plain,
! [SV128: poly_a] :
( ( ( null_a @ ( coeffs_a @ SV128 ) )
= $true )
| ( ( is_zero_a @ SV128 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1606]) ).
thf(1814,plain,
! [SV128: poly_a] :
( ( ( is_zero_a @ SV128 )
= $true )
| ( ( null_a @ ( coeffs_a @ SV128 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1607]) ).
thf(1815,plain,
! [SV128: poly_a] :
( ( ( null_a @ ( coeffs_a @ SV128 ) )
= $true )
| ( ( null_a @ ( coeffs_a @ SV128 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1608]) ).
thf(1816,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ( smult_a @ SV12 @ SV130 )
= zero_zero_poly_a )
= $true )
| ( ( ( smult_a @ SV12 @ SV130 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1613]) ).
thf(1817,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) )
= $true )
| ( ( ( smult_a @ SV12 @ SV130 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1614]) ).
thf(1818,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ( smult_a @ SV12 @ SV130 )
!= zero_zero_poly_a )
= $false )
| ( ( SV12 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1615]) ).
thf(1819,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ~ ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) ) )
= $false )
| ( ( SV12 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1615]) ).
thf(1820,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ( smult_a @ SV12 @ SV130 )
!= zero_zero_poly_a )
= $false )
| ( ( SV130 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1616]) ).
thf(1821,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ~ ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) ) )
= $false )
| ( ( SV130 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1616]) ).
thf(1822,plain,
! [SV132: poly_a] :
( ( ( is_zero_a @ SV132 )
= $true )
| ( ( is_zero_a @ SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1617]) ).
thf(1823,plain,
! [SV132: poly_a] :
( ( ( SV132 = zero_zero_poly_a )
= $true )
| ( ( is_zero_a @ SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1618]) ).
thf(1824,plain,
! [SV132: poly_a] :
( ( ( is_zero_a @ SV132 )
= $true )
| ( ( SV132 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1619]) ).
thf(1825,plain,
! [SV132: poly_a] :
( ( ( SV132 = zero_zero_poly_a )
= $true )
| ( ( SV132 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1620]) ).
thf(1826,plain,
! [SV23: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV23 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1621]) ).
thf(1827,plain,
! [SV23: nat] :
( ( ( SV23 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1622]) ).
thf(1828,plain,
! [SV23: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV23 )
= $false )
| ( ( SV23 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1623]) ).
thf(1829,plain,
! [SV169: a,SV133: a,SV24: a] :
( ( ( ( times_times_a @ SV24 @ SV133 )
!= ( times_times_a @ SV169 @ SV133 ) )
= $false )
| ( ( ( times_times_a @ SV24 @ SV133 )
= ( times_times_a @ SV169 @ SV133 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1625]) ).
thf(1830,plain,
! [SV169: a,SV24: a,SV133: a] :
( ( ( ~ ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) ) )
= $false )
| ( ( ( times_times_a @ SV24 @ SV133 )
= ( times_times_a @ SV169 @ SV133 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1625]) ).
thf(1831,plain,
! [SV169: a,SV133: a,SV24: a] :
( ( ( ( ( times_times_a @ SV24 @ SV133 )
!= ( times_times_a @ SV169 @ SV133 ) )
| ~ ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) ) )
= $false )
| ( ( SV133 = zero_zero_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1626]) ).
thf(1832,plain,
! [SV169: a,SV133: a,SV24: a] :
( ( ( ( ( times_times_a @ SV24 @ SV133 )
!= ( times_times_a @ SV169 @ SV133 ) )
| ~ ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) ) )
= $false )
| ( ( SV24 = SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1627]) ).
thf(1833,plain,
! [SV170: poly_a,SV134: poly_a,SV25: poly_a] :
( ( ( ( times_times_poly_a @ SV25 @ SV134 )
!= ( times_times_poly_a @ SV170 @ SV134 ) )
= $false )
| ( ( ( times_times_poly_a @ SV25 @ SV134 )
= ( times_times_poly_a @ SV170 @ SV134 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1628]) ).
thf(1834,plain,
! [SV170: poly_a,SV25: poly_a,SV134: poly_a] :
( ( ( ~ ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) ) )
= $false )
| ( ( ( times_times_poly_a @ SV25 @ SV134 )
= ( times_times_poly_a @ SV170 @ SV134 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1628]) ).
thf(1835,plain,
! [SV170: poly_a,SV134: poly_a,SV25: poly_a] :
( ( ( ( ( times_times_poly_a @ SV25 @ SV134 )
!= ( times_times_poly_a @ SV170 @ SV134 ) )
| ~ ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) ) )
= $false )
| ( ( SV134 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1629]) ).
thf(1836,plain,
! [SV170: poly_a,SV134: poly_a,SV25: poly_a] :
( ( ( ( ( times_times_poly_a @ SV25 @ SV134 )
!= ( times_times_poly_a @ SV170 @ SV134 ) )
| ~ ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) ) )
= $false )
| ( ( SV25 = SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1630]) ).
thf(1837,plain,
! [SV171: nat,SV135: nat,SV26: nat] :
( ( ( ( times_times_nat @ SV26 @ SV135 )
!= ( times_times_nat @ SV171 @ SV135 ) )
= $false )
| ( ( ( times_times_nat @ SV26 @ SV135 )
= ( times_times_nat @ SV171 @ SV135 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1631]) ).
thf(1838,plain,
! [SV171: nat,SV26: nat,SV135: nat] :
( ( ( ~ ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) ) )
= $false )
| ( ( ( times_times_nat @ SV26 @ SV135 )
= ( times_times_nat @ SV171 @ SV135 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1631]) ).
thf(1839,plain,
! [SV171: nat,SV135: nat,SV26: nat] :
( ( ( ( ( times_times_nat @ SV26 @ SV135 )
!= ( times_times_nat @ SV171 @ SV135 ) )
| ~ ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) ) )
= $false )
| ( ( SV135 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1632]) ).
thf(1840,plain,
! [SV171: nat,SV135: nat,SV26: nat] :
( ( ( ( ( times_times_nat @ SV26 @ SV135 )
!= ( times_times_nat @ SV171 @ SV135 ) )
| ~ ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) ) )
= $false )
| ( ( SV26 = SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1633]) ).
thf(1841,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ( times_times_a @ SV27 @ SV136 )
!= ( times_times_a @ SV27 @ SV172 ) )
= $false )
| ( ( ( times_times_a @ SV27 @ SV136 )
= ( times_times_a @ SV27 @ SV172 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1634]) ).
thf(1842,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ~ ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) ) )
= $false )
| ( ( ( times_times_a @ SV27 @ SV136 )
= ( times_times_a @ SV27 @ SV172 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1634]) ).
thf(1843,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ( ( times_times_a @ SV27 @ SV136 )
!= ( times_times_a @ SV27 @ SV172 ) )
| ~ ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) ) )
= $false )
| ( ( SV27 = zero_zero_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1635]) ).
thf(1844,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ( ( times_times_a @ SV27 @ SV136 )
!= ( times_times_a @ SV27 @ SV172 ) )
| ~ ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) ) )
= $false )
| ( ( SV136 = SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1636]) ).
thf(1845,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ( times_times_poly_a @ SV28 @ SV137 )
!= ( times_times_poly_a @ SV28 @ SV173 ) )
= $false )
| ( ( ( times_times_poly_a @ SV28 @ SV137 )
= ( times_times_poly_a @ SV28 @ SV173 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1637]) ).
thf(1846,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ~ ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) ) )
= $false )
| ( ( ( times_times_poly_a @ SV28 @ SV137 )
= ( times_times_poly_a @ SV28 @ SV173 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1637]) ).
thf(1847,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ( ( times_times_poly_a @ SV28 @ SV137 )
!= ( times_times_poly_a @ SV28 @ SV173 ) )
| ~ ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) ) )
= $false )
| ( ( SV28 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1848,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ( ( times_times_poly_a @ SV28 @ SV137 )
!= ( times_times_poly_a @ SV28 @ SV173 ) )
| ~ ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) ) )
= $false )
| ( ( SV137 = SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1849,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ( times_times_nat @ SV29 @ SV138 )
!= ( times_times_nat @ SV29 @ SV174 ) )
= $false )
| ( ( ( times_times_nat @ SV29 @ SV138 )
= ( times_times_nat @ SV29 @ SV174 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1850,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ~ ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) ) )
= $false )
| ( ( ( times_times_nat @ SV29 @ SV138 )
= ( times_times_nat @ SV29 @ SV174 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1851,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ( ( times_times_nat @ SV29 @ SV138 )
!= ( times_times_nat @ SV29 @ SV174 ) )
| ~ ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) ) )
= $false )
| ( ( SV29 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1852,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ( ( times_times_nat @ SV29 @ SV138 )
!= ( times_times_nat @ SV29 @ SV174 ) )
| ~ ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) ) )
= $false )
| ( ( SV138 = SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1642]) ).
thf(1853,plain,
! [SV139: a,SV30: a] :
( ( ( ( times_times_a @ SV30 @ SV139 )
= zero_zero_a )
= $true )
| ( ( ( times_times_a @ SV30 @ SV139 )
= zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1643]) ).
thf(1854,plain,
! [SV139: a,SV30: a] :
( ( ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) )
= $true )
| ( ( ( times_times_a @ SV30 @ SV139 )
= zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1644]) ).
thf(1855,plain,
! [SV139: a,SV30: a] :
( ( ( ( times_times_a @ SV30 @ SV139 )
!= zero_zero_a )
= $false )
| ( ( SV30 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1645]) ).
thf(1856,plain,
! [SV139: a,SV30: a] :
( ( ( ~ ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) ) )
= $false )
| ( ( SV30 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1645]) ).
thf(1857,plain,
! [SV139: a,SV30: a] :
( ( ( ( times_times_a @ SV30 @ SV139 )
!= zero_zero_a )
= $false )
| ( ( SV139 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1646]) ).
thf(1858,plain,
! [SV139: a,SV30: a] :
( ( ( ~ ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) ) )
= $false )
| ( ( SV139 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1646]) ).
thf(1859,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ( times_times_poly_a @ SV31 @ SV140 )
= zero_zero_poly_a )
= $true )
| ( ( ( times_times_poly_a @ SV31 @ SV140 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1647]) ).
thf(1860,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) )
= $true )
| ( ( ( times_times_poly_a @ SV31 @ SV140 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1648]) ).
thf(1861,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ( times_times_poly_a @ SV31 @ SV140 )
!= zero_zero_poly_a )
= $false )
| ( ( SV31 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1649]) ).
thf(1862,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ~ ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) ) )
= $false )
| ( ( SV31 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1649]) ).
thf(1863,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ( times_times_poly_a @ SV31 @ SV140 )
!= zero_zero_poly_a )
= $false )
| ( ( SV140 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1650]) ).
thf(1864,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ~ ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) ) )
= $false )
| ( ( SV140 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1650]) ).
thf(1865,plain,
! [SV141: nat,SV32: nat] :
( ( ( ( times_times_nat @ SV32 @ SV141 )
= zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV32 @ SV141 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1651]) ).
thf(1866,plain,
! [SV141: nat,SV32: nat] :
( ( ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) )
= $true )
| ( ( ( times_times_nat @ SV32 @ SV141 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1652]) ).
thf(1867,plain,
! [SV141: nat,SV32: nat] :
( ( ( ( times_times_nat @ SV32 @ SV141 )
!= zero_zero_nat )
= $false )
| ( ( SV32 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1653]) ).
thf(1868,plain,
! [SV141: nat,SV32: nat] :
( ( ( ~ ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) ) )
= $false )
| ( ( SV32 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1653]) ).
thf(1869,plain,
! [SV141: nat,SV32: nat] :
( ( ( ( times_times_nat @ SV32 @ SV141 )
!= zero_zero_nat )
= $false )
| ( ( SV141 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(1870,plain,
! [SV141: nat,SV32: nat] :
( ( ( ~ ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) ) )
= $false )
| ( ( SV141 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(1871,plain,
! [SV142: list_a,SV48: list_a] :
( ( ( SV48
= ( append_a @ SV142 @ SV48 ) )
= $true )
| ( ( SV48
= ( append_a @ SV142 @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1687]) ).
thf(1872,plain,
! [SV48: list_a,SV142: list_a] :
( ( ( SV142 = nil_a )
= $true )
| ( ( SV48
= ( append_a @ SV142 @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1688]) ).
thf(1873,plain,
! [SV142: list_a,SV48: list_a] :
( ( ( SV48
= ( append_a @ SV142 @ SV48 ) )
= $true )
| ( ( SV142 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1689]) ).
thf(1874,plain,
! [SV142: list_a] :
( ( ( SV142 = nil_a )
= $true )
| ( ( SV142 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1690]) ).
thf(1875,plain,
! [SV143: list_a,SV49: list_a] :
( ( ( ( append_a @ SV49 @ SV143 )
= SV143 )
= $true )
| ( ( ( append_a @ SV49 @ SV143 )
= SV143 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1691]) ).
thf(1876,plain,
! [SV143: list_a,SV49: list_a] :
( ( ( SV49 = nil_a )
= $true )
| ( ( ( append_a @ SV49 @ SV143 )
= SV143 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1692]) ).
thf(1877,plain,
! [SV143: list_a,SV49: list_a] :
( ( ( ( append_a @ SV49 @ SV143 )
= SV143 )
= $true )
| ( ( SV49 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1693]) ).
thf(1878,plain,
! [SV49: list_a] :
( ( ( SV49 = nil_a )
= $true )
| ( ( SV49 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1694]) ).
thf(1879,plain,
! [SV144: list_a,SV50: list_a] :
( ( ( SV50
= ( append_a @ SV50 @ SV144 ) )
= $true )
| ( ( SV50
= ( append_a @ SV50 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1695]) ).
thf(1880,plain,
! [SV50: list_a,SV144: list_a] :
( ( ( SV144 = nil_a )
= $true )
| ( ( SV50
= ( append_a @ SV50 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1696]) ).
thf(1881,plain,
! [SV144: list_a,SV50: list_a] :
( ( ( SV50
= ( append_a @ SV50 @ SV144 ) )
= $true )
| ( ( SV144 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1697]) ).
thf(1882,plain,
! [SV144: list_a] :
( ( ( SV144 = nil_a )
= $true )
| ( ( SV144 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1698]) ).
thf(1883,plain,
! [SV145: list_a,SV51: list_a] :
( ( ( ( append_a @ SV51 @ SV145 )
= SV51 )
= $true )
| ( ( ( append_a @ SV51 @ SV145 )
= SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1699]) ).
thf(1884,plain,
! [SV51: list_a,SV145: list_a] :
( ( ( SV145 = nil_a )
= $true )
| ( ( ( append_a @ SV51 @ SV145 )
= SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1700]) ).
thf(1885,plain,
! [SV145: list_a,SV51: list_a] :
( ( ( ( append_a @ SV51 @ SV145 )
= SV51 )
= $true )
| ( ( SV145 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1701]) ).
thf(1886,plain,
! [SV145: list_a] :
( ( ( SV145 = nil_a )
= $true )
| ( ( SV145 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1702]) ).
thf(1887,plain,
! [SV57: nat] :
( ( ( SV57 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1888,plain,
! [SV57: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV57 )
= $true )
| ( ( SV57 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1717]) ).
thf(1889,plain,
! [SV57: nat] :
( ( ( SV57 != zero_zero_nat )
= $true )
| ( ( SV57 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1718]) ).
thf(1890,plain,
! [SV194: a,SV61: a,SV175: a] :
( ( ( ( ( times_times_a @ SV175 @ SV61 )
!= ( times_times_a @ SV194 @ SV61 ) )
| ( SV175 != SV194 ) )
= $false )
| ( ( ( times_times_a @ SV175 @ SV61 )
= ( times_times_a @ SV194 @ SV61 ) )
= $false )
| ( ( SV61 = zero_zero_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1891,plain,
! [SV194: a,SV61: a,SV175: a] :
( ( ( ( ( times_times_a @ SV175 @ SV61 )
!= ( times_times_a @ SV194 @ SV61 ) )
| ( SV175 != SV194 ) )
= $false )
| ( ( SV175 = SV194 )
= $false )
| ( ( SV61 = zero_zero_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1720]) ).
thf(1892,plain,
! [SV195: poly_a,SV62: poly_a,SV176: poly_a] :
( ( ( ( ( times_times_poly_a @ SV176 @ SV62 )
!= ( times_times_poly_a @ SV195 @ SV62 ) )
| ( SV176 != SV195 ) )
= $false )
| ( ( ( times_times_poly_a @ SV176 @ SV62 )
= ( times_times_poly_a @ SV195 @ SV62 ) )
= $false )
| ( ( SV62 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1893,plain,
! [SV195: poly_a,SV62: poly_a,SV176: poly_a] :
( ( ( ( ( times_times_poly_a @ SV176 @ SV62 )
!= ( times_times_poly_a @ SV195 @ SV62 ) )
| ( SV176 != SV195 ) )
= $false )
| ( ( SV176 = SV195 )
= $false )
| ( ( SV62 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1894,plain,
! [SV196: nat,SV63: nat,SV177: nat] :
( ( ( ( ( times_times_nat @ SV177 @ SV63 )
!= ( times_times_nat @ SV196 @ SV63 ) )
| ( SV177 != SV196 ) )
= $false )
| ( ( ( times_times_nat @ SV177 @ SV63 )
= ( times_times_nat @ SV196 @ SV63 ) )
= $false )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1723]) ).
thf(1895,plain,
! [SV196: nat,SV63: nat,SV177: nat] :
( ( ( ( ( times_times_nat @ SV177 @ SV63 )
!= ( times_times_nat @ SV196 @ SV63 ) )
| ( SV177 != SV196 ) )
= $false )
| ( ( SV177 = SV196 )
= $false )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(1896,plain,
! [SV197: a,SV178: a,SV64: a] :
( ( ( ( ( times_times_a @ SV64 @ SV178 )
!= ( times_times_a @ SV64 @ SV197 ) )
| ( SV178 != SV197 ) )
= $false )
| ( ( ( times_times_a @ SV64 @ SV178 )
= ( times_times_a @ SV64 @ SV197 ) )
= $false )
| ( ( SV64 = zero_zero_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1725]) ).
thf(1897,plain,
! [SV197: a,SV178: a,SV64: a] :
( ( ( ( ( times_times_a @ SV64 @ SV178 )
!= ( times_times_a @ SV64 @ SV197 ) )
| ( SV178 != SV197 ) )
= $false )
| ( ( SV178 = SV197 )
= $false )
| ( ( SV64 = zero_zero_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1726]) ).
thf(1898,plain,
! [SV198: poly_a,SV179: poly_a,SV65: poly_a] :
( ( ( ( ( times_times_poly_a @ SV65 @ SV179 )
!= ( times_times_poly_a @ SV65 @ SV198 ) )
| ( SV179 != SV198 ) )
= $false )
| ( ( ( times_times_poly_a @ SV65 @ SV179 )
= ( times_times_poly_a @ SV65 @ SV198 ) )
= $false )
| ( ( SV65 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1727]) ).
thf(1899,plain,
! [SV198: poly_a,SV179: poly_a,SV65: poly_a] :
( ( ( ( ( times_times_poly_a @ SV65 @ SV179 )
!= ( times_times_poly_a @ SV65 @ SV198 ) )
| ( SV179 != SV198 ) )
= $false )
| ( ( SV179 = SV198 )
= $false )
| ( ( SV65 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1728]) ).
thf(1900,plain,
! [SV199: nat,SV180: nat,SV66: nat] :
( ( ( ( ( times_times_nat @ SV66 @ SV180 )
!= ( times_times_nat @ SV66 @ SV199 ) )
| ( SV180 != SV199 ) )
= $false )
| ( ( ( times_times_nat @ SV66 @ SV180 )
= ( times_times_nat @ SV66 @ SV199 ) )
= $false )
| ( ( SV66 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1901,plain,
! [SV199: nat,SV180: nat,SV66: nat] :
( ( ( ( ( times_times_nat @ SV66 @ SV180 )
!= ( times_times_nat @ SV66 @ SV199 ) )
| ( SV180 != SV199 ) )
= $false )
| ( ( SV180 = SV199 )
= $false )
| ( ( SV66 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(1902,plain,
! [SV186: list_a,SV80: a,SV216: list_a,SV153: list_a,SV212: list_a] :
( ( ( SV212
= ( append_a @ SV153 @ SV216 ) )
= $false )
| ( ( ( cons_a @ SV80 @ SV212 )
= ( append_a @ SV186 @ SV216 ) )
= $true )
| ( ( ( cons_a @ SV80 @ SV153 )
= SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1731]) ).
thf(1903,plain,
! [SV187: nat,SV156: nat,SV86: nat] :
( ( ( ( times_times_nat @ SV86 @ SV156 )
!= ( times_times_nat @ SV187 @ SV156 ) )
= $false )
| ( ( ( times_times_nat @ SV86 @ SV156 )
= ( times_times_nat @ SV187 @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1736]) ).
thf(1904,plain,
! [SV156: nat,SV187: nat,SV86: nat] :
( ( ( ~ ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV86 @ SV156 )
= ( times_times_nat @ SV187 @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1736]) ).
thf(1905,plain,
! [SV187: nat,SV156: nat,SV86: nat] :
( ( ( ( ( times_times_nat @ SV86 @ SV156 )
!= ( times_times_nat @ SV187 @ SV156 ) )
| ~ ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) ) )
= $false )
| ( ( SV86 = SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1906,plain,
! [SV187: nat,SV156: nat,SV86: nat] :
( ( ( ( ( times_times_nat @ SV86 @ SV156 )
!= ( times_times_nat @ SV187 @ SV156 ) )
| ~ ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) ) )
= $false )
| ( ( SV156 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1738]) ).
thf(1907,plain,
! [SV87: nat] :
( ( ( SV87 != zero_zero_nat )
= $true )
| ( ( SV87 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1739]) ).
thf(1908,plain,
! [SV87: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV87 )
= $true )
| ( ( SV87 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1740]) ).
thf(1909,plain,
! [SV87: nat] :
( ( ( SV87 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1910,plain,
! [SV89: nat] :
( ( ( SV89 != zero_zero_nat )
= $true )
| ( ( SV89 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1743]) ).
thf(1911,plain,
! [SV89: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV89 )
= $true )
| ( ( SV89 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1744]) ).
thf(1912,plain,
! [SV89: nat] :
( ( ( SV89 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1745]) ).
thf(1913,plain,
! [SV157: nat,SV90: nat] :
( ( ( ( times_times_nat @ SV90 @ SV157 )
= zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV90 @ SV157 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1747]) ).
thf(1914,plain,
! [SV157: nat,SV90: nat] :
( ( ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) )
= $true )
| ( ( ( times_times_nat @ SV90 @ SV157 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1748]) ).
thf(1915,plain,
! [SV157: nat,SV90: nat] :
( ( ( ( times_times_nat @ SV90 @ SV157 )
!= zero_zero_nat )
= $false )
| ( ( SV90 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1749]) ).
thf(1916,plain,
! [SV157: nat,SV90: nat] :
( ( ( ~ ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) ) )
= $false )
| ( ( SV90 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1749]) ).
thf(1917,plain,
! [SV157: nat,SV90: nat] :
( ( ( ( times_times_nat @ SV90 @ SV157 )
!= zero_zero_nat )
= $false )
| ( ( SV157 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1750]) ).
thf(1918,plain,
! [SV157: nat,SV90: nat] :
( ( ( ~ ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) ) )
= $false )
| ( ( SV157 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1750]) ).
thf(1919,plain,
! [SV188: nat,SV158: nat,SV92: nat] :
( ( ( ( times_times_nat @ SV92 @ SV158 )
!= ( times_times_nat @ SV92 @ SV188 ) )
= $false )
| ( ( ( times_times_nat @ SV92 @ SV158 )
= ( times_times_nat @ SV92 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1751]) ).
thf(1920,plain,
! [SV92: nat,SV188: nat,SV158: nat] :
( ( ( ~ ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) ) )
= $false )
| ( ( ( times_times_nat @ SV92 @ SV158 )
= ( times_times_nat @ SV92 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1751]) ).
thf(1921,plain,
! [SV188: nat,SV158: nat,SV92: nat] :
( ( ( ( ( times_times_nat @ SV92 @ SV158 )
!= ( times_times_nat @ SV92 @ SV188 ) )
| ~ ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) ) )
= $false )
| ( ( SV158 = SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1752]) ).
thf(1922,plain,
! [SV188: nat,SV158: nat,SV92: nat] :
( ( ( ( ( times_times_nat @ SV92 @ SV158 )
!= ( times_times_nat @ SV92 @ SV188 ) )
| ~ ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) ) )
= $false )
| ( ( SV92 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(1923,plain,
! [SV94: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV94 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV94 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1754]) ).
thf(1924,plain,
! [SV94: nat] :
( ( ( SV94 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV94 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1755]) ).
thf(1925,plain,
! [SV94: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( SV94 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1756]) ).
thf(1926,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ( times_times_nat @ SV100 @ SV160 )
!= ( times_times_nat @ SV100 @ SV189 ) )
= $false )
| ( ( ( times_times_nat @ SV100 @ SV160 )
= ( times_times_nat @ SV100 @ SV189 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1758]) ).
thf(1927,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ~ ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) ) )
= $false )
| ( ( ( times_times_nat @ SV100 @ SV160 )
= ( times_times_nat @ SV100 @ SV189 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1758]) ).
thf(1928,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ( ( times_times_nat @ SV100 @ SV160 )
!= ( times_times_nat @ SV100 @ SV189 ) )
| ~ ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) ) )
= $false )
| ( ( SV100 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1759]) ).
thf(1929,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ( ( times_times_nat @ SV100 @ SV160 )
!= ( times_times_nat @ SV100 @ SV189 ) )
| ~ ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) ) )
= $false )
| ( ( SV160 = SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1760]) ).
thf(1930,plain,
! [SV101: list_a > $o] :
( ( ( ( ( sK40_X2 @ SV101 )
!= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
= $true )
| ( ( ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1761]) ).
thf(1931,plain,
! [SV101: list_a > $o] :
( ( ( ~ ( ~ ( ( ( sK40_X2 @ SV101 )
= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
| ~ ~ ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) ) ) )
= $true )
| ( ( ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1762]) ).
thf(1932,plain,
! [SV221: list_a,SV217: a,SV102: list_a > $o] :
( ( ( ( sK25_SY345 @ SV102 )
= ( cons_a @ SV217 @ SV221 ) )
= $false )
| ( ( SV102 @ ( sK25_SY345 @ SV102 ) )
= $true )
| ( ( ~ ( SV102 @ nil_a )
| ! [SY475: list_a] : ( SV102 @ SY475 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1933,plain,
! [SV228: list_a,SV102: list_a > $o] :
( ( ( SV102 @ SV228 )
= $true )
| ( ( SV102 @ nil_a )
= $false )
| ( ( SV102 @ ( cons_a @ ( sK24_X2 @ SV102 ) @ ( sK25_SY345 @ SV102 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(1934,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ( append_a @ SV103 @ SV161 )
= nil_a )
= $true )
| ( ( ( append_a @ SV103 @ SV161 )
= nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1765]) ).
thf(1935,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) )
= $true )
| ( ( ( append_a @ SV103 @ SV161 )
= nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1766]) ).
thf(1936,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( SV103 = nil_a )
= $false )
| ( ( SV161 != nil_a )
= $true )
| ( ( ~ ( ( ( append_a @ SV103 @ SV161 )
!= nil_a )
| ~ ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1767]) ).
thf(1937,plain,
! [SV229: list_a,SV162: a > a,SV104: ( a > a ) > list_a > list_a > $o] :
( ( ( ! [SY558: list_a] : ( SV104 @ SV162 @ SV229 @ SY558 ) )
= $true )
| ( ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) @ ( cons_a @ ( sK54_F2 @ SV162 @ SV104 @ ( sK55_SY373 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) ) )
= $true )
| ( ( SV104 @ ( sK58_F2 @ SV162 @ SV104 ) @ nil_a @ ( sK59_SY379 @ SV162 @ SV104 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(1938,plain,
! [SV162: a > a,SV104: ( a > a ) > list_a > list_a > $o] :
( ( ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( cons_a @ ( sK55_SY373 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) )
= $false )
| ( ( ! [SY529: list_a,SY530: list_a] : ( SV104 @ SV162 @ SY529 @ SY530 ) )
= $true )
| ( ( SV104 @ ( sK58_F2 @ SV162 @ SV104 ) @ nil_a @ ( sK59_SY379 @ SV162 @ SV104 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1939,plain,
! [SV203: a,SV190: list_a,SV163: a,SV105: list_a] :
( ( ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
!= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
| ~ ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) )
= $false )
| ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1940,plain,
! [SV203: a,SV163: a,SV190: list_a,SV105: list_a] :
( ( ( ( SV105 != SV190 )
| ( SV163 != SV203 ) )
= $true )
| ( ( ~ ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
!= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
| ~ ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1771]) ).
thf(1941,plain,
! [SV230: list_a,SV222: a > a > $o,SV106: ( a > a > $o ) > list_a > $o] :
( ( ( SV106 @ SV222 @ SV230 )
= $true )
| ( ( SV106 @ ( sK36_P5 @ SV106 ) @ ( sK38_SY361 @ SV106 ) )
= $true )
| ( ( SV106 @ ( sK39_P5 @ SV106 ) @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(1942,plain,
! [SV231: a > a > $o,SV106: ( a > a > $o ) > list_a > $o] :
( ( ( ! [SY559: list_a] : ( SV106 @ SV231 @ SY559 ) )
= $true )
| ( ( SV106 @ ( sK36_P5 @ SV106 ) @ ( cons_a @ ( sK37_SY359 @ SV106 ) @ ( sK38_SY361 @ SV106 ) ) )
= $false )
| ( ( SV106 @ ( sK39_P5 @ SV106 ) @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(1943,plain,
! [SV107: nat > $o] :
( ( ( ~ ~ ( SV107 @ ( sK1_N2 @ SV107 ) ) )
= $false )
| ( ( ! [SY486: nat] : ( SV107 @ SY486 ) )
= $true )
| ( ( SV107 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1775]) ).
thf(1944,plain,
! [SV107: nat > $o] :
( ( ( ~ ! [SY485: nat] :
( ~ ( ord_less_nat @ SY485 @ ( sK1_N2 @ SV107 ) )
| ( SV107 @ SY485 ) ) )
= $false )
| ( ( ! [SY486: nat] : ( SV107 @ SY486 ) )
= $true )
| ( ( SV107 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1775]) ).
thf(1945,plain,
! [SV232: list_a,SV108: list_a > $o] :
( ( ( SV108 @ SV232 )
= $true )
| ( ( SV108 @ ( cons_a @ ( sK4_X1 @ SV108 ) @ ( sK5_SY329 @ SV108 ) ) )
= $false )
| ( ( SV108 @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(1946,plain,
! [SV109: list_a > $o] :
( ( ( SV109 @ ( sK20_SY343 @ SV109 ) )
= $true )
| ( ( ! [SY488: list_a] : ( SV109 @ SY488 ) )
= $true )
| ( ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
= $false )
| ( ( SV109 @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1778]) ).
thf(1947,plain,
! [SV109: list_a > $o] :
( ( ( ~ ( ~ ( SV109 @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) )
| ~ ~ ( SV109 @ ( cons_a @ ( sK18_X2 @ SV109 ) @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) ) ) ) )
= $true )
| ( ( ! [SY488: list_a] : ( SV109 @ SY488 ) )
= $true )
| ( ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
= $false )
| ( ( SV109 @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1779]) ).
thf(1948,plain,
! [SV204: list_a,SV191: a,SV164: list_a,SV110: a] :
( ( ( ( ( cons_a @ SV110 @ SV164 )
!= ( cons_a @ SV191 @ SV204 ) )
| ~ ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) )
= $false )
| ( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1780]) ).
thf(1949,plain,
! [SV204: list_a,SV164: list_a,SV191: a,SV110: a] :
( ( ( ( SV110 != SV191 )
| ( SV164 != SV204 ) )
= $true )
| ( ( ~ ( ( ( cons_a @ SV110 @ SV164 )
!= ( cons_a @ SV191 @ SV204 ) )
| ~ ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1781]) ).
thf(1950,plain,
! [SV233: list_a,SV225: list_a,SV111: list_a > list_a > $o] :
( ( ( SV111 @ SV225 @ SV233 )
= $true )
| ( ( SV111 @ ( sK16_SY340 @ SV111 ) @ ( sK15_SY338 @ SV111 ) )
= $true )
| ( ( SV111 @ nil_a @ ( sK17_X_1 @ SV111 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(1951,plain,
! [SV234: list_a,SV111: list_a > list_a > $o] :
( ( ( ! [SY560: list_a] : ( SV111 @ SV234 @ SY560 ) )
= $true )
| ( ( SV111 @ ( cons_a @ ( sK14_X2 @ SV111 ) @ ( sK15_SY338 @ SV111 ) ) @ ( sK16_SY340 @ SV111 ) )
= $false )
| ( ( SV111 @ nil_a @ ( sK17_X_1 @ SV111 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(1952,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ( pCons_a @ SV112 @ SV165 )
= zero_zero_poly_a )
= $true )
| ( ( ( pCons_a @ SV112 @ SV165 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1784]) ).
thf(1953,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) )
= $true )
| ( ( ( pCons_a @ SV112 @ SV165 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1785]) ).
thf(1954,plain,
! [SV165: poly_a,SV112: a] :
( ( ( SV112 = zero_zero_a )
= $false )
| ( ( SV165 != zero_zero_poly_a )
= $true )
| ( ( ~ ( ( ( pCons_a @ SV112 @ SV165 )
!= zero_zero_poly_a )
| ~ ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1786]) ).
thf(1955,plain,
! [SV235: poly_a,SV226: poly_a,SV113: poly_a > poly_a > $o] :
( ( ( SV113 @ SV226 @ SV235 )
= $true )
| ( ( SV113 @ ( sK85_SY400 @ SV113 ) @ ( sK87_SY405 @ SV113 ) )
= $true )
| ( ( SV113 @ zero_zero_poly_a @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(1956,plain,
! [SV236: poly_a,SV113: poly_a > poly_a > $o] :
( ( ( ! [SY561: poly_a] : ( SV113 @ SV236 @ SY561 ) )
= $true )
| ( ( SV113 @ ( pCons_a @ ( sK84_A2 @ SV113 ) @ ( sK85_SY400 @ SV113 ) ) @ ( pCons_a @ ( sK86_SY403 @ SV113 ) @ ( sK87_SY405 @ SV113 ) ) )
= $false )
| ( ( SV113 @ zero_zero_poly_a @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(1957,plain,
! [SV114: list_a > list_a > $o] :
( ( ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) )
= $false )
| ( ( ! [SY497: list_a,SY498: list_a] : ( SV114 @ SY497 @ SY498 ) )
= $true )
| ( ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a )
= $false )
| ( ( SV114 @ ( sK72_SY386 @ SV114 ) @ ( sK74_SY391 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(1958,plain,
! [SV114: list_a > list_a > $o] :
( ( ( ~ ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) ) )
= $true )
| ( ( ! [SY497: list_a,SY498: list_a] : ( SV114 @ SY497 @ SY498 ) )
= $true )
| ( ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a )
= $false )
| ( ( SV114 @ ( cons_a @ ( sK71_X2 @ SV114 ) @ ( sK72_SY386 @ SV114 ) ) @ ( cons_a @ ( sK73_SY389 @ SV114 ) @ ( sK74_SY391 @ SV114 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(1959,plain,
! [SV115: list_a,SV192: list_a > $o] :
( ( ( ( sK52_SY372 @ SV192 @ SV115 )
!= nil_a )
= $true )
| ( ( SV192 @ SV115 )
= $true )
| ( ( SV192 @ ( cons_a @ ( sK53_X2 @ SV192 @ SV115 ) @ nil_a ) )
= $false )
| ( ( SV115 = nil_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1791]) ).
thf(1960,plain,
! [SV115: list_a,SV192: list_a > $o] :
( ( ( ~ ( ~ ( SV192 @ ( sK52_SY372 @ SV192 @ SV115 ) )
| ~ ~ ( SV192 @ ( cons_a @ ( sK51_X2 @ SV192 @ SV115 ) @ ( sK52_SY372 @ SV192 @ SV115 ) ) ) ) )
= $true )
| ( ( SV192 @ SV115 )
= $true )
| ( ( SV192 @ ( cons_a @ ( sK53_X2 @ SV192 @ SV115 ) @ nil_a ) )
= $false )
| ( ( SV115 = nil_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1792]) ).
thf(1961,plain,
! [SV117: ( a > a > $o ) > list_a > $o] :
( ( ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) )
= $true )
| ( ( ! [SY501: a > a > $o,SY502: list_a] : ( SV117 @ SY501 @ SY502 ) )
= $true )
| ( ( SV117 @ ( sK48_P5 @ SV117 ) @ ( cons_a @ ( sK49_SY371 @ SV117 ) @ nil_a ) )
= $false )
| ( ( SV117 @ ( sK50_P5 @ SV117 ) @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1793]) ).
thf(1962,plain,
! [SV117: ( a > a > $o ) > list_a > $o] :
( ( ( ~ ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK45_SY365 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) ) ) )
= $true )
| ( ( ! [SY501: a > a > $o,SY502: list_a] : ( SV117 @ SY501 @ SY502 ) )
= $true )
| ( ( SV117 @ ( sK48_P5 @ SV117 ) @ ( cons_a @ ( sK49_SY371 @ SV117 ) @ nil_a ) )
= $false )
| ( ( SV117 @ ( sK50_P5 @ SV117 ) @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1794]) ).
thf(1963,plain,
! [SV118: list_a > list_a > $o] :
( ( ( SV118 @ ( sK27_SY350 @ SV118 ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) )
= $true )
| ( ( ! [SY503: list_a,SY504: list_a] : ( SV118 @ SY503 @ SY504 ) )
= $true )
| ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1795]) ).
thf(1964,plain,
! [SV118: list_a > list_a > $o] :
( ( ( ~ ( ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( sK29_SY355 @ SV118 ) )
| ~ ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) ) ) )
= $true )
| ( ( ! [SY503: list_a,SY504: list_a] : ( SV118 @ SY503 @ SY504 ) )
= $true )
| ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1796]) ).
thf(1965,plain,
! [SV119: list_a > list_a > $o] :
( ( ( ~ ( SV119 @ ( sK7_SY330 @ SV119 ) @ ( sK9_SY335 @ SV119 ) )
| ~ ~ ( SV119 @ ( cons_a @ ( sK6_X2 @ SV119 ) @ ( sK7_SY330 @ SV119 ) ) @ ( cons_a @ ( sK8_SY333 @ SV119 ) @ ( sK9_SY335 @ SV119 ) ) ) )
= $false )
| ( ( ! [SY505: list_a,SY506: list_a] : ( SV119 @ SY505 @ SY506 ) )
= $true )
| ( ( SV119 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SV119 ) @ ( sK11_SY336 @ SV119 ) ) )
= $false )
| ( ( SV119 @ ( cons_a @ ( sK12_X2 @ SV119 ) @ ( sK13_SY337 @ SV119 ) ) @ nil_a )
= $false )
| ( ( SV119 @ nil_a @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1966,plain,
! [SV120: poly_a > $o] :
( ( ( ( sK88_A2 @ SV120 )
= zero_zero_a )
= $false )
| ( ( ( sK89_SY406 @ SV120 )
!= zero_zero_poly_a )
= $true )
| ( ( ! [SY507: poly_a] : ( SV120 @ SY507 ) )
= $true )
| ( ( SV120 @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1798]) ).
thf(1967,plain,
! [SV120: poly_a > $o] :
( ( ( ~ ( SV120 @ ( sK89_SY406 @ SV120 ) ) )
= $false )
| ( ( ! [SY507: poly_a] : ( SV120 @ SY507 ) )
= $true )
| ( ( SV120 @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1799]) ).
thf(1968,plain,
! [SV120: poly_a > $o] :
( ( ( ~ ~ ( SV120 @ ( pCons_a @ ( sK88_A2 @ SV120 ) @ ( sK89_SY406 @ SV120 ) ) ) )
= $false )
| ( ( ! [SY507: poly_a] : ( SV120 @ SY507 ) )
= $true )
| ( ( SV120 @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1799]) ).
thf(1969,plain,
! [SV121: list_a] :
( ( ( SV121 != nil_a )
= $true )
| ( ( SV121 = nil_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1800]) ).
thf(1970,plain,
! [SV121: list_a] :
( ( ( ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) )
= $true )
| ( ( SV121 = nil_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1801]) ).
thf(1971,plain,
! [SV220: a,SV121: list_a] :
( ( ( ! [SY554: list_a] :
( SV121
!= ( cons_a @ SV220 @ SY554 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV121 != nil_a ) )
| ~ ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1802]) ).
thf(1972,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( nil_a
= ( append_a @ SV122 @ SV166 ) )
= $true )
| ( ( nil_a
= ( append_a @ SV122 @ SV166 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1803]) ).
thf(1973,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) )
= $true )
| ( ( nil_a
= ( append_a @ SV122 @ SV166 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1804]) ).
thf(1974,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( SV122 = nil_a )
= $false )
| ( ( SV166 != nil_a )
= $true )
| ( ( ~ ( ( nil_a
!= ( append_a @ SV122 @ SV166 ) )
| ~ ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(1975,plain,
! [SV123: list_a > list_a > $o] :
( ( ( SV123 @ ( sK76_SY392 @ SV123 ) @ ( sK78_SY397 @ SV123 ) )
= $true )
| ( ( ! [SY511: list_a,SY512: list_a] : ( SV123 @ SY511 @ SY512 ) )
= $true )
| ( ( SV123 @ nil_a @ ( cons_a @ ( sK79_V @ SV123 ) @ ( sK80_SY398 @ SV123 ) ) )
= $false )
| ( ( SV123 @ ( sK81_Xs2 @ SV123 ) @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1806]) ).
thf(1976,plain,
! [SV123: list_a > list_a > $o] :
( ( ( ~ ( SV123 @ ( cons_a @ ( sK75_X2 @ SV123 ) @ ( sK76_SY392 @ SV123 ) ) @ ( cons_a @ ( sK77_SY395 @ SV123 ) @ ( sK78_SY397 @ SV123 ) ) ) )
= $true )
| ( ( ! [SY511: list_a,SY512: list_a] : ( SV123 @ SY511 @ SY512 ) )
= $true )
| ( ( SV123 @ nil_a @ ( cons_a @ ( sK79_V @ SV123 ) @ ( sK80_SY398 @ SV123 ) ) )
= $false )
| ( ( SV123 @ ( sK81_Xs2 @ SV123 ) @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1807]) ).
thf(1977,plain,
! [SV237: list_a,SV124: list_a > $o] :
( ( ( SV124 @ SV237 )
= $true )
| ( ( SV124 @ ( cons_a @ ( sK62_X2 @ SV124 ) @ ( sK63_SY381 @ SV124 ) ) )
= $false )
| ( ( SV124 @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(1978,plain,
! [SV193: poly_a,SV126: poly_a] :
( ( ( SV126 != SV193 )
= $false )
| ( ( SV126 = SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1810]) ).
thf(1979,plain,
! [SV193: poly_a,SV126: poly_a] :
( ( ( ( coeffs_a @ SV126 )
!= ( coeffs_a @ SV193 ) )
= $false )
| ( ( SV126 = SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1810]) ).
thf(1980,plain,
! [SV193: poly_a,SV126: poly_a] :
( ( ( SV126 != SV193 )
= $false )
| ( ( ( coeffs_a @ SV126 )
= ( coeffs_a @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1811]) ).
thf(1981,plain,
! [SV193: poly_a,SV126: poly_a] :
( ( ( ( coeffs_a @ SV126 )
!= ( coeffs_a @ SV193 ) )
= $false )
| ( ( ( coeffs_a @ SV126 )
= ( coeffs_a @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1811]) ).
thf(1982,plain,
! [SV130: poly_a,SV12: a] :
( ( ( SV12 = zero_zero_a )
= $true )
| ( ( SV130 = zero_zero_poly_a )
= $true )
| ( ( ( smult_a @ SV12 @ SV130 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1817]) ).
thf(1983,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ( smult_a @ SV12 @ SV130 )
= zero_zero_poly_a )
= $true )
| ( ( SV12 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1818]) ).
thf(1984,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) )
= $true )
| ( ( SV12 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1819]) ).
thf(1985,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ( smult_a @ SV12 @ SV130 )
= zero_zero_poly_a )
= $true )
| ( ( SV130 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1820]) ).
thf(1986,plain,
! [SV130: poly_a,SV12: a] :
( ( ( ( SV12 = zero_zero_a )
| ( SV130 = zero_zero_poly_a ) )
= $true )
| ( ( SV130 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1821]) ).
thf(1987,plain,
! [SV23: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV23 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1826]) ).
thf(1988,plain,
! [SV169: a,SV133: a,SV24: a] :
( ( ( ( times_times_a @ SV24 @ SV133 )
= ( times_times_a @ SV169 @ SV133 ) )
= $true )
| ( ( ( times_times_a @ SV24 @ SV133 )
= ( times_times_a @ SV169 @ SV133 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1829]) ).
thf(1989,plain,
! [SV169: a,SV24: a,SV133: a] :
( ( ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) )
= $true )
| ( ( ( times_times_a @ SV24 @ SV133 )
= ( times_times_a @ SV169 @ SV133 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1830]) ).
thf(1990,plain,
! [SV169: a,SV133: a,SV24: a] :
( ( ( ( times_times_a @ SV24 @ SV133 )
!= ( times_times_a @ SV169 @ SV133 ) )
= $false )
| ( ( SV133 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1831]) ).
thf(1991,plain,
! [SV169: a,SV24: a,SV133: a] :
( ( ( ~ ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) ) )
= $false )
| ( ( SV133 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1831]) ).
thf(1992,plain,
! [SV169: a,SV133: a,SV24: a] :
( ( ( ( times_times_a @ SV24 @ SV133 )
!= ( times_times_a @ SV169 @ SV133 ) )
= $false )
| ( ( SV24 = SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1832]) ).
thf(1993,plain,
! [SV169: a,SV24: a,SV133: a] :
( ( ( ~ ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) ) )
= $false )
| ( ( SV24 = SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1832]) ).
thf(1994,plain,
! [SV170: poly_a,SV134: poly_a,SV25: poly_a] :
( ( ( ( times_times_poly_a @ SV25 @ SV134 )
= ( times_times_poly_a @ SV170 @ SV134 ) )
= $true )
| ( ( ( times_times_poly_a @ SV25 @ SV134 )
= ( times_times_poly_a @ SV170 @ SV134 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1833]) ).
thf(1995,plain,
! [SV170: poly_a,SV25: poly_a,SV134: poly_a] :
( ( ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) )
= $true )
| ( ( ( times_times_poly_a @ SV25 @ SV134 )
= ( times_times_poly_a @ SV170 @ SV134 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1834]) ).
thf(1996,plain,
! [SV170: poly_a,SV134: poly_a,SV25: poly_a] :
( ( ( ( times_times_poly_a @ SV25 @ SV134 )
!= ( times_times_poly_a @ SV170 @ SV134 ) )
= $false )
| ( ( SV134 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1835]) ).
thf(1997,plain,
! [SV170: poly_a,SV25: poly_a,SV134: poly_a] :
( ( ( ~ ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) ) )
= $false )
| ( ( SV134 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1835]) ).
thf(1998,plain,
! [SV170: poly_a,SV134: poly_a,SV25: poly_a] :
( ( ( ( times_times_poly_a @ SV25 @ SV134 )
!= ( times_times_poly_a @ SV170 @ SV134 ) )
= $false )
| ( ( SV25 = SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1836]) ).
thf(1999,plain,
! [SV170: poly_a,SV25: poly_a,SV134: poly_a] :
( ( ( ~ ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) ) )
= $false )
| ( ( SV25 = SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1836]) ).
thf(2000,plain,
! [SV171: nat,SV135: nat,SV26: nat] :
( ( ( ( times_times_nat @ SV26 @ SV135 )
= ( times_times_nat @ SV171 @ SV135 ) )
= $true )
| ( ( ( times_times_nat @ SV26 @ SV135 )
= ( times_times_nat @ SV171 @ SV135 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1837]) ).
thf(2001,plain,
! [SV171: nat,SV26: nat,SV135: nat] :
( ( ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) )
= $true )
| ( ( ( times_times_nat @ SV26 @ SV135 )
= ( times_times_nat @ SV171 @ SV135 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1838]) ).
thf(2002,plain,
! [SV171: nat,SV135: nat,SV26: nat] :
( ( ( ( times_times_nat @ SV26 @ SV135 )
!= ( times_times_nat @ SV171 @ SV135 ) )
= $false )
| ( ( SV135 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1839]) ).
thf(2003,plain,
! [SV171: nat,SV26: nat,SV135: nat] :
( ( ( ~ ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) ) )
= $false )
| ( ( SV135 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1839]) ).
thf(2004,plain,
! [SV171: nat,SV135: nat,SV26: nat] :
( ( ( ( times_times_nat @ SV26 @ SV135 )
!= ( times_times_nat @ SV171 @ SV135 ) )
= $false )
| ( ( SV26 = SV171 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1840]) ).
thf(2005,plain,
! [SV171: nat,SV26: nat,SV135: nat] :
( ( ( ~ ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) ) )
= $false )
| ( ( SV26 = SV171 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1840]) ).
thf(2006,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ( times_times_a @ SV27 @ SV136 )
= ( times_times_a @ SV27 @ SV172 ) )
= $true )
| ( ( ( times_times_a @ SV27 @ SV136 )
= ( times_times_a @ SV27 @ SV172 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1841]) ).
thf(2007,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) )
= $true )
| ( ( ( times_times_a @ SV27 @ SV136 )
= ( times_times_a @ SV27 @ SV172 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1842]) ).
thf(2008,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ( times_times_a @ SV27 @ SV136 )
!= ( times_times_a @ SV27 @ SV172 ) )
= $false )
| ( ( SV27 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1843]) ).
thf(2009,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ~ ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) ) )
= $false )
| ( ( SV27 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1843]) ).
thf(2010,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ( times_times_a @ SV27 @ SV136 )
!= ( times_times_a @ SV27 @ SV172 ) )
= $false )
| ( ( SV136 = SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1844]) ).
thf(2011,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ~ ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) ) )
= $false )
| ( ( SV136 = SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1844]) ).
thf(2012,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ( times_times_poly_a @ SV28 @ SV137 )
= ( times_times_poly_a @ SV28 @ SV173 ) )
= $true )
| ( ( ( times_times_poly_a @ SV28 @ SV137 )
= ( times_times_poly_a @ SV28 @ SV173 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1845]) ).
thf(2013,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) )
= $true )
| ( ( ( times_times_poly_a @ SV28 @ SV137 )
= ( times_times_poly_a @ SV28 @ SV173 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1846]) ).
thf(2014,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ( times_times_poly_a @ SV28 @ SV137 )
!= ( times_times_poly_a @ SV28 @ SV173 ) )
= $false )
| ( ( SV28 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1847]) ).
thf(2015,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ~ ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) ) )
= $false )
| ( ( SV28 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1847]) ).
thf(2016,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ( times_times_poly_a @ SV28 @ SV137 )
!= ( times_times_poly_a @ SV28 @ SV173 ) )
= $false )
| ( ( SV137 = SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1848]) ).
thf(2017,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ~ ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) ) )
= $false )
| ( ( SV137 = SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1848]) ).
thf(2018,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ( times_times_nat @ SV29 @ SV138 )
= ( times_times_nat @ SV29 @ SV174 ) )
= $true )
| ( ( ( times_times_nat @ SV29 @ SV138 )
= ( times_times_nat @ SV29 @ SV174 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1849]) ).
thf(2019,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) )
= $true )
| ( ( ( times_times_nat @ SV29 @ SV138 )
= ( times_times_nat @ SV29 @ SV174 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1850]) ).
thf(2020,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ( times_times_nat @ SV29 @ SV138 )
!= ( times_times_nat @ SV29 @ SV174 ) )
= $false )
| ( ( SV29 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1851]) ).
thf(2021,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ~ ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) ) )
= $false )
| ( ( SV29 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1851]) ).
thf(2022,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ( times_times_nat @ SV29 @ SV138 )
!= ( times_times_nat @ SV29 @ SV174 ) )
= $false )
| ( ( SV138 = SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1852]) ).
thf(2023,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ~ ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) ) )
= $false )
| ( ( SV138 = SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1852]) ).
thf(2024,plain,
! [SV139: a,SV30: a] :
( ( ( SV30 = zero_zero_a )
= $true )
| ( ( SV139 = zero_zero_a )
= $true )
| ( ( ( times_times_a @ SV30 @ SV139 )
= zero_zero_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1854]) ).
thf(2025,plain,
! [SV139: a,SV30: a] :
( ( ( ( times_times_a @ SV30 @ SV139 )
= zero_zero_a )
= $true )
| ( ( SV30 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1855]) ).
thf(2026,plain,
! [SV139: a,SV30: a] :
( ( ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) )
= $true )
| ( ( SV30 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(2027,plain,
! [SV139: a,SV30: a] :
( ( ( ( times_times_a @ SV30 @ SV139 )
= zero_zero_a )
= $true )
| ( ( SV139 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1857]) ).
thf(2028,plain,
! [SV139: a,SV30: a] :
( ( ( ( SV30 = zero_zero_a )
| ( SV139 = zero_zero_a ) )
= $true )
| ( ( SV139 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1858]) ).
thf(2029,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( SV31 = zero_zero_poly_a )
= $true )
| ( ( SV140 = zero_zero_poly_a )
= $true )
| ( ( ( times_times_poly_a @ SV31 @ SV140 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1860]) ).
thf(2030,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ( times_times_poly_a @ SV31 @ SV140 )
= zero_zero_poly_a )
= $true )
| ( ( SV31 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1861]) ).
thf(2031,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) )
= $true )
| ( ( SV31 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1862]) ).
thf(2032,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ( times_times_poly_a @ SV31 @ SV140 )
= zero_zero_poly_a )
= $true )
| ( ( SV140 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1863]) ).
thf(2033,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( ( SV31 = zero_zero_poly_a )
| ( SV140 = zero_zero_poly_a ) )
= $true )
| ( ( SV140 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1864]) ).
thf(2034,plain,
! [SV141: nat,SV32: nat] :
( ( ( SV32 = zero_zero_nat )
= $true )
| ( ( SV141 = zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV32 @ SV141 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1866]) ).
thf(2035,plain,
! [SV141: nat,SV32: nat] :
( ( ( ( times_times_nat @ SV32 @ SV141 )
= zero_zero_nat )
= $true )
| ( ( SV32 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1867]) ).
thf(2036,plain,
! [SV141: nat,SV32: nat] :
( ( ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) )
= $true )
| ( ( SV32 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1868]) ).
thf(2037,plain,
! [SV141: nat,SV32: nat] :
( ( ( ( times_times_nat @ SV32 @ SV141 )
= zero_zero_nat )
= $true )
| ( ( SV141 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1869]) ).
thf(2038,plain,
! [SV141: nat,SV32: nat] :
( ( ( ( SV32 = zero_zero_nat )
| ( SV141 = zero_zero_nat ) )
= $true )
| ( ( SV141 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1870]) ).
thf(2039,plain,
! [SV57: nat] :
( ( ( SV57 = zero_zero_nat )
= $false )
| ( ( SV57 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(2040,plain,
! [SV194: a,SV61: a,SV175: a] :
( ( ( ( times_times_a @ SV175 @ SV61 )
!= ( times_times_a @ SV194 @ SV61 ) )
= $false )
| ( ( ( times_times_a @ SV175 @ SV61 )
= ( times_times_a @ SV194 @ SV61 ) )
= $false )
| ( ( SV61 = zero_zero_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(2041,plain,
! [SV61: a,SV194: a,SV175: a] :
( ( ( SV175 != SV194 )
= $false )
| ( ( ( times_times_a @ SV175 @ SV61 )
= ( times_times_a @ SV194 @ SV61 ) )
= $false )
| ( ( SV61 = zero_zero_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(2042,plain,
! [SV194: a,SV61: a,SV175: a] :
( ( ( ( times_times_a @ SV175 @ SV61 )
!= ( times_times_a @ SV194 @ SV61 ) )
= $false )
| ( ( SV175 = SV194 )
= $false )
| ( ( SV61 = zero_zero_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1891]) ).
thf(2043,plain,
! [SV61: a,SV194: a,SV175: a] :
( ( ( SV175 != SV194 )
= $false )
| ( ( SV175 = SV194 )
= $false )
| ( ( SV61 = zero_zero_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1891]) ).
thf(2044,plain,
! [SV195: poly_a,SV62: poly_a,SV176: poly_a] :
( ( ( ( times_times_poly_a @ SV176 @ SV62 )
!= ( times_times_poly_a @ SV195 @ SV62 ) )
= $false )
| ( ( ( times_times_poly_a @ SV176 @ SV62 )
= ( times_times_poly_a @ SV195 @ SV62 ) )
= $false )
| ( ( SV62 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1892]) ).
thf(2045,plain,
! [SV62: poly_a,SV195: poly_a,SV176: poly_a] :
( ( ( SV176 != SV195 )
= $false )
| ( ( ( times_times_poly_a @ SV176 @ SV62 )
= ( times_times_poly_a @ SV195 @ SV62 ) )
= $false )
| ( ( SV62 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1892]) ).
thf(2046,plain,
! [SV195: poly_a,SV62: poly_a,SV176: poly_a] :
( ( ( ( times_times_poly_a @ SV176 @ SV62 )
!= ( times_times_poly_a @ SV195 @ SV62 ) )
= $false )
| ( ( SV176 = SV195 )
= $false )
| ( ( SV62 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1893]) ).
thf(2047,plain,
! [SV62: poly_a,SV195: poly_a,SV176: poly_a] :
( ( ( SV176 != SV195 )
= $false )
| ( ( SV176 = SV195 )
= $false )
| ( ( SV62 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1893]) ).
thf(2048,plain,
! [SV196: nat,SV63: nat,SV177: nat] :
( ( ( ( times_times_nat @ SV177 @ SV63 )
!= ( times_times_nat @ SV196 @ SV63 ) )
= $false )
| ( ( ( times_times_nat @ SV177 @ SV63 )
= ( times_times_nat @ SV196 @ SV63 ) )
= $false )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1894]) ).
thf(2049,plain,
! [SV63: nat,SV196: nat,SV177: nat] :
( ( ( SV177 != SV196 )
= $false )
| ( ( ( times_times_nat @ SV177 @ SV63 )
= ( times_times_nat @ SV196 @ SV63 ) )
= $false )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1894]) ).
thf(2050,plain,
! [SV196: nat,SV63: nat,SV177: nat] :
( ( ( ( times_times_nat @ SV177 @ SV63 )
!= ( times_times_nat @ SV196 @ SV63 ) )
= $false )
| ( ( SV177 = SV196 )
= $false )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1895]) ).
thf(2051,plain,
! [SV63: nat,SV196: nat,SV177: nat] :
( ( ( SV177 != SV196 )
= $false )
| ( ( SV177 = SV196 )
= $false )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1895]) ).
thf(2052,plain,
! [SV197: a,SV178: a,SV64: a] :
( ( ( ( times_times_a @ SV64 @ SV178 )
!= ( times_times_a @ SV64 @ SV197 ) )
= $false )
| ( ( ( times_times_a @ SV64 @ SV178 )
= ( times_times_a @ SV64 @ SV197 ) )
= $false )
| ( ( SV64 = zero_zero_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(2053,plain,
! [SV64: a,SV197: a,SV178: a] :
( ( ( SV178 != SV197 )
= $false )
| ( ( ( times_times_a @ SV64 @ SV178 )
= ( times_times_a @ SV64 @ SV197 ) )
= $false )
| ( ( SV64 = zero_zero_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(2054,plain,
! [SV197: a,SV178: a,SV64: a] :
( ( ( ( times_times_a @ SV64 @ SV178 )
!= ( times_times_a @ SV64 @ SV197 ) )
= $false )
| ( ( SV178 = SV197 )
= $false )
| ( ( SV64 = zero_zero_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1897]) ).
thf(2055,plain,
! [SV64: a,SV197: a,SV178: a] :
( ( ( SV178 != SV197 )
= $false )
| ( ( SV178 = SV197 )
= $false )
| ( ( SV64 = zero_zero_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1897]) ).
thf(2056,plain,
! [SV198: poly_a,SV179: poly_a,SV65: poly_a] :
( ( ( ( times_times_poly_a @ SV65 @ SV179 )
!= ( times_times_poly_a @ SV65 @ SV198 ) )
= $false )
| ( ( ( times_times_poly_a @ SV65 @ SV179 )
= ( times_times_poly_a @ SV65 @ SV198 ) )
= $false )
| ( ( SV65 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1898]) ).
thf(2057,plain,
! [SV65: poly_a,SV198: poly_a,SV179: poly_a] :
( ( ( SV179 != SV198 )
= $false )
| ( ( ( times_times_poly_a @ SV65 @ SV179 )
= ( times_times_poly_a @ SV65 @ SV198 ) )
= $false )
| ( ( SV65 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1898]) ).
thf(2058,plain,
! [SV198: poly_a,SV179: poly_a,SV65: poly_a] :
( ( ( ( times_times_poly_a @ SV65 @ SV179 )
!= ( times_times_poly_a @ SV65 @ SV198 ) )
= $false )
| ( ( SV179 = SV198 )
= $false )
| ( ( SV65 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1899]) ).
thf(2059,plain,
! [SV65: poly_a,SV198: poly_a,SV179: poly_a] :
( ( ( SV179 != SV198 )
= $false )
| ( ( SV179 = SV198 )
= $false )
| ( ( SV65 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1899]) ).
thf(2060,plain,
! [SV199: nat,SV180: nat,SV66: nat] :
( ( ( ( times_times_nat @ SV66 @ SV180 )
!= ( times_times_nat @ SV66 @ SV199 ) )
= $false )
| ( ( ( times_times_nat @ SV66 @ SV180 )
= ( times_times_nat @ SV66 @ SV199 ) )
= $false )
| ( ( SV66 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1900]) ).
thf(2061,plain,
! [SV66: nat,SV199: nat,SV180: nat] :
( ( ( SV180 != SV199 )
= $false )
| ( ( ( times_times_nat @ SV66 @ SV180 )
= ( times_times_nat @ SV66 @ SV199 ) )
= $false )
| ( ( SV66 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1900]) ).
thf(2062,plain,
! [SV199: nat,SV180: nat,SV66: nat] :
( ( ( ( times_times_nat @ SV66 @ SV180 )
!= ( times_times_nat @ SV66 @ SV199 ) )
= $false )
| ( ( SV180 = SV199 )
= $false )
| ( ( SV66 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1901]) ).
thf(2063,plain,
! [SV66: nat,SV199: nat,SV180: nat] :
( ( ( SV180 != SV199 )
= $false )
| ( ( SV180 = SV199 )
= $false )
| ( ( SV66 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1901]) ).
thf(2064,plain,
! [SV187: nat,SV156: nat,SV86: nat] :
( ( ( ( times_times_nat @ SV86 @ SV156 )
= ( times_times_nat @ SV187 @ SV156 ) )
= $true )
| ( ( ( times_times_nat @ SV86 @ SV156 )
= ( times_times_nat @ SV187 @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1903]) ).
thf(2065,plain,
! [SV156: nat,SV187: nat,SV86: nat] :
( ( ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) )
= $true )
| ( ( ( times_times_nat @ SV86 @ SV156 )
= ( times_times_nat @ SV187 @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1904]) ).
thf(2066,plain,
! [SV187: nat,SV156: nat,SV86: nat] :
( ( ( ( times_times_nat @ SV86 @ SV156 )
!= ( times_times_nat @ SV187 @ SV156 ) )
= $false )
| ( ( SV86 = SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1905]) ).
thf(2067,plain,
! [SV156: nat,SV187: nat,SV86: nat] :
( ( ( ~ ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) ) )
= $false )
| ( ( SV86 = SV187 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1905]) ).
thf(2068,plain,
! [SV187: nat,SV156: nat,SV86: nat] :
( ( ( ( times_times_nat @ SV86 @ SV156 )
!= ( times_times_nat @ SV187 @ SV156 ) )
= $false )
| ( ( SV156 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1906]) ).
thf(2069,plain,
! [SV156: nat,SV187: nat,SV86: nat] :
( ( ( ~ ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) ) )
= $false )
| ( ( SV156 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1906]) ).
thf(2070,plain,
! [SV87: nat] :
( ( ( SV87 = zero_zero_nat )
= $false )
| ( ( SV87 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1907]) ).
thf(2071,plain,
! [SV89: nat] :
( ( ( SV89 = zero_zero_nat )
= $false )
| ( ( SV89 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1910]) ).
thf(2072,plain,
! [SV157: nat,SV90: nat] :
( ( ( SV90 = zero_zero_nat )
= $true )
| ( ( SV157 = zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV90 @ SV157 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1914]) ).
thf(2073,plain,
! [SV157: nat,SV90: nat] :
( ( ( ( times_times_nat @ SV90 @ SV157 )
= zero_zero_nat )
= $true )
| ( ( SV90 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1915]) ).
thf(2074,plain,
! [SV157: nat,SV90: nat] :
( ( ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) )
= $true )
| ( ( SV90 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1916]) ).
thf(2075,plain,
! [SV157: nat,SV90: nat] :
( ( ( ( times_times_nat @ SV90 @ SV157 )
= zero_zero_nat )
= $true )
| ( ( SV157 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1917]) ).
thf(2076,plain,
! [SV157: nat,SV90: nat] :
( ( ( ( SV90 = zero_zero_nat )
| ( SV157 = zero_zero_nat ) )
= $true )
| ( ( SV157 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1918]) ).
thf(2077,plain,
! [SV188: nat,SV158: nat,SV92: nat] :
( ( ( ( times_times_nat @ SV92 @ SV158 )
= ( times_times_nat @ SV92 @ SV188 ) )
= $true )
| ( ( ( times_times_nat @ SV92 @ SV158 )
= ( times_times_nat @ SV92 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1919]) ).
thf(2078,plain,
! [SV92: nat,SV188: nat,SV158: nat] :
( ( ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) )
= $true )
| ( ( ( times_times_nat @ SV92 @ SV158 )
= ( times_times_nat @ SV92 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1920]) ).
thf(2079,plain,
! [SV188: nat,SV158: nat,SV92: nat] :
( ( ( ( times_times_nat @ SV92 @ SV158 )
!= ( times_times_nat @ SV92 @ SV188 ) )
= $false )
| ( ( SV158 = SV188 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1921]) ).
thf(2080,plain,
! [SV92: nat,SV188: nat,SV158: nat] :
( ( ( ~ ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) ) )
= $false )
| ( ( SV158 = SV188 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1921]) ).
thf(2081,plain,
! [SV188: nat,SV158: nat,SV92: nat] :
( ( ( ( times_times_nat @ SV92 @ SV158 )
!= ( times_times_nat @ SV92 @ SV188 ) )
= $false )
| ( ( SV92 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1922]) ).
thf(2082,plain,
! [SV92: nat,SV188: nat,SV158: nat] :
( ( ( ~ ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) ) )
= $false )
| ( ( SV92 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1922]) ).
thf(2083,plain,
! [SV94: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(2084,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ( times_times_nat @ SV100 @ SV160 )
= ( times_times_nat @ SV100 @ SV189 ) )
= $true )
| ( ( ( times_times_nat @ SV100 @ SV160 )
= ( times_times_nat @ SV100 @ SV189 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1926]) ).
thf(2085,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) )
= $true )
| ( ( ( times_times_nat @ SV100 @ SV160 )
= ( times_times_nat @ SV100 @ SV189 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1927]) ).
thf(2086,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ( times_times_nat @ SV100 @ SV160 )
!= ( times_times_nat @ SV100 @ SV189 ) )
= $false )
| ( ( SV100 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1928]) ).
thf(2087,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ~ ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) ) )
= $false )
| ( ( SV100 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1928]) ).
thf(2088,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ( times_times_nat @ SV100 @ SV160 )
!= ( times_times_nat @ SV100 @ SV189 ) )
= $false )
| ( ( SV160 = SV189 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1929]) ).
thf(2089,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ~ ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) ) )
= $false )
| ( ( SV160 = SV189 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1929]) ).
thf(2090,plain,
! [SV101: list_a > $o] :
( ( ( ( sK40_X2 @ SV101 )
!= ( sK41_SY362 @ SV101 ) )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) )
= $true )
| ( ( ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1930]) ).
thf(2091,plain,
! [SV101: list_a > $o] :
( ( ( ~ ( ( ( sK40_X2 @ SV101 )
= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
| ~ ~ ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) ) )
= $false )
| ( ( ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(2092,plain,
! [SV221: list_a,SV217: a,SV102: list_a > $o] :
( ( ( ~ ( SV102 @ nil_a ) )
= $true )
| ( ( ! [SY475: list_a] : ( SV102 @ SY475 ) )
= $true )
| ( ( SV102 @ ( sK25_SY345 @ SV102 ) )
= $true )
| ( ( ( sK25_SY345 @ SV102 )
= ( cons_a @ SV217 @ SV221 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1932]) ).
thf(2093,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ( SV103 != nil_a )
| ( SV161 != nil_a ) )
= $false )
| ( ( ( append_a @ SV103 @ SV161 )
= nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(2094,plain,
! [SV103: list_a,SV161: list_a] :
( ( ( SV161 = nil_a )
= $false )
| ( ( SV103 = nil_a )
= $false )
| ( ( ~ ( ( ( append_a @ SV103 @ SV161 )
!= nil_a )
| ~ ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1936]) ).
thf(2095,plain,
! [SV238: list_a,SV229: list_a,SV162: a > a,SV104: ( a > a ) > list_a > list_a > $o] :
( ( ( SV104 @ SV162 @ SV229 @ SV238 )
= $true )
| ( ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) @ ( cons_a @ ( sK54_F2 @ SV162 @ SV104 @ ( sK55_SY373 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) ) )
= $true )
| ( ( SV104 @ ( sK58_F2 @ SV162 @ SV104 ) @ nil_a @ ( sK59_SY379 @ SV162 @ SV104 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2096,plain,
! [SV239: list_a,SV162: a > a,SV104: ( a > a ) > list_a > list_a > $o] :
( ( ( ! [SY562: list_a] : ( SV104 @ SV162 @ SV239 @ SY562 ) )
= $true )
| ( ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( cons_a @ ( sK55_SY373 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) )
= $false )
| ( ( SV104 @ ( sK58_F2 @ SV162 @ SV104 ) @ nil_a @ ( sK59_SY379 @ SV162 @ SV104 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2097,plain,
! [SV203: a,SV190: list_a,SV163: a,SV105: list_a] :
( ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
!= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
= $false )
| ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1939]) ).
thf(2098,plain,
! [SV203: a,SV163: a,SV190: list_a,SV105: list_a] :
( ( ( ~ ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) )
= $false )
| ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1939]) ).
thf(2099,plain,
! [SV203: a,SV163: a,SV190: list_a,SV105: list_a] :
( ( ( SV105 != SV190 )
= $true )
| ( ( SV163 != SV203 )
= $true )
| ( ( ~ ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
!= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
| ~ ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1940]) ).
thf(2100,plain,
! [SV240: list_a,SV231: a > a > $o,SV106: ( a > a > $o ) > list_a > $o] :
( ( ( SV106 @ SV231 @ SV240 )
= $true )
| ( ( SV106 @ ( sK36_P5 @ SV106 ) @ ( cons_a @ ( sK37_SY359 @ SV106 ) @ ( sK38_SY361 @ SV106 ) ) )
= $false )
| ( ( SV106 @ ( sK39_P5 @ SV106 ) @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2101,plain,
! [SV107: nat > $o] :
( ( ( ~ ( SV107 @ ( sK1_N2 @ SV107 ) ) )
= $true )
| ( ( ! [SY486: nat] : ( SV107 @ SY486 ) )
= $true )
| ( ( SV107 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1943]) ).
thf(2102,plain,
! [SV107: nat > $o] :
( ( ( ! [SY485: nat] :
( ~ ( ord_less_nat @ SY485 @ ( sK1_N2 @ SV107 ) )
| ( SV107 @ SY485 ) ) )
= $true )
| ( ( ! [SY486: nat] : ( SV107 @ SY486 ) )
= $true )
| ( ( SV107 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1944]) ).
thf(2103,plain,
! [SV241: list_a,SV109: list_a > $o] :
( ( ( SV109 @ SV241 )
= $true )
| ( ( SV109 @ ( sK20_SY343 @ SV109 ) )
= $true )
| ( ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
= $false )
| ( ( SV109 @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2104,plain,
! [SV109: list_a > $o] :
( ( ( ~ ( SV109 @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) )
| ~ ~ ( SV109 @ ( cons_a @ ( sK18_X2 @ SV109 ) @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) ) ) )
= $false )
| ( ( ! [SY488: list_a] : ( SV109 @ SY488 ) )
= $true )
| ( ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
= $false )
| ( ( SV109 @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1947]) ).
thf(2105,plain,
! [SV204: list_a,SV191: a,SV164: list_a,SV110: a] :
( ( ( ( cons_a @ SV110 @ SV164 )
!= ( cons_a @ SV191 @ SV204 ) )
= $false )
| ( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SV204 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1948]) ).
thf(2106,plain,
! [SV204: list_a,SV164: list_a,SV191: a,SV110: a] :
( ( ( ~ ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) )
= $false )
| ( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SV204 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1948]) ).
thf(2107,plain,
! [SV204: list_a,SV164: list_a,SV191: a,SV110: a] :
( ( ( SV110 != SV191 )
= $true )
| ( ( SV164 != SV204 )
= $true )
| ( ( ~ ( ( ( cons_a @ SV110 @ SV164 )
!= ( cons_a @ SV191 @ SV204 ) )
| ~ ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1949]) ).
thf(2108,plain,
! [SV242: list_a,SV234: list_a,SV111: list_a > list_a > $o] :
( ( ( SV111 @ SV234 @ SV242 )
= $true )
| ( ( SV111 @ ( cons_a @ ( sK14_X2 @ SV111 ) @ ( sK15_SY338 @ SV111 ) ) @ ( sK16_SY340 @ SV111 ) )
= $false )
| ( ( SV111 @ nil_a @ ( sK17_X_1 @ SV111 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2109,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) )
= $false )
| ( ( ( pCons_a @ SV112 @ SV165 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1953]) ).
thf(2110,plain,
! [SV112: a,SV165: poly_a] :
( ( ( SV165 = zero_zero_poly_a )
= $false )
| ( ( SV112 = zero_zero_a )
= $false )
| ( ( ~ ( ( ( pCons_a @ SV112 @ SV165 )
!= zero_zero_poly_a )
| ~ ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1954]) ).
thf(2111,plain,
! [SV243: poly_a,SV236: poly_a,SV113: poly_a > poly_a > $o] :
( ( ( SV113 @ SV236 @ SV243 )
= $true )
| ( ( SV113 @ ( pCons_a @ ( sK84_A2 @ SV113 ) @ ( sK85_SY400 @ SV113 ) ) @ ( pCons_a @ ( sK86_SY403 @ SV113 ) @ ( sK87_SY405 @ SV113 ) ) )
= $false )
| ( ( SV113 @ zero_zero_poly_a @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2112,plain,
! [SV244: list_a,SV114: list_a > list_a > $o] :
( ( ( ! [SY563: list_a] : ( SV114 @ SV244 @ SY563 ) )
= $true )
| ( ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) )
= $false )
| ( ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a )
= $false )
| ( ( SV114 @ ( sK72_SY386 @ SV114 ) @ ( sK74_SY391 @ SV114 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2113,plain,
! [SV114: list_a > list_a > $o] :
( ( ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) )
= $false )
| ( ( ! [SY497: list_a,SY498: list_a] : ( SV114 @ SY497 @ SY498 ) )
= $true )
| ( ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a )
= $false )
| ( ( SV114 @ ( cons_a @ ( sK71_X2 @ SV114 ) @ ( sK72_SY386 @ SV114 ) ) @ ( cons_a @ ( sK73_SY389 @ SV114 ) @ ( sK74_SY391 @ SV114 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2114,plain,
! [SV115: list_a,SV192: list_a > $o] :
( ( ( ( sK52_SY372 @ SV192 @ SV115 )
= nil_a )
= $false )
| ( ( SV192 @ SV115 )
= $true )
| ( ( SV192 @ ( cons_a @ ( sK53_X2 @ SV192 @ SV115 ) @ nil_a ) )
= $false )
| ( ( SV115 = nil_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1959]) ).
thf(2115,plain,
! [SV115: list_a,SV192: list_a > $o] :
( ( ( ~ ( SV192 @ ( sK52_SY372 @ SV192 @ SV115 ) )
| ~ ~ ( SV192 @ ( cons_a @ ( sK51_X2 @ SV192 @ SV115 ) @ ( sK52_SY372 @ SV192 @ SV115 ) ) ) )
= $false )
| ( ( SV192 @ SV115 )
= $true )
| ( ( SV192 @ ( cons_a @ ( sK53_X2 @ SV192 @ SV115 ) @ nil_a ) )
= $false )
| ( ( SV115 = nil_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(2116,plain,
! [SV245: a > a > $o,SV117: ( a > a > $o ) > list_a > $o] :
( ( ( ! [SY564: list_a] : ( SV117 @ SV245 @ SY564 ) )
= $true )
| ( ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) )
= $true )
| ( ( SV117 @ ( sK48_P5 @ SV117 ) @ ( cons_a @ ( sK49_SY371 @ SV117 ) @ nil_a ) )
= $false )
| ( ( SV117 @ ( sK50_P5 @ SV117 ) @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2117,plain,
! [SV117: ( a > a > $o ) > list_a > $o] :
( ( ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK45_SY365 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) ) )
= $false )
| ( ( ! [SY501: a > a > $o,SY502: list_a] : ( SV117 @ SY501 @ SY502 ) )
= $true )
| ( ( SV117 @ ( sK48_P5 @ SV117 ) @ ( cons_a @ ( sK49_SY371 @ SV117 ) @ nil_a ) )
= $false )
| ( ( SV117 @ ( sK50_P5 @ SV117 ) @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1962]) ).
thf(2118,plain,
! [SV246: list_a,SV118: list_a > list_a > $o] :
( ( ( ! [SY565: list_a] : ( SV118 @ SV246 @ SY565 ) )
= $true )
| ( ( SV118 @ ( sK27_SY350 @ SV118 ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) )
= $true )
| ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2119,plain,
! [SV118: list_a > list_a > $o] :
( ( ( ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( sK29_SY355 @ SV118 ) )
| ~ ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) ) )
= $false )
| ( ( ! [SY503: list_a,SY504: list_a] : ( SV118 @ SY503 @ SY504 ) )
= $true )
| ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2120,plain,
! [SV119: list_a > list_a > $o] :
( ( ( ~ ( SV119 @ ( sK7_SY330 @ SV119 ) @ ( sK9_SY335 @ SV119 ) ) )
= $false )
| ( ( ! [SY505: list_a,SY506: list_a] : ( SV119 @ SY505 @ SY506 ) )
= $true )
| ( ( SV119 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SV119 ) @ ( sK11_SY336 @ SV119 ) ) )
= $false )
| ( ( SV119 @ ( cons_a @ ( sK12_X2 @ SV119 ) @ ( sK13_SY337 @ SV119 ) ) @ nil_a )
= $false )
| ( ( SV119 @ nil_a @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1965]) ).
thf(2121,plain,
! [SV119: list_a > list_a > $o] :
( ( ( ~ ~ ( SV119 @ ( cons_a @ ( sK6_X2 @ SV119 ) @ ( sK7_SY330 @ SV119 ) ) @ ( cons_a @ ( sK8_SY333 @ SV119 ) @ ( sK9_SY335 @ SV119 ) ) ) )
= $false )
| ( ( ! [SY505: list_a,SY506: list_a] : ( SV119 @ SY505 @ SY506 ) )
= $true )
| ( ( SV119 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SV119 ) @ ( sK11_SY336 @ SV119 ) ) )
= $false )
| ( ( SV119 @ ( cons_a @ ( sK12_X2 @ SV119 ) @ ( sK13_SY337 @ SV119 ) ) @ nil_a )
= $false )
| ( ( SV119 @ nil_a @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1965]) ).
thf(2122,plain,
! [SV120: poly_a > $o] :
( ( ( ( sK89_SY406 @ SV120 )
= zero_zero_poly_a )
= $false )
| ( ( ( sK88_A2 @ SV120 )
= zero_zero_a )
= $false )
| ( ( ! [SY507: poly_a] : ( SV120 @ SY507 ) )
= $true )
| ( ( SV120 @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(2123,plain,
! [SV120: poly_a > $o] :
( ( ( SV120 @ ( sK89_SY406 @ SV120 ) )
= $true )
| ( ( ! [SY507: poly_a] : ( SV120 @ SY507 ) )
= $true )
| ( ( SV120 @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1967]) ).
thf(2124,plain,
! [SV120: poly_a > $o] :
( ( ( ~ ( SV120 @ ( pCons_a @ ( sK88_A2 @ SV120 ) @ ( sK89_SY406 @ SV120 ) ) ) )
= $true )
| ( ( ! [SY507: poly_a] : ( SV120 @ SY507 ) )
= $true )
| ( ( SV120 @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1968]) ).
thf(2125,plain,
! [SV121: list_a] :
( ( ( SV121 = nil_a )
= $false )
| ( ( SV121 = nil_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1969]) ).
thf(2126,plain,
! [SV121: list_a] :
( ( ( ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) )
= $false )
| ( ( SV121 = nil_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1970]) ).
thf(2127,plain,
! [SV247: list_a,SV220: a,SV121: list_a] :
( ( ( SV121
!= ( cons_a @ SV220 @ SV247 ) )
= $true )
| ( ( ~ ( ~ ( ( SV121 != nil_a ) )
| ~ ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2128,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( ( SV122 != nil_a )
| ( SV166 != nil_a ) )
= $false )
| ( ( nil_a
= ( append_a @ SV122 @ SV166 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1973]) ).
thf(2129,plain,
! [SV122: list_a,SV166: list_a] :
( ( ( SV166 = nil_a )
= $false )
| ( ( SV122 = nil_a )
= $false )
| ( ( ~ ( ( nil_a
!= ( append_a @ SV122 @ SV166 ) )
| ~ ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1974]) ).
thf(2130,plain,
! [SV248: list_a,SV123: list_a > list_a > $o] :
( ( ( ! [SY566: list_a] : ( SV123 @ SV248 @ SY566 ) )
= $true )
| ( ( SV123 @ ( sK76_SY392 @ SV123 ) @ ( sK78_SY397 @ SV123 ) )
= $true )
| ( ( SV123 @ nil_a @ ( cons_a @ ( sK79_V @ SV123 ) @ ( sK80_SY398 @ SV123 ) ) )
= $false )
| ( ( SV123 @ ( sK81_Xs2 @ SV123 ) @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2131,plain,
! [SV123: list_a > list_a > $o] :
( ( ( SV123 @ ( cons_a @ ( sK75_X2 @ SV123 ) @ ( sK76_SY392 @ SV123 ) ) @ ( cons_a @ ( sK77_SY395 @ SV123 ) @ ( sK78_SY397 @ SV123 ) ) )
= $false )
| ( ( ! [SY511: list_a,SY512: list_a] : ( SV123 @ SY511 @ SY512 ) )
= $true )
| ( ( SV123 @ nil_a @ ( cons_a @ ( sK79_V @ SV123 ) @ ( sK80_SY398 @ SV123 ) ) )
= $false )
| ( ( SV123 @ ( sK81_Xs2 @ SV123 ) @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1976]) ).
thf(2132,plain,
! [SV193: poly_a,SV126: poly_a] :
( ( ( SV126 = SV193 )
= $true )
| ( ( SV126 = SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1978]) ).
thf(2133,plain,
! [SV193: poly_a,SV126: poly_a] :
( ( ( ( coeffs_a @ SV126 )
= ( coeffs_a @ SV193 ) )
= $true )
| ( ( SV126 = SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1979]) ).
thf(2134,plain,
! [SV193: poly_a,SV126: poly_a] :
( ( ( SV126 = SV193 )
= $true )
| ( ( ( coeffs_a @ SV126 )
= ( coeffs_a @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1980]) ).
thf(2135,plain,
! [SV193: poly_a,SV126: poly_a] :
( ( ( ( coeffs_a @ SV126 )
= ( coeffs_a @ SV193 ) )
= $true )
| ( ( ( coeffs_a @ SV126 )
= ( coeffs_a @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1981]) ).
thf(2136,plain,
! [SV130: poly_a,SV12: a] :
( ( ( SV12 = zero_zero_a )
= $true )
| ( ( SV130 = zero_zero_poly_a )
= $true )
| ( ( SV12 = zero_zero_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1984]) ).
thf(2137,plain,
! [SV130: poly_a,SV12: a] :
( ( ( SV12 = zero_zero_a )
= $true )
| ( ( SV130 = zero_zero_poly_a )
= $true )
| ( ( SV130 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1986]) ).
thf(2138,plain,
! [SV169: a,SV24: a,SV133: a] :
( ( ( SV133 = zero_zero_a )
= $true )
| ( ( SV24 = SV169 )
= $true )
| ( ( ( times_times_a @ SV24 @ SV133 )
= ( times_times_a @ SV169 @ SV133 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1989]) ).
thf(2139,plain,
! [SV169: a,SV133: a,SV24: a] :
( ( ( ( times_times_a @ SV24 @ SV133 )
= ( times_times_a @ SV169 @ SV133 ) )
= $true )
| ( ( SV133 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1990]) ).
thf(2140,plain,
! [SV169: a,SV24: a,SV133: a] :
( ( ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) )
= $true )
| ( ( SV133 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1991]) ).
thf(2141,plain,
! [SV169: a,SV133: a,SV24: a] :
( ( ( ( times_times_a @ SV24 @ SV133 )
= ( times_times_a @ SV169 @ SV133 ) )
= $true )
| ( ( SV24 = SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1992]) ).
thf(2142,plain,
! [SV169: a,SV24: a,SV133: a] :
( ( ( ( SV133 = zero_zero_a )
| ( SV24 = SV169 ) )
= $true )
| ( ( SV24 = SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1993]) ).
thf(2143,plain,
! [SV170: poly_a,SV25: poly_a,SV134: poly_a] :
( ( ( SV134 = zero_zero_poly_a )
= $true )
| ( ( SV25 = SV170 )
= $true )
| ( ( ( times_times_poly_a @ SV25 @ SV134 )
= ( times_times_poly_a @ SV170 @ SV134 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1995]) ).
thf(2144,plain,
! [SV170: poly_a,SV134: poly_a,SV25: poly_a] :
( ( ( ( times_times_poly_a @ SV25 @ SV134 )
= ( times_times_poly_a @ SV170 @ SV134 ) )
= $true )
| ( ( SV134 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1996]) ).
thf(2145,plain,
! [SV170: poly_a,SV25: poly_a,SV134: poly_a] :
( ( ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) )
= $true )
| ( ( SV134 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1997]) ).
thf(2146,plain,
! [SV170: poly_a,SV134: poly_a,SV25: poly_a] :
( ( ( ( times_times_poly_a @ SV25 @ SV134 )
= ( times_times_poly_a @ SV170 @ SV134 ) )
= $true )
| ( ( SV25 = SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1998]) ).
thf(2147,plain,
! [SV170: poly_a,SV25: poly_a,SV134: poly_a] :
( ( ( ( SV134 = zero_zero_poly_a )
| ( SV25 = SV170 ) )
= $true )
| ( ( SV25 = SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1999]) ).
thf(2148,plain,
! [SV171: nat,SV26: nat,SV135: nat] :
( ( ( SV135 = zero_zero_nat )
= $true )
| ( ( SV26 = SV171 )
= $true )
| ( ( ( times_times_nat @ SV26 @ SV135 )
= ( times_times_nat @ SV171 @ SV135 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2001]) ).
thf(2149,plain,
! [SV171: nat,SV135: nat,SV26: nat] :
( ( ( ( times_times_nat @ SV26 @ SV135 )
= ( times_times_nat @ SV171 @ SV135 ) )
= $true )
| ( ( SV135 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2002]) ).
thf(2150,plain,
! [SV171: nat,SV26: nat,SV135: nat] :
( ( ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) )
= $true )
| ( ( SV135 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2003]) ).
thf(2151,plain,
! [SV171: nat,SV135: nat,SV26: nat] :
( ( ( ( times_times_nat @ SV26 @ SV135 )
= ( times_times_nat @ SV171 @ SV135 ) )
= $true )
| ( ( SV26 = SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2004]) ).
thf(2152,plain,
! [SV171: nat,SV26: nat,SV135: nat] :
( ( ( ( SV135 = zero_zero_nat )
| ( SV26 = SV171 ) )
= $true )
| ( ( SV26 = SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2005]) ).
thf(2153,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( SV27 = zero_zero_a )
= $true )
| ( ( SV136 = SV172 )
= $true )
| ( ( ( times_times_a @ SV27 @ SV136 )
= ( times_times_a @ SV27 @ SV172 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2007]) ).
thf(2154,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ( times_times_a @ SV27 @ SV136 )
= ( times_times_a @ SV27 @ SV172 ) )
= $true )
| ( ( SV27 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2008]) ).
thf(2155,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) )
= $true )
| ( ( SV27 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2009]) ).
thf(2156,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ( times_times_a @ SV27 @ SV136 )
= ( times_times_a @ SV27 @ SV172 ) )
= $true )
| ( ( SV136 = SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2010]) ).
thf(2157,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( ( SV27 = zero_zero_a )
| ( SV136 = SV172 ) )
= $true )
| ( ( SV136 = SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2011]) ).
thf(2158,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( SV28 = zero_zero_poly_a )
= $true )
| ( ( SV137 = SV173 )
= $true )
| ( ( ( times_times_poly_a @ SV28 @ SV137 )
= ( times_times_poly_a @ SV28 @ SV173 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2013]) ).
thf(2159,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ( times_times_poly_a @ SV28 @ SV137 )
= ( times_times_poly_a @ SV28 @ SV173 ) )
= $true )
| ( ( SV28 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2014]) ).
thf(2160,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) )
= $true )
| ( ( SV28 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2015]) ).
thf(2161,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ( times_times_poly_a @ SV28 @ SV137 )
= ( times_times_poly_a @ SV28 @ SV173 ) )
= $true )
| ( ( SV137 = SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2016]) ).
thf(2162,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( ( SV28 = zero_zero_poly_a )
| ( SV137 = SV173 ) )
= $true )
| ( ( SV137 = SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2017]) ).
thf(2163,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( SV29 = zero_zero_nat )
= $true )
| ( ( SV138 = SV174 )
= $true )
| ( ( ( times_times_nat @ SV29 @ SV138 )
= ( times_times_nat @ SV29 @ SV174 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2019]) ).
thf(2164,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ( times_times_nat @ SV29 @ SV138 )
= ( times_times_nat @ SV29 @ SV174 ) )
= $true )
| ( ( SV29 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2020]) ).
thf(2165,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) )
= $true )
| ( ( SV29 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2021]) ).
thf(2166,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ( times_times_nat @ SV29 @ SV138 )
= ( times_times_nat @ SV29 @ SV174 ) )
= $true )
| ( ( SV138 = SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2022]) ).
thf(2167,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( ( SV29 = zero_zero_nat )
| ( SV138 = SV174 ) )
= $true )
| ( ( SV138 = SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2023]) ).
thf(2168,plain,
! [SV139: a,SV30: a] :
( ( ( SV30 = zero_zero_a )
= $true )
| ( ( SV139 = zero_zero_a )
= $true )
| ( ( SV30 = zero_zero_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2026]) ).
thf(2169,plain,
! [SV139: a,SV30: a] :
( ( ( SV30 = zero_zero_a )
= $true )
| ( ( SV139 = zero_zero_a )
= $true )
| ( ( SV139 = zero_zero_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2028]) ).
thf(2170,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( SV31 = zero_zero_poly_a )
= $true )
| ( ( SV140 = zero_zero_poly_a )
= $true )
| ( ( SV31 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2031]) ).
thf(2171,plain,
! [SV140: poly_a,SV31: poly_a] :
( ( ( SV31 = zero_zero_poly_a )
= $true )
| ( ( SV140 = zero_zero_poly_a )
= $true )
| ( ( SV140 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2033]) ).
thf(2172,plain,
! [SV141: nat,SV32: nat] :
( ( ( SV32 = zero_zero_nat )
= $true )
| ( ( SV141 = zero_zero_nat )
= $true )
| ( ( SV32 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2036]) ).
thf(2173,plain,
! [SV141: nat,SV32: nat] :
( ( ( SV32 = zero_zero_nat )
= $true )
| ( ( SV141 = zero_zero_nat )
= $true )
| ( ( SV141 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2038]) ).
thf(2174,plain,
! [SV194: a,SV61: a,SV175: a] :
( ( ( ( times_times_a @ SV175 @ SV61 )
= ( times_times_a @ SV194 @ SV61 ) )
= $true )
| ( ( ( times_times_a @ SV175 @ SV61 )
= ( times_times_a @ SV194 @ SV61 ) )
= $false )
| ( ( SV61 = zero_zero_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2040]) ).
thf(2175,plain,
! [SV61: a,SV194: a,SV175: a] :
( ( ( SV175 = SV194 )
= $true )
| ( ( ( times_times_a @ SV175 @ SV61 )
= ( times_times_a @ SV194 @ SV61 ) )
= $false )
| ( ( SV61 = zero_zero_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2041]) ).
thf(2176,plain,
! [SV194: a,SV61: a,SV175: a] :
( ( ( ( times_times_a @ SV175 @ SV61 )
= ( times_times_a @ SV194 @ SV61 ) )
= $true )
| ( ( SV175 = SV194 )
= $false )
| ( ( SV61 = zero_zero_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2042]) ).
thf(2177,plain,
! [SV61: a,SV194: a,SV175: a] :
( ( ( SV175 = SV194 )
= $true )
| ( ( SV175 = SV194 )
= $false )
| ( ( SV61 = zero_zero_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2043]) ).
thf(2178,plain,
! [SV195: poly_a,SV62: poly_a,SV176: poly_a] :
( ( ( ( times_times_poly_a @ SV176 @ SV62 )
= ( times_times_poly_a @ SV195 @ SV62 ) )
= $true )
| ( ( ( times_times_poly_a @ SV176 @ SV62 )
= ( times_times_poly_a @ SV195 @ SV62 ) )
= $false )
| ( ( SV62 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2044]) ).
thf(2179,plain,
! [SV62: poly_a,SV195: poly_a,SV176: poly_a] :
( ( ( SV176 = SV195 )
= $true )
| ( ( ( times_times_poly_a @ SV176 @ SV62 )
= ( times_times_poly_a @ SV195 @ SV62 ) )
= $false )
| ( ( SV62 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2045]) ).
thf(2180,plain,
! [SV195: poly_a,SV62: poly_a,SV176: poly_a] :
( ( ( ( times_times_poly_a @ SV176 @ SV62 )
= ( times_times_poly_a @ SV195 @ SV62 ) )
= $true )
| ( ( SV176 = SV195 )
= $false )
| ( ( SV62 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2046]) ).
thf(2181,plain,
! [SV62: poly_a,SV195: poly_a,SV176: poly_a] :
( ( ( SV176 = SV195 )
= $true )
| ( ( SV176 = SV195 )
= $false )
| ( ( SV62 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2047]) ).
thf(2182,plain,
! [SV196: nat,SV63: nat,SV177: nat] :
( ( ( ( times_times_nat @ SV177 @ SV63 )
= ( times_times_nat @ SV196 @ SV63 ) )
= $true )
| ( ( ( times_times_nat @ SV177 @ SV63 )
= ( times_times_nat @ SV196 @ SV63 ) )
= $false )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2048]) ).
thf(2183,plain,
! [SV63: nat,SV196: nat,SV177: nat] :
( ( ( SV177 = SV196 )
= $true )
| ( ( ( times_times_nat @ SV177 @ SV63 )
= ( times_times_nat @ SV196 @ SV63 ) )
= $false )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2049]) ).
thf(2184,plain,
! [SV196: nat,SV63: nat,SV177: nat] :
( ( ( ( times_times_nat @ SV177 @ SV63 )
= ( times_times_nat @ SV196 @ SV63 ) )
= $true )
| ( ( SV177 = SV196 )
= $false )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2050]) ).
thf(2185,plain,
! [SV63: nat,SV196: nat,SV177: nat] :
( ( ( SV177 = SV196 )
= $true )
| ( ( SV177 = SV196 )
= $false )
| ( ( SV63 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2051]) ).
thf(2186,plain,
! [SV197: a,SV178: a,SV64: a] :
( ( ( ( times_times_a @ SV64 @ SV178 )
= ( times_times_a @ SV64 @ SV197 ) )
= $true )
| ( ( ( times_times_a @ SV64 @ SV178 )
= ( times_times_a @ SV64 @ SV197 ) )
= $false )
| ( ( SV64 = zero_zero_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2052]) ).
thf(2187,plain,
! [SV64: a,SV197: a,SV178: a] :
( ( ( SV178 = SV197 )
= $true )
| ( ( ( times_times_a @ SV64 @ SV178 )
= ( times_times_a @ SV64 @ SV197 ) )
= $false )
| ( ( SV64 = zero_zero_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2053]) ).
thf(2188,plain,
! [SV197: a,SV178: a,SV64: a] :
( ( ( ( times_times_a @ SV64 @ SV178 )
= ( times_times_a @ SV64 @ SV197 ) )
= $true )
| ( ( SV178 = SV197 )
= $false )
| ( ( SV64 = zero_zero_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2054]) ).
thf(2189,plain,
! [SV64: a,SV197: a,SV178: a] :
( ( ( SV178 = SV197 )
= $true )
| ( ( SV178 = SV197 )
= $false )
| ( ( SV64 = zero_zero_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2055]) ).
thf(2190,plain,
! [SV198: poly_a,SV179: poly_a,SV65: poly_a] :
( ( ( ( times_times_poly_a @ SV65 @ SV179 )
= ( times_times_poly_a @ SV65 @ SV198 ) )
= $true )
| ( ( ( times_times_poly_a @ SV65 @ SV179 )
= ( times_times_poly_a @ SV65 @ SV198 ) )
= $false )
| ( ( SV65 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2056]) ).
thf(2191,plain,
! [SV65: poly_a,SV198: poly_a,SV179: poly_a] :
( ( ( SV179 = SV198 )
= $true )
| ( ( ( times_times_poly_a @ SV65 @ SV179 )
= ( times_times_poly_a @ SV65 @ SV198 ) )
= $false )
| ( ( SV65 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2057]) ).
thf(2192,plain,
! [SV198: poly_a,SV179: poly_a,SV65: poly_a] :
( ( ( ( times_times_poly_a @ SV65 @ SV179 )
= ( times_times_poly_a @ SV65 @ SV198 ) )
= $true )
| ( ( SV179 = SV198 )
= $false )
| ( ( SV65 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2058]) ).
thf(2193,plain,
! [SV65: poly_a,SV198: poly_a,SV179: poly_a] :
( ( ( SV179 = SV198 )
= $true )
| ( ( SV179 = SV198 )
= $false )
| ( ( SV65 = zero_zero_poly_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2059]) ).
thf(2194,plain,
! [SV199: nat,SV180: nat,SV66: nat] :
( ( ( ( times_times_nat @ SV66 @ SV180 )
= ( times_times_nat @ SV66 @ SV199 ) )
= $true )
| ( ( ( times_times_nat @ SV66 @ SV180 )
= ( times_times_nat @ SV66 @ SV199 ) )
= $false )
| ( ( SV66 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2060]) ).
thf(2195,plain,
! [SV66: nat,SV199: nat,SV180: nat] :
( ( ( SV180 = SV199 )
= $true )
| ( ( ( times_times_nat @ SV66 @ SV180 )
= ( times_times_nat @ SV66 @ SV199 ) )
= $false )
| ( ( SV66 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2061]) ).
thf(2196,plain,
! [SV199: nat,SV180: nat,SV66: nat] :
( ( ( ( times_times_nat @ SV66 @ SV180 )
= ( times_times_nat @ SV66 @ SV199 ) )
= $true )
| ( ( SV180 = SV199 )
= $false )
| ( ( SV66 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2062]) ).
thf(2197,plain,
! [SV66: nat,SV199: nat,SV180: nat] :
( ( ( SV180 = SV199 )
= $true )
| ( ( SV180 = SV199 )
= $false )
| ( ( SV66 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2063]) ).
thf(2198,plain,
! [SV156: nat,SV187: nat,SV86: nat] :
( ( ( SV86 = SV187 )
= $true )
| ( ( SV156 = zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV86 @ SV156 )
= ( times_times_nat @ SV187 @ SV156 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2065]) ).
thf(2199,plain,
! [SV187: nat,SV156: nat,SV86: nat] :
( ( ( ( times_times_nat @ SV86 @ SV156 )
= ( times_times_nat @ SV187 @ SV156 ) )
= $true )
| ( ( SV86 = SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2066]) ).
thf(2200,plain,
! [SV156: nat,SV187: nat,SV86: nat] :
( ( ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) )
= $true )
| ( ( SV86 = SV187 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2067]) ).
thf(2201,plain,
! [SV187: nat,SV156: nat,SV86: nat] :
( ( ( ( times_times_nat @ SV86 @ SV156 )
= ( times_times_nat @ SV187 @ SV156 ) )
= $true )
| ( ( SV156 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2068]) ).
thf(2202,plain,
! [SV156: nat,SV187: nat,SV86: nat] :
( ( ( ( SV86 = SV187 )
| ( SV156 = zero_zero_nat ) )
= $true )
| ( ( SV156 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2069]) ).
thf(2203,plain,
! [SV157: nat,SV90: nat] :
( ( ( SV90 = zero_zero_nat )
= $true )
| ( ( SV157 = zero_zero_nat )
= $true )
| ( ( SV90 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2074]) ).
thf(2204,plain,
! [SV157: nat,SV90: nat] :
( ( ( SV90 = zero_zero_nat )
= $true )
| ( ( SV157 = zero_zero_nat )
= $true )
| ( ( SV157 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2076]) ).
thf(2205,plain,
! [SV92: nat,SV188: nat,SV158: nat] :
( ( ( SV158 = SV188 )
= $true )
| ( ( SV92 = zero_zero_nat )
= $true )
| ( ( ( times_times_nat @ SV92 @ SV158 )
= ( times_times_nat @ SV92 @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2078]) ).
thf(2206,plain,
! [SV188: nat,SV158: nat,SV92: nat] :
( ( ( ( times_times_nat @ SV92 @ SV158 )
= ( times_times_nat @ SV92 @ SV188 ) )
= $true )
| ( ( SV158 = SV188 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2079]) ).
thf(2207,plain,
! [SV92: nat,SV188: nat,SV158: nat] :
( ( ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) )
= $true )
| ( ( SV158 = SV188 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2080]) ).
thf(2208,plain,
! [SV188: nat,SV158: nat,SV92: nat] :
( ( ( ( times_times_nat @ SV92 @ SV158 )
= ( times_times_nat @ SV92 @ SV188 ) )
= $true )
| ( ( SV92 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2081]) ).
thf(2209,plain,
! [SV92: nat,SV188: nat,SV158: nat] :
( ( ( ( SV158 = SV188 )
| ( SV92 = zero_zero_nat ) )
= $true )
| ( ( SV92 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2082]) ).
thf(2210,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( SV100 = zero_zero_nat )
= $true )
| ( ( SV160 = SV189 )
= $true )
| ( ( ( times_times_nat @ SV100 @ SV160 )
= ( times_times_nat @ SV100 @ SV189 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2085]) ).
thf(2211,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ( times_times_nat @ SV100 @ SV160 )
= ( times_times_nat @ SV100 @ SV189 ) )
= $true )
| ( ( SV100 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2086]) ).
thf(2212,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) )
= $true )
| ( ( SV100 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2087]) ).
thf(2213,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ( times_times_nat @ SV100 @ SV160 )
= ( times_times_nat @ SV100 @ SV189 ) )
= $true )
| ( ( SV160 = SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2088]) ).
thf(2214,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( ( SV100 = zero_zero_nat )
| ( SV160 = SV189 ) )
= $true )
| ( ( SV160 = SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2089]) ).
thf(2215,plain,
! [SV101: list_a > $o] :
( ( ( ( sK40_X2 @ SV101 )
= ( sK41_SY362 @ SV101 ) )
= $false )
| ( ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) )
= $true )
| ( ( ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2090]) ).
thf(2216,plain,
! [SV101: list_a > $o] :
( ( ( ~ ( ( ( sK40_X2 @ SV101 )
= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) ) )
= $false )
| ( ( ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2091]) ).
thf(2217,plain,
! [SV101: list_a > $o] :
( ( ( ~ ~ ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) ) )
= $false )
| ( ( ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2091]) ).
thf(2218,plain,
! [SV221: list_a,SV217: a,SV102: list_a > $o] :
( ( ( SV102 @ nil_a )
= $false )
| ( ( ! [SY475: list_a] : ( SV102 @ SY475 ) )
= $true )
| ( ( SV102 @ ( sK25_SY345 @ SV102 ) )
= $true )
| ( ( ( sK25_SY345 @ SV102 )
= ( cons_a @ SV217 @ SV221 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2092]) ).
thf(2219,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( SV103 != nil_a )
= $false )
| ( ( ( append_a @ SV103 @ SV161 )
= nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2093]) ).
thf(2220,plain,
! [SV103: list_a,SV161: list_a] :
( ( ( SV161 != nil_a )
= $false )
| ( ( ( append_a @ SV103 @ SV161 )
= nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2093]) ).
thf(2221,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ( ( append_a @ SV103 @ SV161 )
!= nil_a )
| ~ ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) )
= $false )
| ( ( SV103 = nil_a )
= $false )
| ( ( SV161 = nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2094]) ).
thf(2222,plain,
! [SV249: list_a,SV239: list_a,SV162: a > a,SV104: ( a > a ) > list_a > list_a > $o] :
( ( ( SV104 @ SV162 @ SV239 @ SV249 )
= $true )
| ( ( SV104 @ ( sK54_F2 @ SV162 @ SV104 ) @ ( cons_a @ ( sK55_SY373 @ SV162 @ SV104 ) @ ( sK56_SY376 @ SV162 @ SV104 ) ) @ ( sK57_SY378 @ SV162 @ SV104 ) )
= $false )
| ( ( SV104 @ ( sK58_F2 @ SV162 @ SV104 ) @ nil_a @ ( sK59_SY379 @ SV162 @ SV104 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2223,plain,
! [SV203: a,SV190: list_a,SV163: a,SV105: list_a] :
( ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
= $true )
| ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2097]) ).
thf(2224,plain,
! [SV203: a,SV163: a,SV190: list_a,SV105: list_a] :
( ( ( ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) )
= $true )
| ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2098]) ).
thf(2225,plain,
! [SV203: a,SV163: a,SV190: list_a,SV105: list_a] :
( ( ( SV105 = SV190 )
= $false )
| ( ( SV163 != SV203 )
= $true )
| ( ( ~ ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
!= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
| ~ ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2099]) ).
thf(2226,plain,
! [SV107: nat > $o] :
( ( ( SV107 @ ( sK1_N2 @ SV107 ) )
= $false )
| ( ( ! [SY486: nat] : ( SV107 @ SY486 ) )
= $true )
| ( ( SV107 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2101]) ).
thf(2227,plain,
! [SV107: nat > $o,SV250: nat] :
( ( ( ~ ( ord_less_nat @ SV250 @ ( sK1_N2 @ SV107 ) )
| ( SV107 @ SV250 ) )
= $true )
| ( ( ! [SY486: nat] : ( SV107 @ SY486 ) )
= $true )
| ( ( SV107 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2228,plain,
! [SV109: list_a > $o] :
( ( ( ~ ( SV109 @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) ) )
= $false )
| ( ( ! [SY488: list_a] : ( SV109 @ SY488 ) )
= $true )
| ( ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
= $false )
| ( ( SV109 @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2104]) ).
thf(2229,plain,
! [SV109: list_a > $o] :
( ( ( ~ ~ ( SV109 @ ( cons_a @ ( sK18_X2 @ SV109 ) @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) ) ) )
= $false )
| ( ( ! [SY488: list_a] : ( SV109 @ SY488 ) )
= $true )
| ( ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
= $false )
| ( ( SV109 @ nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2104]) ).
thf(2230,plain,
! [SV204: list_a,SV191: a,SV164: list_a,SV110: a] :
( ( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SV204 ) )
= $true )
| ( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2105]) ).
thf(2231,plain,
! [SV204: list_a,SV164: list_a,SV191: a,SV110: a] :
( ( ( ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) )
= $true )
| ( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2106]) ).
thf(2232,plain,
! [SV204: list_a,SV164: list_a,SV191: a,SV110: a] :
( ( ( SV110 = SV191 )
= $false )
| ( ( SV164 != SV204 )
= $true )
| ( ( ~ ( ( ( cons_a @ SV110 @ SV164 )
!= ( cons_a @ SV191 @ SV204 ) )
| ~ ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2233,plain,
! [SV165: poly_a,SV112: a] :
( ( ( SV112 != zero_zero_a )
= $false )
| ( ( ( pCons_a @ SV112 @ SV165 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2109]) ).
thf(2234,plain,
! [SV112: a,SV165: poly_a] :
( ( ( SV165 != zero_zero_poly_a )
= $false )
| ( ( ( pCons_a @ SV112 @ SV165 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2109]) ).
thf(2235,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ( ( pCons_a @ SV112 @ SV165 )
!= zero_zero_poly_a )
| ~ ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) )
= $false )
| ( ( SV112 = zero_zero_a )
= $false )
| ( ( SV165 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2236,plain,
! [SV251: list_a,SV244: list_a,SV114: list_a > list_a > $o] :
( ( ( SV114 @ SV244 @ SV251 )
= $true )
| ( ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) )
= $false )
| ( ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a )
= $false )
| ( ( SV114 @ ( sK72_SY386 @ SV114 ) @ ( sK74_SY391 @ SV114 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2237,plain,
! [SV252: list_a,SV114: list_a > list_a > $o] :
( ( ( ! [SY567: list_a] : ( SV114 @ SV252 @ SY567 ) )
= $true )
| ( ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) )
= $false )
| ( ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a )
= $false )
| ( ( SV114 @ ( cons_a @ ( sK71_X2 @ SV114 ) @ ( sK72_SY386 @ SV114 ) ) @ ( cons_a @ ( sK73_SY389 @ SV114 ) @ ( sK74_SY391 @ SV114 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2238,plain,
! [SV115: list_a,SV192: list_a > $o] :
( ( ( ~ ( SV192 @ ( sK52_SY372 @ SV192 @ SV115 ) ) )
= $false )
| ( ( SV192 @ SV115 )
= $true )
| ( ( SV192 @ ( cons_a @ ( sK53_X2 @ SV192 @ SV115 ) @ nil_a ) )
= $false )
| ( ( SV115 = nil_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2115]) ).
thf(2239,plain,
! [SV115: list_a,SV192: list_a > $o] :
( ( ( ~ ~ ( SV192 @ ( cons_a @ ( sK51_X2 @ SV192 @ SV115 ) @ ( sK52_SY372 @ SV192 @ SV115 ) ) ) )
= $false )
| ( ( SV192 @ SV115 )
= $true )
| ( ( SV192 @ ( cons_a @ ( sK53_X2 @ SV192 @ SV115 ) @ nil_a ) )
= $false )
| ( ( SV115 = nil_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2115]) ).
thf(2240,plain,
! [SV253: list_a,SV245: a > a > $o,SV117: ( a > a > $o ) > list_a > $o] :
( ( ( SV117 @ SV245 @ SV253 )
= $true )
| ( ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) )
= $true )
| ( ( SV117 @ ( sK48_P5 @ SV117 ) @ ( cons_a @ ( sK49_SY371 @ SV117 ) @ nil_a ) )
= $false )
| ( ( SV117 @ ( sK50_P5 @ SV117 ) @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2241,plain,
! [SV254: a > a > $o,SV117: ( a > a > $o ) > list_a > $o] :
( ( ( ! [SY568: list_a] : ( SV117 @ SV254 @ SY568 ) )
= $true )
| ( ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK45_SY365 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) ) )
= $false )
| ( ( SV117 @ ( sK48_P5 @ SV117 ) @ ( cons_a @ ( sK49_SY371 @ SV117 ) @ nil_a ) )
= $false )
| ( ( SV117 @ ( sK50_P5 @ SV117 ) @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2242,plain,
! [SV255: list_a,SV246: list_a,SV118: list_a > list_a > $o] :
( ( ( SV118 @ SV246 @ SV255 )
= $true )
| ( ( SV118 @ ( sK27_SY350 @ SV118 ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) )
= $true )
| ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2243,plain,
! [SV118: list_a > list_a > $o] :
( ( ( ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( sK29_SY355 @ SV118 ) ) )
= $false )
| ( ( ! [SY503: list_a,SY504: list_a] : ( SV118 @ SY503 @ SY504 ) )
= $true )
| ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2119]) ).
thf(2244,plain,
! [SV118: list_a > list_a > $o] :
( ( ( ~ ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) ) )
= $false )
| ( ( ! [SY503: list_a,SY504: list_a] : ( SV118 @ SY503 @ SY504 ) )
= $true )
| ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2119]) ).
thf(2245,plain,
! [SV119: list_a > list_a > $o] :
( ( ( SV119 @ ( sK7_SY330 @ SV119 ) @ ( sK9_SY335 @ SV119 ) )
= $true )
| ( ( ! [SY505: list_a,SY506: list_a] : ( SV119 @ SY505 @ SY506 ) )
= $true )
| ( ( SV119 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SV119 ) @ ( sK11_SY336 @ SV119 ) ) )
= $false )
| ( ( SV119 @ ( cons_a @ ( sK12_X2 @ SV119 ) @ ( sK13_SY337 @ SV119 ) ) @ nil_a )
= $false )
| ( ( SV119 @ nil_a @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2120]) ).
thf(2246,plain,
! [SV119: list_a > list_a > $o] :
( ( ( ~ ( SV119 @ ( cons_a @ ( sK6_X2 @ SV119 ) @ ( sK7_SY330 @ SV119 ) ) @ ( cons_a @ ( sK8_SY333 @ SV119 ) @ ( sK9_SY335 @ SV119 ) ) ) )
= $true )
| ( ( ! [SY505: list_a,SY506: list_a] : ( SV119 @ SY505 @ SY506 ) )
= $true )
| ( ( SV119 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SV119 ) @ ( sK11_SY336 @ SV119 ) ) )
= $false )
| ( ( SV119 @ ( cons_a @ ( sK12_X2 @ SV119 ) @ ( sK13_SY337 @ SV119 ) ) @ nil_a )
= $false )
| ( ( SV119 @ nil_a @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2121]) ).
thf(2247,plain,
! [SV256: poly_a,SV120: poly_a > $o] :
( ( ( SV120 @ SV256 )
= $true )
| ( ( ( sK88_A2 @ SV120 )
= zero_zero_a )
= $false )
| ( ( ( sK89_SY406 @ SV120 )
= zero_zero_poly_a )
= $false )
| ( ( SV120 @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2248,plain,
! [SV257: poly_a,SV120: poly_a > $o] :
( ( ( SV120 @ SV257 )
= $true )
| ( ( SV120 @ ( sK89_SY406 @ SV120 ) )
= $true )
| ( ( SV120 @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(2249,plain,
! [SV120: poly_a > $o] :
( ( ( SV120 @ ( pCons_a @ ( sK88_A2 @ SV120 ) @ ( sK89_SY406 @ SV120 ) ) )
= $false )
| ( ( ! [SY507: poly_a] : ( SV120 @ SY507 ) )
= $true )
| ( ( SV120 @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2124]) ).
thf(2250,plain,
! [SV121: list_a] :
( ( ( ~ ~ ! [SY569: list_a] :
( SV121
!= ( cons_a @ ( sK90_SY508 @ SV121 ) @ SY569 ) ) )
= $false )
| ( ( SV121 = nil_a )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2126]) ).
thf(2251,plain,
! [SV247: list_a,SV220: a,SV121: list_a] :
( ( ( SV121
= ( cons_a @ SV220 @ SV247 ) )
= $false )
| ( ( ~ ( ~ ( ( SV121 != nil_a ) )
| ~ ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2252,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( SV122 != nil_a )
= $false )
| ( ( nil_a
= ( append_a @ SV122 @ SV166 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2128]) ).
thf(2253,plain,
! [SV122: list_a,SV166: list_a] :
( ( ( SV166 != nil_a )
= $false )
| ( ( nil_a
= ( append_a @ SV122 @ SV166 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2128]) ).
thf(2254,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( ( nil_a
!= ( append_a @ SV122 @ SV166 ) )
| ~ ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) )
= $false )
| ( ( SV122 = nil_a )
= $false )
| ( ( SV166 = nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2255,plain,
! [SV258: list_a,SV248: list_a,SV123: list_a > list_a > $o] :
( ( ( SV123 @ SV248 @ SV258 )
= $true )
| ( ( SV123 @ ( sK76_SY392 @ SV123 ) @ ( sK78_SY397 @ SV123 ) )
= $true )
| ( ( SV123 @ nil_a @ ( cons_a @ ( sK79_V @ SV123 ) @ ( sK80_SY398 @ SV123 ) ) )
= $false )
| ( ( SV123 @ ( sK81_Xs2 @ SV123 ) @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2256,plain,
! [SV259: list_a,SV123: list_a > list_a > $o] :
( ( ( ! [SY570: list_a] : ( SV123 @ SV259 @ SY570 ) )
= $true )
| ( ( SV123 @ ( cons_a @ ( sK75_X2 @ SV123 ) @ ( sK76_SY392 @ SV123 ) ) @ ( cons_a @ ( sK77_SY395 @ SV123 ) @ ( sK78_SY397 @ SV123 ) ) )
= $false )
| ( ( SV123 @ nil_a @ ( cons_a @ ( sK79_V @ SV123 ) @ ( sK80_SY398 @ SV123 ) ) )
= $false )
| ( ( SV123 @ ( sK81_Xs2 @ SV123 ) @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2257,plain,
! [SV169: a,SV24: a,SV133: a] :
( ( ( SV133 = zero_zero_a )
= $true )
| ( ( SV24 = SV169 )
= $true )
| ( ( SV133 = zero_zero_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2140]) ).
thf(2258,plain,
! [SV169: a,SV24: a,SV133: a] :
( ( ( SV133 = zero_zero_a )
= $true )
| ( ( SV24 = SV169 )
= $true )
| ( ( SV24 = SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2142]) ).
thf(2259,plain,
! [SV170: poly_a,SV25: poly_a,SV134: poly_a] :
( ( ( SV134 = zero_zero_poly_a )
= $true )
| ( ( SV25 = SV170 )
= $true )
| ( ( SV134 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2145]) ).
thf(2260,plain,
! [SV170: poly_a,SV25: poly_a,SV134: poly_a] :
( ( ( SV134 = zero_zero_poly_a )
= $true )
| ( ( SV25 = SV170 )
= $true )
| ( ( SV25 = SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2147]) ).
thf(2261,plain,
! [SV171: nat,SV26: nat,SV135: nat] :
( ( ( SV135 = zero_zero_nat )
= $true )
| ( ( SV26 = SV171 )
= $true )
| ( ( SV135 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2150]) ).
thf(2262,plain,
! [SV171: nat,SV26: nat,SV135: nat] :
( ( ( SV135 = zero_zero_nat )
= $true )
| ( ( SV26 = SV171 )
= $true )
| ( ( SV26 = SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2152]) ).
thf(2263,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( SV27 = zero_zero_a )
= $true )
| ( ( SV136 = SV172 )
= $true )
| ( ( SV27 = zero_zero_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2264,plain,
! [SV172: a,SV136: a,SV27: a] :
( ( ( SV27 = zero_zero_a )
= $true )
| ( ( SV136 = SV172 )
= $true )
| ( ( SV136 = SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2157]) ).
thf(2265,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( SV28 = zero_zero_poly_a )
= $true )
| ( ( SV137 = SV173 )
= $true )
| ( ( SV28 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2160]) ).
thf(2266,plain,
! [SV173: poly_a,SV137: poly_a,SV28: poly_a] :
( ( ( SV28 = zero_zero_poly_a )
= $true )
| ( ( SV137 = SV173 )
= $true )
| ( ( SV137 = SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2162]) ).
thf(2267,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( SV29 = zero_zero_nat )
= $true )
| ( ( SV138 = SV174 )
= $true )
| ( ( SV29 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2165]) ).
thf(2268,plain,
! [SV174: nat,SV138: nat,SV29: nat] :
( ( ( SV29 = zero_zero_nat )
= $true )
| ( ( SV138 = SV174 )
= $true )
| ( ( SV138 = SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2167]) ).
thf(2269,plain,
! [SV156: nat,SV187: nat,SV86: nat] :
( ( ( SV86 = SV187 )
= $true )
| ( ( SV156 = zero_zero_nat )
= $true )
| ( ( SV86 = SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2200]) ).
thf(2270,plain,
! [SV156: nat,SV187: nat,SV86: nat] :
( ( ( SV86 = SV187 )
= $true )
| ( ( SV156 = zero_zero_nat )
= $true )
| ( ( SV156 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2202]) ).
thf(2271,plain,
! [SV92: nat,SV188: nat,SV158: nat] :
( ( ( SV158 = SV188 )
= $true )
| ( ( SV92 = zero_zero_nat )
= $true )
| ( ( SV158 = SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2207]) ).
thf(2272,plain,
! [SV92: nat,SV188: nat,SV158: nat] :
( ( ( SV158 = SV188 )
= $true )
| ( ( SV92 = zero_zero_nat )
= $true )
| ( ( SV92 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2209]) ).
thf(2273,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( SV100 = zero_zero_nat )
= $true )
| ( ( SV160 = SV189 )
= $true )
| ( ( SV100 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2212]) ).
thf(2274,plain,
! [SV189: nat,SV160: nat,SV100: nat] :
( ( ( SV100 = zero_zero_nat )
= $true )
| ( ( SV160 = SV189 )
= $true )
| ( ( SV160 = SV189 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2214]) ).
thf(2275,plain,
! [SV260: list_a,SV101: list_a > $o] :
( ( ( SV101 @ SV260 )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) )
= $true )
| ( ( ( sK40_X2 @ SV101 )
= ( sK41_SY362 @ SV101 ) )
= $false )
| ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2276,plain,
! [SV101: list_a > $o] :
( ( ( ( ( sK40_X2 @ SV101 )
= ( sK41_SY362 @ SV101 ) )
| ( SV101 @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
= $true )
| ( ( ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2216]) ).
thf(2277,plain,
! [SV101: list_a > $o] :
( ( ( ~ ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) ) )
= $true )
| ( ( ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2217]) ).
thf(2278,plain,
! [SV221: list_a,SV217: a,SV261: list_a,SV102: list_a > $o] :
( ( ( SV102 @ SV261 )
= $true )
| ( ( SV102 @ nil_a )
= $false )
| ( ( SV102 @ ( sK25_SY345 @ SV102 ) )
= $true )
| ( ( ( sK25_SY345 @ SV102 )
= ( cons_a @ SV217 @ SV221 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2279,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( SV103 = nil_a )
= $true )
| ( ( ( append_a @ SV103 @ SV161 )
= nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2219]) ).
thf(2280,plain,
! [SV103: list_a,SV161: list_a] :
( ( ( SV161 = nil_a )
= $true )
| ( ( ( append_a @ SV103 @ SV161 )
= nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2220]) ).
thf(2281,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ( append_a @ SV103 @ SV161 )
!= nil_a )
= $false )
| ( ( SV103 = nil_a )
= $false )
| ( ( SV161 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2221]) ).
thf(2282,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ~ ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) )
= $false )
| ( ( SV103 = nil_a )
= $false )
| ( ( SV161 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2221]) ).
thf(2283,plain,
! [SV203: a,SV163: a,SV190: list_a,SV105: list_a] :
( ( ( ( SV105 != SV190 )
| ( SV163 != SV203 ) )
= $false )
| ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2224]) ).
thf(2284,plain,
! [SV190: list_a,SV105: list_a,SV203: a,SV163: a] :
( ( ( SV163 = SV203 )
= $false )
| ( ( SV105 = SV190 )
= $false )
| ( ( ~ ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
!= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
| ~ ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2225]) ).
thf(2285,plain,
! [SV262: nat,SV107: nat > $o] :
( ( ( SV107 @ SV262 )
= $true )
| ( ( SV107 @ ( sK1_N2 @ SV107 ) )
= $false )
| ( ( SV107 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(2286,plain,
! [SV107: nat > $o,SV250: nat] :
( ( ( ~ ( ord_less_nat @ SV250 @ ( sK1_N2 @ SV107 ) ) )
= $true )
| ( ( SV107 @ SV250 )
= $true )
| ( ( ! [SY486: nat] : ( SV107 @ SY486 ) )
= $true )
| ( ( SV107 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2227]) ).
thf(2287,plain,
! [SV109: list_a > $o] :
( ( ( SV109 @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) )
= $true )
| ( ( ! [SY488: list_a] : ( SV109 @ SY488 ) )
= $true )
| ( ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
= $false )
| ( ( SV109 @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2228]) ).
thf(2288,plain,
! [SV109: list_a > $o] :
( ( ( ~ ( SV109 @ ( cons_a @ ( sK18_X2 @ SV109 ) @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) ) ) )
= $true )
| ( ( ! [SY488: list_a] : ( SV109 @ SY488 ) )
= $true )
| ( ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
= $false )
| ( ( SV109 @ nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2229]) ).
thf(2289,plain,
! [SV204: list_a,SV164: list_a,SV191: a,SV110: a] :
( ( ( ( SV110 != SV191 )
| ( SV164 != SV204 ) )
= $false )
| ( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2231]) ).
thf(2290,plain,
! [SV191: a,SV110: a,SV204: list_a,SV164: list_a] :
( ( ( SV164 = SV204 )
= $false )
| ( ( SV110 = SV191 )
= $false )
| ( ( ~ ( ( ( cons_a @ SV110 @ SV164 )
!= ( cons_a @ SV191 @ SV204 ) )
| ~ ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2232]) ).
thf(2291,plain,
! [SV165: poly_a,SV112: a] :
( ( ( SV112 = zero_zero_a )
= $true )
| ( ( ( pCons_a @ SV112 @ SV165 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2233]) ).
thf(2292,plain,
! [SV112: a,SV165: poly_a] :
( ( ( SV165 = zero_zero_poly_a )
= $true )
| ( ( ( pCons_a @ SV112 @ SV165 )
= zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2234]) ).
thf(2293,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ( pCons_a @ SV112 @ SV165 )
!= zero_zero_poly_a )
= $false )
| ( ( SV112 = zero_zero_a )
= $false )
| ( ( SV165 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2235]) ).
thf(2294,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ~ ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) )
= $false )
| ( ( SV112 = zero_zero_a )
= $false )
| ( ( SV165 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2235]) ).
thf(2295,plain,
! [SV263: list_a,SV252: list_a,SV114: list_a > list_a > $o] :
( ( ( SV114 @ SV252 @ SV263 )
= $true )
| ( ( SV114 @ nil_a @ ( cons_a @ ( sK68_Y2 @ SV114 ) @ ( sK69_SY385 @ SV114 ) ) )
= $false )
| ( ( SV114 @ ( sK70_Xs2 @ SV114 ) @ nil_a )
= $false )
| ( ( SV114 @ ( cons_a @ ( sK71_X2 @ SV114 ) @ ( sK72_SY386 @ SV114 ) ) @ ( cons_a @ ( sK73_SY389 @ SV114 ) @ ( sK74_SY391 @ SV114 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2296,plain,
! [SV115: list_a,SV192: list_a > $o] :
( ( ( SV192 @ ( sK52_SY372 @ SV192 @ SV115 ) )
= $true )
| ( ( SV192 @ SV115 )
= $true )
| ( ( SV192 @ ( cons_a @ ( sK53_X2 @ SV192 @ SV115 ) @ nil_a ) )
= $false )
| ( ( SV115 = nil_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2238]) ).
thf(2297,plain,
! [SV115: list_a,SV192: list_a > $o] :
( ( ( ~ ( SV192 @ ( cons_a @ ( sK51_X2 @ SV192 @ SV115 ) @ ( sK52_SY372 @ SV192 @ SV115 ) ) ) )
= $true )
| ( ( SV192 @ SV115 )
= $true )
| ( ( SV192 @ ( cons_a @ ( sK53_X2 @ SV192 @ SV115 ) @ nil_a ) )
= $false )
| ( ( SV115 = nil_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2239]) ).
thf(2298,plain,
! [SV264: list_a,SV254: a > a > $o,SV117: ( a > a > $o ) > list_a > $o] :
( ( ( SV117 @ SV254 @ SV264 )
= $true )
| ( ( SV117 @ ( sK44_P5 @ SV117 ) @ ( cons_a @ ( sK45_SY365 @ SV117 ) @ ( cons_a @ ( sK46_SY368 @ SV117 ) @ ( sK47_SY370 @ SV117 ) ) ) )
= $false )
| ( ( SV117 @ ( sK48_P5 @ SV117 ) @ ( cons_a @ ( sK49_SY371 @ SV117 ) @ nil_a ) )
= $false )
| ( ( SV117 @ ( sK50_P5 @ SV117 ) @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(2299,plain,
! [SV118: list_a > list_a > $o] :
( ( ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( sK29_SY355 @ SV118 ) )
= $true )
| ( ( ! [SY503: list_a,SY504: list_a] : ( SV118 @ SY503 @ SY504 ) )
= $true )
| ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2243]) ).
thf(2300,plain,
! [SV118: list_a > list_a > $o] :
( ( ( ~ ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) ) )
= $true )
| ( ( ! [SY503: list_a,SY504: list_a] : ( SV118 @ SY503 @ SY504 ) )
= $true )
| ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2244]) ).
thf(2301,plain,
! [SV265: list_a,SV119: list_a > list_a > $o] :
( ( ( ! [SY571: list_a] : ( SV119 @ SV265 @ SY571 ) )
= $true )
| ( ( SV119 @ ( sK7_SY330 @ SV119 ) @ ( sK9_SY335 @ SV119 ) )
= $true )
| ( ( SV119 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SV119 ) @ ( sK11_SY336 @ SV119 ) ) )
= $false )
| ( ( SV119 @ ( cons_a @ ( sK12_X2 @ SV119 ) @ ( sK13_SY337 @ SV119 ) ) @ nil_a )
= $false )
| ( ( SV119 @ nil_a @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2302,plain,
! [SV119: list_a > list_a > $o] :
( ( ( SV119 @ ( cons_a @ ( sK6_X2 @ SV119 ) @ ( sK7_SY330 @ SV119 ) ) @ ( cons_a @ ( sK8_SY333 @ SV119 ) @ ( sK9_SY335 @ SV119 ) ) )
= $false )
| ( ( ! [SY505: list_a,SY506: list_a] : ( SV119 @ SY505 @ SY506 ) )
= $true )
| ( ( SV119 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SV119 ) @ ( sK11_SY336 @ SV119 ) ) )
= $false )
| ( ( SV119 @ ( cons_a @ ( sK12_X2 @ SV119 ) @ ( sK13_SY337 @ SV119 ) ) @ nil_a )
= $false )
| ( ( SV119 @ nil_a @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2246]) ).
thf(2303,plain,
! [SV266: poly_a,SV120: poly_a > $o] :
( ( ( SV120 @ SV266 )
= $true )
| ( ( SV120 @ ( pCons_a @ ( sK88_A2 @ SV120 ) @ ( sK89_SY406 @ SV120 ) ) )
= $false )
| ( ( SV120 @ zero_zero_poly_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2304,plain,
! [SV121: list_a] :
( ( ( ~ ! [SY569: list_a] :
( SV121
!= ( cons_a @ ( sK90_SY508 @ SV121 ) @ SY569 ) ) )
= $true )
| ( ( SV121 = nil_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2250]) ).
thf(2305,plain,
! [SV247: list_a,SV220: a,SV121: list_a] :
( ( ( ~ ( ( SV121 != nil_a ) )
| ~ ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) )
= $false )
| ( ( SV121
= ( cons_a @ SV220 @ SV247 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2251]) ).
thf(2306,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( SV122 = nil_a )
= $true )
| ( ( nil_a
= ( append_a @ SV122 @ SV166 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2252]) ).
thf(2307,plain,
! [SV122: list_a,SV166: list_a] :
( ( ( SV166 = nil_a )
= $true )
| ( ( nil_a
= ( append_a @ SV122 @ SV166 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2253]) ).
thf(2308,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( nil_a
!= ( append_a @ SV122 @ SV166 ) )
= $false )
| ( ( SV122 = nil_a )
= $false )
| ( ( SV166 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2254]) ).
thf(2309,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( ~ ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) )
= $false )
| ( ( SV122 = nil_a )
= $false )
| ( ( SV166 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2254]) ).
thf(2310,plain,
! [SV267: list_a,SV259: list_a,SV123: list_a > list_a > $o] :
( ( ( SV123 @ SV259 @ SV267 )
= $true )
| ( ( SV123 @ ( cons_a @ ( sK75_X2 @ SV123 ) @ ( sK76_SY392 @ SV123 ) ) @ ( cons_a @ ( sK77_SY395 @ SV123 ) @ ( sK78_SY397 @ SV123 ) ) )
= $false )
| ( ( SV123 @ nil_a @ ( cons_a @ ( sK79_V @ SV123 ) @ ( sK80_SY398 @ SV123 ) ) )
= $false )
| ( ( SV123 @ ( sK81_Xs2 @ SV123 ) @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2311,plain,
! [SV101: list_a > $o] :
( ( ( ( sK40_X2 @ SV101 )
= ( sK41_SY362 @ SV101 ) )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) )
= $true )
| ( ( ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2276]) ).
thf(2312,plain,
! [SV101: list_a > $o] :
( ( ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
= $false )
| ( ( ! [SY472: list_a] : ( SV101 @ SY472 ) )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2313,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ( append_a @ SV103 @ SV161 )
= nil_a )
= $true )
| ( ( SV103 = nil_a )
= $false )
| ( ( SV161 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2281]) ).
thf(2314,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ~ ( ( SV103 != nil_a )
| ( SV161 != nil_a ) ) )
= $true )
| ( ( SV103 = nil_a )
= $false )
| ( ( SV161 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2282]) ).
thf(2315,plain,
! [SV203: a,SV163: a,SV190: list_a,SV105: list_a] :
( ( ( SV105 != SV190 )
= $false )
| ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2283]) ).
thf(2316,plain,
! [SV190: list_a,SV105: list_a,SV203: a,SV163: a] :
( ( ( SV163 != SV203 )
= $false )
| ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2283]) ).
thf(2317,plain,
! [SV203: a,SV190: list_a,SV163: a,SV105: list_a] :
( ( ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
!= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
| ~ ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) )
= $false )
| ( ( SV105 = SV190 )
= $false )
| ( ( SV163 = SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2284]) ).
thf(2318,plain,
! [SV107: nat > $o,SV250: nat] :
( ( ( ord_less_nat @ SV250 @ ( sK1_N2 @ SV107 ) )
= $false )
| ( ( SV107 @ SV250 )
= $true )
| ( ( ! [SY486: nat] : ( SV107 @ SY486 ) )
= $true )
| ( ( SV107 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2286]) ).
thf(2319,plain,
! [SV268: list_a,SV109: list_a > $o] :
( ( ( SV109 @ SV268 )
= $true )
| ( ( SV109 @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) )
= $true )
| ( ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
= $false )
| ( ( SV109 @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2287]) ).
thf(2320,plain,
! [SV109: list_a > $o] :
( ( ( SV109 @ ( cons_a @ ( sK18_X2 @ SV109 ) @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) ) )
= $false )
| ( ( ! [SY488: list_a] : ( SV109 @ SY488 ) )
= $true )
| ( ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
= $false )
| ( ( SV109 @ nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2321,plain,
! [SV204: list_a,SV164: list_a,SV191: a,SV110: a] :
( ( ( SV110 != SV191 )
= $false )
| ( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SV204 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2289]) ).
thf(2322,plain,
! [SV191: a,SV110: a,SV204: list_a,SV164: list_a] :
( ( ( SV164 != SV204 )
= $false )
| ( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SV204 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2289]) ).
thf(2323,plain,
! [SV204: list_a,SV191: a,SV164: list_a,SV110: a] :
( ( ( ( ( cons_a @ SV110 @ SV164 )
!= ( cons_a @ SV191 @ SV204 ) )
| ~ ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) )
= $false )
| ( ( SV110 = SV191 )
= $false )
| ( ( SV164 = SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2290]) ).
thf(2324,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ( pCons_a @ SV112 @ SV165 )
= zero_zero_poly_a )
= $true )
| ( ( SV112 = zero_zero_a )
= $false )
| ( ( SV165 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2293]) ).
thf(2325,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ~ ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) ) )
= $true )
| ( ( SV112 = zero_zero_a )
= $false )
| ( ( SV165 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2294]) ).
thf(2326,plain,
! [SV115: list_a,SV192: list_a > $o] :
( ( ( SV192 @ ( cons_a @ ( sK51_X2 @ SV192 @ SV115 ) @ ( sK52_SY372 @ SV192 @ SV115 ) ) )
= $false )
| ( ( SV192 @ SV115 )
= $true )
| ( ( SV192 @ ( cons_a @ ( sK53_X2 @ SV192 @ SV115 ) @ nil_a ) )
= $false )
| ( ( SV115 = nil_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2297]) ).
thf(2327,plain,
! [SV269: list_a,SV118: list_a > list_a > $o] :
( ( ( ! [SY572: list_a] : ( SV118 @ SV269 @ SY572 ) )
= $true )
| ( ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( sK29_SY355 @ SV118 ) )
= $true )
| ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(2328,plain,
! [SV118: list_a > list_a > $o] :
( ( ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) )
= $false )
| ( ( ! [SY503: list_a,SY504: list_a] : ( SV118 @ SY503 @ SY504 ) )
= $true )
| ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2300]) ).
thf(2329,plain,
! [SV270: list_a,SV265: list_a,SV119: list_a > list_a > $o] :
( ( ( SV119 @ SV265 @ SV270 )
= $true )
| ( ( SV119 @ ( sK7_SY330 @ SV119 ) @ ( sK9_SY335 @ SV119 ) )
= $true )
| ( ( SV119 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SV119 ) @ ( sK11_SY336 @ SV119 ) ) )
= $false )
| ( ( SV119 @ ( cons_a @ ( sK12_X2 @ SV119 ) @ ( sK13_SY337 @ SV119 ) ) @ nil_a )
= $false )
| ( ( SV119 @ nil_a @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2330,plain,
! [SV271: list_a,SV119: list_a > list_a > $o] :
( ( ( ! [SY573: list_a] : ( SV119 @ SV271 @ SY573 ) )
= $true )
| ( ( SV119 @ ( cons_a @ ( sK6_X2 @ SV119 ) @ ( sK7_SY330 @ SV119 ) ) @ ( cons_a @ ( sK8_SY333 @ SV119 ) @ ( sK9_SY335 @ SV119 ) ) )
= $false )
| ( ( SV119 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SV119 ) @ ( sK11_SY336 @ SV119 ) ) )
= $false )
| ( ( SV119 @ ( cons_a @ ( sK12_X2 @ SV119 ) @ ( sK13_SY337 @ SV119 ) ) @ nil_a )
= $false )
| ( ( SV119 @ nil_a @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(2331,plain,
! [SV121: list_a] :
( ( ( ! [SY569: list_a] :
( SV121
!= ( cons_a @ ( sK90_SY508 @ SV121 ) @ SY569 ) ) )
= $false )
| ( ( SV121 = nil_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2304]) ).
thf(2332,plain,
! [SV247: list_a,SV220: a,SV121: list_a] :
( ( ( ~ ( ( SV121 != nil_a ) ) )
= $false )
| ( ( SV121
= ( cons_a @ SV220 @ SV247 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2305]) ).
thf(2333,plain,
! [SV247: list_a,SV220: a,SV121: list_a] :
( ( ( ~ ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) )
= $false )
| ( ( SV121
= ( cons_a @ SV220 @ SV247 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2305]) ).
thf(2334,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( nil_a
= ( append_a @ SV122 @ SV166 ) )
= $true )
| ( ( SV122 = nil_a )
= $false )
| ( ( SV166 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2308]) ).
thf(2335,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( ~ ( ( SV122 != nil_a )
| ( SV166 != nil_a ) ) )
= $true )
| ( ( SV122 = nil_a )
= $false )
| ( ( SV166 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2309]) ).
thf(2336,plain,
! [SV272: list_a,SV101: list_a > $o] :
( ( ( SV101 @ SV272 )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) )
= $true )
| ( ( ( sK40_X2 @ SV101 )
= ( sK41_SY362 @ SV101 ) )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(2337,plain,
! [SV273: list_a,SV101: list_a > $o] :
( ( ( SV101 @ SV273 )
= $true )
| ( ( SV101 @ ( cons_a @ ( sK40_X2 @ SV101 ) @ ( cons_a @ ( sK41_SY362 @ SV101 ) @ ( sK42_SY364 @ SV101 ) ) ) )
= $false )
| ( ( SV101 @ ( cons_a @ ( sK43_X2 @ SV101 ) @ nil_a ) )
= $false )
| ( ( SV101 @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(2338,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( ( SV103 != nil_a )
| ( SV161 != nil_a ) )
= $false )
| ( ( SV103 = nil_a )
= $false )
| ( ( SV161 = nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2314]) ).
thf(2339,plain,
! [SV203: a,SV163: a,SV190: list_a,SV105: list_a] :
( ( ( SV105 = SV190 )
= $true )
| ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2315]) ).
thf(2340,plain,
! [SV190: list_a,SV105: list_a,SV203: a,SV163: a] :
( ( ( SV163 = SV203 )
= $true )
| ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2316]) ).
thf(2341,plain,
! [SV203: a,SV190: list_a,SV163: a,SV105: list_a] :
( ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
!= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
= $false )
| ( ( SV105 = SV190 )
= $false )
| ( ( SV163 = SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2317]) ).
thf(2342,plain,
! [SV203: a,SV163: a,SV190: list_a,SV105: list_a] :
( ( ( ~ ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) )
= $false )
| ( ( SV105 = SV190 )
= $false )
| ( ( SV163 = SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2317]) ).
thf(2343,plain,
! [SV250: nat,SV274: nat,SV107: nat > $o] :
( ( ( SV107 @ SV274 )
= $true )
| ( ( SV107 @ SV250 )
= $true )
| ( ( ord_less_nat @ SV250 @ ( sK1_N2 @ SV107 ) )
= $false )
| ( ( SV107 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(2344,plain,
! [SV275: list_a,SV109: list_a > $o] :
( ( ( SV109 @ SV275 )
= $true )
| ( ( SV109 @ ( cons_a @ ( sK18_X2 @ SV109 ) @ ( cons_a @ ( sK19_SY341 @ SV109 ) @ ( sK20_SY343 @ SV109 ) ) ) )
= $false )
| ( ( SV109 @ ( cons_a @ ( sK21_X2 @ SV109 ) @ nil_a ) )
= $false )
| ( ( SV109 @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(2345,plain,
! [SV204: list_a,SV164: list_a,SV191: a,SV110: a] :
( ( ( SV110 = SV191 )
= $true )
| ( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2321]) ).
thf(2346,plain,
! [SV191: a,SV110: a,SV204: list_a,SV164: list_a] :
( ( ( SV164 = SV204 )
= $true )
| ( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2322]) ).
thf(2347,plain,
! [SV204: list_a,SV191: a,SV164: list_a,SV110: a] :
( ( ( ( cons_a @ SV110 @ SV164 )
!= ( cons_a @ SV191 @ SV204 ) )
= $false )
| ( ( SV110 = SV191 )
= $false )
| ( ( SV164 = SV204 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2323]) ).
thf(2348,plain,
! [SV204: list_a,SV164: list_a,SV191: a,SV110: a] :
( ( ( ~ ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) )
= $false )
| ( ( SV110 = SV191 )
= $false )
| ( ( SV164 = SV204 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2323]) ).
thf(2349,plain,
! [SV165: poly_a,SV112: a] :
( ( ( ( SV112 != zero_zero_a )
| ( SV165 != zero_zero_poly_a ) )
= $false )
| ( ( SV112 = zero_zero_a )
= $false )
| ( ( SV165 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2350,plain,
! [SV276: list_a,SV269: list_a,SV118: list_a > list_a > $o] :
( ( ( SV118 @ SV269 @ SV276 )
= $true )
| ( ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( sK29_SY355 @ SV118 ) )
= $true )
| ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(2351,plain,
! [SV277: list_a,SV118: list_a > list_a > $o] :
( ( ( ! [SY574: list_a] : ( SV118 @ SV277 @ SY574 ) )
= $true )
| ( ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) )
= $false )
| ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(2352,plain,
! [SV278: list_a,SV271: list_a,SV119: list_a > list_a > $o] :
( ( ( SV119 @ SV271 @ SV278 )
= $true )
| ( ( SV119 @ ( cons_a @ ( sK6_X2 @ SV119 ) @ ( sK7_SY330 @ SV119 ) ) @ ( cons_a @ ( sK8_SY333 @ SV119 ) @ ( sK9_SY335 @ SV119 ) ) )
= $false )
| ( ( SV119 @ nil_a @ ( cons_a @ ( sK10_Y2 @ SV119 ) @ ( sK11_SY336 @ SV119 ) ) )
= $false )
| ( ( SV119 @ ( cons_a @ ( sK12_X2 @ SV119 ) @ ( sK13_SY337 @ SV119 ) ) @ nil_a )
= $false )
| ( ( SV119 @ nil_a @ nil_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(2353,plain,
! [SV121: list_a] :
( ( ( SV121
!= ( cons_a @ ( sK90_SY508 @ SV121 ) @ ( sK91_SY569 @ SV121 ) ) )
= $false )
| ( ( SV121 = nil_a )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2331]) ).
thf(2354,plain,
! [SV247: list_a,SV220: a,SV121: list_a] :
( ( ( SV121 != nil_a )
= $true )
| ( ( SV121
= ( cons_a @ SV220 @ SV247 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2332]) ).
thf(2355,plain,
! [SV247: list_a,SV220: a,SV121: list_a] :
( ( ( ~ ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) )
= $true )
| ( ( SV121
= ( cons_a @ SV220 @ SV247 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2333]) ).
thf(2356,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( ( SV122 != nil_a )
| ( SV166 != nil_a ) )
= $false )
| ( ( SV122 = nil_a )
= $false )
| ( ( SV166 = nil_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2335]) ).
thf(2357,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( SV103 != nil_a )
= $false )
| ( ( SV103 = nil_a )
= $false )
| ( ( SV161 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2338]) ).
thf(2358,plain,
! [SV103: list_a,SV161: list_a] :
( ( ( SV161 != nil_a )
= $false )
| ( ( SV103 = nil_a )
= $false )
| ( ( SV161 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2338]) ).
thf(2359,plain,
! [SV203: a,SV190: list_a,SV163: a,SV105: list_a] :
( ( ( ( append_a @ SV105 @ ( cons_a @ SV163 @ nil_a ) )
= ( append_a @ SV190 @ ( cons_a @ SV203 @ nil_a ) ) )
= $true )
| ( ( SV105 = SV190 )
= $false )
| ( ( SV163 = SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2341]) ).
thf(2360,plain,
! [SV203: a,SV163: a,SV190: list_a,SV105: list_a] :
( ( ( ~ ( ( SV105 != SV190 )
| ( SV163 != SV203 ) ) )
= $true )
| ( ( SV105 = SV190 )
= $false )
| ( ( SV163 = SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2342]) ).
thf(2361,plain,
! [SV204: list_a,SV191: a,SV164: list_a,SV110: a] :
( ( ( ( cons_a @ SV110 @ SV164 )
= ( cons_a @ SV191 @ SV204 ) )
= $true )
| ( ( SV110 = SV191 )
= $false )
| ( ( SV164 = SV204 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2347]) ).
thf(2362,plain,
! [SV204: list_a,SV164: list_a,SV191: a,SV110: a] :
( ( ( ~ ( ( SV110 != SV191 )
| ( SV164 != SV204 ) ) )
= $true )
| ( ( SV110 = SV191 )
= $false )
| ( ( SV164 = SV204 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2348]) ).
thf(2363,plain,
! [SV165: poly_a,SV112: a] :
( ( ( SV112 != zero_zero_a )
= $false )
| ( ( SV112 = zero_zero_a )
= $false )
| ( ( SV165 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2349]) ).
thf(2364,plain,
! [SV112: a,SV165: poly_a] :
( ( ( SV165 != zero_zero_poly_a )
= $false )
| ( ( SV112 = zero_zero_a )
= $false )
| ( ( SV165 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2349]) ).
thf(2365,plain,
! [SV279: list_a,SV277: list_a,SV118: list_a > list_a > $o] :
( ( ( SV118 @ SV277 @ SV279 )
= $true )
| ( ( SV118 @ ( cons_a @ ( sK26_X2 @ SV118 ) @ ( sK27_SY350 @ SV118 ) ) @ ( cons_a @ ( sK28_SY353 @ SV118 ) @ ( sK29_SY355 @ SV118 ) ) )
= $false )
| ( ( SV118 @ ( sK30_Xs2 @ SV118 ) @ nil_a )
= $false )
| ( ( SV118 @ nil_a @ ( sK31_X_1 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(2366,plain,
! [SV121: list_a] :
( ( ( SV121
= ( cons_a @ ( sK90_SY508 @ SV121 ) @ ( sK91_SY569 @ SV121 ) ) )
= $true )
| ( ( SV121 = nil_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2353]) ).
thf(2367,plain,
! [SV247: list_a,SV220: a,SV121: list_a] :
( ( ( SV121 = nil_a )
= $false )
| ( ( SV121
= ( cons_a @ SV220 @ SV247 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2354]) ).
thf(2368,plain,
! [SV247: list_a,SV220: a,SV121: list_a] :
( ( ( ! [SY508: a] :
~ ~ ! [SY509: list_a] :
( SV121
!= ( cons_a @ SY508 @ SY509 ) ) )
= $false )
| ( ( SV121
= ( cons_a @ SV220 @ SV247 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2369,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( SV122 != nil_a )
= $false )
| ( ( SV122 = nil_a )
= $false )
| ( ( SV166 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2356]) ).
thf(2370,plain,
! [SV122: list_a,SV166: list_a] :
( ( ( SV166 != nil_a )
= $false )
| ( ( SV122 = nil_a )
= $false )
| ( ( SV166 = nil_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2356]) ).
thf(2371,plain,
! [SV161: list_a,SV103: list_a] :
( ( ( SV103 = nil_a )
= $true )
| ( ( SV103 = nil_a )
= $false )
| ( ( SV161 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2357]) ).
thf(2372,plain,
! [SV103: list_a,SV161: list_a] :
( ( ( SV161 = nil_a )
= $true )
| ( ( SV103 = nil_a )
= $false )
| ( ( SV161 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2358]) ).
thf(2373,plain,
! [SV203: a,SV163: a,SV190: list_a,SV105: list_a] :
( ( ( ( SV105 != SV190 )
| ( SV163 != SV203 ) )
= $false )
| ( ( SV105 = SV190 )
= $false )
| ( ( SV163 = SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2360]) ).
thf(2374,plain,
! [SV204: list_a,SV164: list_a,SV191: a,SV110: a] :
( ( ( ( SV110 != SV191 )
| ( SV164 != SV204 ) )
= $false )
| ( ( SV110 = SV191 )
= $false )
| ( ( SV164 = SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2362]) ).
thf(2375,plain,
! [SV165: poly_a,SV112: a] :
( ( ( SV112 = zero_zero_a )
= $true )
| ( ( SV112 = zero_zero_a )
= $false )
| ( ( SV165 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2363]) ).
thf(2376,plain,
! [SV112: a,SV165: poly_a] :
( ( ( SV165 = zero_zero_poly_a )
= $true )
| ( ( SV112 = zero_zero_a )
= $false )
| ( ( SV165 = zero_zero_poly_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2364]) ).
thf(2377,plain,
! [SV220: a,SV247: list_a,SV121: list_a] :
( ( ( ~ ~ ! [SY575: list_a] :
( SV121
!= ( cons_a @ ( sK92_SY508 @ SV247 @ SV220 @ SV121 ) @ SY575 ) ) )
= $false )
| ( ( SV121
= ( cons_a @ SV220 @ SV247 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2368]) ).
thf(2378,plain,
! [SV166: list_a,SV122: list_a] :
( ( ( SV122 = nil_a )
= $true )
| ( ( SV122 = nil_a )
= $false )
| ( ( SV166 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2369]) ).
thf(2379,plain,
! [SV122: list_a,SV166: list_a] :
( ( ( SV166 = nil_a )
= $true )
| ( ( SV122 = nil_a )
= $false )
| ( ( SV166 = nil_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2370]) ).
thf(2380,plain,
! [SV203: a,SV163: a,SV190: list_a,SV105: list_a] :
( ( ( SV105 != SV190 )
= $false )
| ( ( SV105 = SV190 )
= $false )
| ( ( SV163 = SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2373]) ).
thf(2381,plain,
! [SV190: list_a,SV105: list_a,SV203: a,SV163: a] :
( ( ( SV163 != SV203 )
= $false )
| ( ( SV105 = SV190 )
= $false )
| ( ( SV163 = SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2373]) ).
thf(2382,plain,
! [SV204: list_a,SV164: list_a,SV191: a,SV110: a] :
( ( ( SV110 != SV191 )
= $false )
| ( ( SV110 = SV191 )
= $false )
| ( ( SV164 = SV204 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2374]) ).
thf(2383,plain,
! [SV191: a,SV110: a,SV204: list_a,SV164: list_a] :
( ( ( SV164 != SV204 )
= $false )
| ( ( SV110 = SV191 )
= $false )
| ( ( SV164 = SV204 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2374]) ).
thf(2384,plain,
! [SV220: a,SV247: list_a,SV121: list_a] :
( ( ( ~ ! [SY575: list_a] :
( SV121
!= ( cons_a @ ( sK92_SY508 @ SV247 @ SV220 @ SV121 ) @ SY575 ) ) )
= $true )
| ( ( SV121
= ( cons_a @ SV220 @ SV247 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2377]) ).
thf(2385,plain,
! [SV203: a,SV163: a,SV190: list_a,SV105: list_a] :
( ( ( SV105 = SV190 )
= $true )
| ( ( SV105 = SV190 )
= $false )
| ( ( SV163 = SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2380]) ).
thf(2386,plain,
! [SV190: list_a,SV105: list_a,SV203: a,SV163: a] :
( ( ( SV163 = SV203 )
= $true )
| ( ( SV105 = SV190 )
= $false )
| ( ( SV163 = SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2381]) ).
thf(2387,plain,
! [SV204: list_a,SV164: list_a,SV191: a,SV110: a] :
( ( ( SV110 = SV191 )
= $true )
| ( ( SV110 = SV191 )
= $false )
| ( ( SV164 = SV204 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2382]) ).
thf(2388,plain,
! [SV191: a,SV110: a,SV204: list_a,SV164: list_a] :
( ( ( SV164 = SV204 )
= $true )
| ( ( SV110 = SV191 )
= $false )
| ( ( SV164 = SV204 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2383]) ).
thf(2389,plain,
! [SV220: a,SV247: list_a,SV121: list_a] :
( ( ( ! [SY575: list_a] :
( SV121
!= ( cons_a @ ( sK92_SY508 @ SV247 @ SV220 @ SV121 ) @ SY575 ) ) )
= $false )
| ( ( SV121
= ( cons_a @ SV220 @ SV247 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2384]) ).
thf(2390,plain,
! [SV220: a,SV247: list_a,SV121: list_a] :
( ( ( SV121
!= ( cons_a @ ( sK92_SY508 @ SV247 @ SV220 @ SV121 ) @ ( sK93_SY575 @ SV220 @ SV247 @ SV121 ) ) )
= $false )
| ( ( SV121
= ( cons_a @ SV220 @ SV247 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2389]) ).
thf(2391,plain,
! [SV220: a,SV247: list_a,SV121: list_a] :
( ( ( SV121
= ( cons_a @ ( sK92_SY508 @ SV247 @ SV220 @ SV121 ) @ ( sK93_SY575 @ SV220 @ SV247 @ SV121 ) ) )
= $true )
| ( ( SV121
= ( cons_a @ SV220 @ SV247 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2390]) ).
thf(2392,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[556,2391,2388,2387,2386,2385,2379,2378,2376,2375,2372,2371,2367,2366,2365,2361,2359,2352,2350,2346,2345,2344,2343,2340,2339,2337,2336,2334,2329,2326,2324,2319,2313,2310,2307,2306,2303,2298,2296,2295,2292,2291,2285,2280,2279,2278,2275,2274,2273,2272,2271,2270,2269,2268,2267,2266,2265,2264,2263,2262,2261,2260,2259,2258,2257,2255,2248,2247,2242,2240,2236,2230,2223,2222,2213,2211,2210,2208,2206,2205,2204,2203,2201,2199,2198,2197,2196,2195,2194,2193,2192,2191,2190,2189,2188,2187,2186,2185,2184,2183,2182,2181,2180,2179,2178,2177,2176,2175,2174,2173,2172,2171,2170,2169,2168,2166,2164,2163,2161,2159,2158,2156,2154,2153,2151,2149,2148,2146,2144,2143,2141,2139,2138,2137,2136,2135,2134,2133,2132,2125,2114,2111,2108,2103,2100,2095,2084,2083,2077,2075,2073,2072,2071,2070,2064,2039,2037,2035,2034,2032,2030,2029,2027,2025,2024,2018,2012,2006,2000,1994,1988,1987,1985,1983,1982,1977,1972,1955,1952,1950,1945,1941,1934,1933,1925,1924,1913,1912,1911,1909,1908,1902,1888,1887,1886,1885,1884,1883,1882,1881,1880,1879,1878,1877,1876,1875,1874,1873,1872,1871,1865,1859,1853,1828,1827,1825,1824,1823,1822,1816,1815,1814,1813,1812,1808,1776,1774,1757,1746,1742,1735,1734,1733,1732,1715,1714,1713,1712,1711,1710,1709,1708,1707,1706,1705,1704,1703,1686,1685,1684,1683,1682,1681,1680,1679,1678,1677,1676,1675,1674,1673,1672,1671,1670,1669,1668,1667,1666,1665,1664,1663,1662,1661,1660,1659,1658,1657,1656,1655,1624,1612,1611,1610,1609,1592,1591,1588,1587,1581,1580,1560,1559,1379,1296,1290,1280,1266,1265,1264,1263,1262,1261,1260,1258,1256,1254,1252,1250,1248,1208,1202,1167,1163,1158,1155,1120,1118,1116,1114,1112,1110,1102,1098,1083,1073,1063,1057,1054,1053,1051,1036,1032,1030,1028,1026,1016,1014,1012,1002,1001,999,997,995,992,987,958,956,955,954,952,949,947,946,943,935,934,932,919,918,916,913,911,909,903,901,899,897,895,893,891,889,878,873,870,868,864,836,834,826,817,816,807,806,805,792,791,790,781,776,767,766,765,764,763,762,749,748,747,745,743,742,741,739,738,734,733,732,729,727,726,680,616,615,578,576,568,566,564,560]) ).
thf(2393,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2392]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP044^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.15 % Computer : n007.cluster.edu
% 0.10/0.15 % Model : x86_64 x86_64
% 0.10/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.15 % Memory : 8046.5625MB
% 0.10/0.15 % OS : Linux 6.8.0-71-generic
% 0.10/0.15 % CPULimit : 300
% 0.10/0.15 % WCLimit : 300
% 0.10/0.15 % DateTime : Tue Oct 6 11:13:00 UTC 2026
% 0.10/0.15 % CPUTime :
% 0.10/0.15 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.87/2.36 ..
% 12.87/2.36
% 12.87/2.36 No.of.Axioms: 346
% 12.87/2.36
% 12.87/2.36 Length.of.Defs: 0
% 12.87/2.36
% 12.87/2.36 Contains.Choice.Funs: false
% 12.87/2.36 ........................................................
% 12.87/2.36
% 12.87/2.36 ********************************
% 12.87/2.36 * All subproblems solved! *
% 12.87/2.36 ********************************
% 12.87/2.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:144,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2392,loop_count:0,foatp_calls:1,translation:fof_full)
% 12.87/2.36
% 12.87/2.36 %**** Beginning of derivation protocol ****
% 12.87/2.36 % SZS output start CNFRefutation
% See solution above
% 12.87/2.37
% 12.87/2.37 %**** End of derivation protocol ****
% 12.87/2.37 %**** no. of clauses in derivation: 2191 ****
% 12.87/2.37 %**** clause counter: 2392 ****
% 12.87/2.37
% 12.87/2.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:144,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2392,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------