%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP108^1 : 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 : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:24:08 AM UTC 2026
% Result : Theorem 15.69s 2.88s
% Output : CNFRefutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 166
% Syntax : Number of formulae : 1640 ( 696 unt; 0 typ; 0 def)
% Number of atoms : 11644 (5211 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 30874 (2307 ~;3064 |; 27 &;25077 @)
% ( 0 <=>; 399 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 89 ( 89 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 55 usr; 15 con; 0-3 aty)
% Number of variables : 3372 ( 64 ^;3300 !; 8 ?;3372 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_int,type,
int: $tType ).
thf(tp_partia1833973666xt_a_b,type,
partia1833973666xt_a_b: $tType ).
thf(tp_product_prod_a_a,type,
product_prod_a_a: $tType ).
thf(tp_set_a,type,
set_a: $tType ).
thf(tp_a_inv_a_b,type,
a_inv_a_b: partia1833973666xt_a_b > a > a ).
thf(tp_a_l_coset_a_b,type,
a_l_coset_a_b: partia1833973666xt_a_b > a > set_a > set_a ).
thf(tp_a_minus_a_b,type,
a_minus_a_b: partia1833973666xt_a_b > a > a > a ).
thf(tp_add_a_b,type,
add_a_b: partia1833973666xt_a_b > a > a > a ).
thf(tp_add_pow_a_b_int,type,
add_pow_a_b_int: partia1833973666xt_a_b > int > a > a ).
thf(tp_additi2104487374up_a_b,type,
additi2104487374up_a_b: set_a > partia1833973666xt_a_b > $o ).
thf(tp_bot_bot_set_a,type,
bot_bot_set_a: set_a ).
thf(tp_collect_a,type,
collect_a: ( a > $o ) > set_a ).
thf(tp_locali1648887798ac_a_b,type,
locali1648887798ac_a_b: partia1833973666xt_a_b > set_a > $o ).
thf(tp_locali425460998xt_a_b,type,
locali425460998xt_a_b: partia1833973666xt_a_b > set_a > $o ).
thf(tp_locali807230110ng_a_b,type,
locali807230110ng_a_b: partia1833973666xt_a_b > set_a > $o ).
thf(tp_locali880295127ng_a_b,type,
locali880295127ng_a_b: partia1833973666xt_a_b > set_a > $o ).
thf(tp_member_a,type,
member_a: a > set_a > $o ).
thf(tp_minus_minus_int,type,
minus_minus_int: int > int > int ).
thf(tp_minus_minus_set_a,type,
minus_minus_set_a: set_a > set_a > set_a ).
thf(tp_mult_a_ring_ext_a_b,type,
mult_a_ring_ext_a_b: partia1833973666xt_a_b > a > a > a ).
thf(tp_ord_less_eq_int,type,
ord_less_eq_int: int > int > $o ).
thf(tp_ord_less_eq_set_a,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(tp_partia1066395285xt_a_b,type,
partia1066395285xt_a_b: partia1833973666xt_a_b > set_a ).
thf(tp_plus_plus_int,type,
plus_plus_int: int > int > int ).
thf(tp_product_fst_a_a,type,
product_fst_a_a: product_prod_a_a > a ).
thf(tp_product_snd_a_a,type,
product_snd_a_a: product_prod_a_a > a ).
thf(tp_r,type,
r: partia1833973666xt_a_b ).
thf(tp_r2,type,
r2: a ).
thf(tp_r3,type,
r3: a ).
thf(tp_s,type,
s: set_a ).
thf(tp_s2,type,
s2: a ).
thf(tp_s3,type,
s3: a ).
thf(tp_sK10_X3,type,
sK10_X3: a > a ).
thf(tp_sK11_X3,type,
sK11_X3: ( a > a > $o ) > a ).
thf(tp_sK12_SY249,type,
sK12_SY249: ( a > a > $o ) > a ).
thf(tp_sK13_SY364,type,
sK13_SY364: set_a > a ).
thf(tp_sK14_SY365,type,
sK14_SY365: ( a > $o ) > a ).
thf(tp_sK15_SY366,type,
sK15_SY366: ( a > $o ) > a ).
thf(tp_sK16_SY428,type,
sK16_SY428: set_a > set_a > a ).
thf(tp_sK17_SY373,type,
sK17_SY373: set_a > a ).
thf(tp_sK18_SY373,type,
sK18_SY373: a > set_a > a ).
thf(tp_sK1_Y2,type,
sK1_Y2: set_a > a ).
thf(tp_sK2_X3,type,
sK2_X3: set_a > set_a > a ).
thf(tp_sK3_X3,type,
sK3_X3: set_a > a ).
thf(tp_sK4_SY248,type,
sK4_SY248: set_a > a ).
thf(tp_sK5_X3,type,
sK5_X3: set_a > a ).
thf(tp_sK6_T2,type,
sK6_T2: a ).
thf(tp_sK7_T,type,
sK7_T: a ).
thf(tp_sK8_X3,type,
sK8_X3: a > a ).
thf(tp_sK9_X3,type,
sK9_X3: a > a ).
thf(tp_semiring_a_b,type,
semiring_a_b: partia1833973666xt_a_b > $o ).
thf(tp_set_add_a_b,type,
set_add_a_b: partia1833973666xt_a_b > set_a > set_a > set_a ).
thf(tp_t,type,
t: a ).
thf(tp_t2,type,
t2: a ).
thf(tp_uminus_uminus_int,type,
uminus_uminus_int: int > int ).
thf(tp_uminus_uminus_set_a,type,
uminus_uminus_set_a: set_a > set_a ).
thf(tp_x,type,
x: product_prod_a_a ).
thf(tp_y,type,
y: product_prod_a_a ).
thf(tp_zero_a_b,type,
zero_a_b: partia1833973666xt_a_b > a ).
thf(1,axiom,
( ord_less_eq_set_a
= ( ^ [A4: set_a,B4: set_a] :
! [X2: a] :
( ( member_a @ X2 @ A4 )
=> ( member_a @ X2 @ B4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_subset__eq) ).
thf(3,axiom,
! [A2: set_a,B3: set_a,C: a] :
( ( ord_less_eq_set_a @ A2 @ B3 )
=> ( ( member_a @ C @ A2 )
=> ( member_a @ C @ B3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_subsetD) ).
thf(4,axiom,
! [A2: set_a,B3: set_a,X: a] :
( ( ord_less_eq_set_a @ A2 @ B3 )
=> ( ( member_a @ X @ A2 )
=> ( member_a @ X @ B3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_in__mono) ).
thf(5,axiom,
! [A2: set_a] :
( ( ? [X2: a] : ( member_a @ X2 @ A2 ) )
= ( A2 != bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_ex__in__conv) ).
thf(6,axiom,
! [A2: set_a] :
( ! [Y2: a] :
~ ( member_a @ Y2 @ A2 )
=> ( A2 = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_equals0I) ).
thf(7,axiom,
! [A2: set_a,A: a] :
( ( A2 = bot_bot_set_a )
=> ~ ( member_a @ A @ A2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_equals0D) ).
thf(8,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_emptyE) ).
thf(9,axiom,
! [A2: set_a] :
( ( minus_minus_set_a @ A2 @ A2 )
= bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_Diff__cancel) ).
thf(10,axiom,
! [A2: set_a] :
( ( minus_minus_set_a @ bot_bot_set_a @ A2 )
= bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_empty__Diff) ).
thf(11,axiom,
! [A2: set_a] :
( ( minus_minus_set_a @ A2 @ bot_bot_set_a )
= A2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_Diff__empty) ).
thf(12,axiom,
! [A2: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_empty__subsetI) ).
thf(13,axiom,
! [A2: set_a] :
( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
= ( A2 = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_subset__empty) ).
thf(17,axiom,
! [A2: set_a,B3: set_a] :
( ! [X3: a] :
( ( member_a @ X3 @ A2 )
=> ( member_a @ X3 @ B3 ) )
=> ( ord_less_eq_set_a @ A2 @ B3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_subsetI) ).
thf(18,axiom,
! [P: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ P ) )
= ( ! [X2: a] :
~ ( P @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_empty__Collect__eq) ).
thf(19,axiom,
! [P: a > $o] :
( ( ( collect_a @ P )
= bot_bot_set_a )
= ( ! [X2: a] :
~ ( P @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_Collect__empty__eq) ).
thf(20,axiom,
! [A2: set_a] :
( ( ! [X2: a] :
~ ( member_a @ X2 @ A2 ) )
= ( A2 = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_all__not__in__conv) ).
thf(21,axiom,
! [C: a] :
~ ( member_a @ C @ bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_empty__iff) ).
thf(23,axiom,
! [H: set_a,K2: set_a] :
( ( additi2104487374up_a_b @ H @ r )
=> ( ( additi2104487374up_a_b @ K2 @ r )
=> ( additi2104487374up_a_b @ ( set_add_a_b @ r @ H @ K2 ) @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_add__additive__subgroups) ).
thf(24,axiom,
! [A2: set_a,B3: set_a] :
( ( ord_less_eq_set_a @ A2 @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ord_less_eq_set_a @ B3 @ ( partia1066395285xt_a_b @ r ) )
=> ( ord_less_eq_set_a @ ( set_add_a_b @ r @ A2 @ B3 ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_set__add__closed) ).
thf(25,axiom,
! [H: set_a,K2: set_a] :
( ( ord_less_eq_set_a @ H @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ord_less_eq_set_a @ K2 @ ( partia1066395285xt_a_b @ r ) )
=> ( ord_less_eq_set_a @ ( set_add_a_b @ r @ H @ K2 ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_setadd__subset__G) ).
thf(27,axiom,
( ( partia1066395285xt_a_b @ r )
!= bot_bot_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_carrier__not__empty) ).
thf(30,axiom,
! [H: set_a] :
( ( ord_less_eq_set_a @ H @ ( partia1066395285xt_a_b @ r ) )
=> ( ( H != bot_bot_set_a )
=> ( ! [X3: a] :
( ( member_a @ X3 @ H )
=> ( member_a @ ( a_inv_a_b @ r @ X3 ) @ H ) )
=> ( ! [X3: a] :
( ( member_a @ X3 @ H )
=> ! [Xa: a] :
( ( member_a @ Xa @ H )
=> ( member_a @ ( add_a_b @ r @ X3 @ Xa ) @ H ) ) )
=> ( member_a @ ( zero_a_b @ r ) @ H ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_add_Oone__in__subset) ).
thf(101,axiom,
! [M: partia1833973666xt_a_b,S2: set_a] :
( ( locali425460998xt_a_b @ M @ S2 )
=> ( ord_less_eq_set_a @ S2 @ ( partia1066395285xt_a_b @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_Localization__Mirabelle__afvchqjmgj_Osubmonoid_Osubset) ).
thf(102,axiom,
ord_less_eq_set_a @ s @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_subset) ).
thf(103,axiom,
! [X: a,I: int,J: int] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ ( plus_plus_int @ I @ J ) @ X )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) @ ( add_pow_a_b_int @ r @ J @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_add_Oint__pow__mult) ).
thf(104,axiom,
! [X: a,I: int] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ ( uminus_uminus_int @ I ) @ X )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_add_Oint__pow__neg) ).
thf(105,axiom,
! [X: a,N: int,M2: int] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ ( minus_minus_int @ N @ M2 ) @ X )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ N @ X ) @ ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ M2 @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_add_Oint__pow__diff) ).
thf(106,axiom,
! [R: partia1833973666xt_a_b,X: a,Y: a,Z: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
=> ( ( mult_a_ring_ext_a_b @ R @ ( add_a_b @ R @ X @ Y ) @ Z )
= ( add_a_b @ R @ ( mult_a_ring_ext_a_b @ R @ X @ Z ) @ ( mult_a_ring_ext_a_b @ R @ Y @ Z ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_semiring_Ol__distr) ).
thf(107,axiom,
! [R: partia1833973666xt_a_b] :
( ( semiring_a_b @ R )
=> ( member_a @ ( zero_a_b @ R ) @ ( partia1066395285xt_a_b @ R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_semiring_Osemiring__simprules_I2_J) ).
thf(108,axiom,
! [R: partia1833973666xt_a_b,X: a,Y: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
=> ( member_a @ ( add_a_b @ R @ X @ Y ) @ ( partia1066395285xt_a_b @ R ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_semiring_Osemiring__simprules_I1_J) ).
thf(109,axiom,
! [R: partia1833973666xt_a_b,X: a,Y: a,Z: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
=> ( ( add_a_b @ R @ ( add_a_b @ R @ X @ Y ) @ Z )
= ( add_a_b @ R @ X @ ( add_a_b @ R @ Y @ Z ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_semiring_Osemiring__simprules_I5_J) ).
thf(110,axiom,
! [R: partia1833973666xt_a_b,X: a,Y: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
=> ( ( add_a_b @ R @ X @ Y )
= ( add_a_b @ R @ Y @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_semiring_Osemiring__simprules_I7_J) ).
thf(111,axiom,
! [R: partia1833973666xt_a_b,X: a,Y: a,Z: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
=> ( ( add_a_b @ R @ X @ ( add_a_b @ R @ Y @ Z ) )
= ( add_a_b @ R @ Y @ ( add_a_b @ R @ X @ Z ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_semiring_Osemiring__simprules_I12_J) ).
thf(112,axiom,
! [R: partia1833973666xt_a_b,X: a,Y: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
=> ( member_a @ ( mult_a_ring_ext_a_b @ R @ X @ Y ) @ ( partia1066395285xt_a_b @ R ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_semiring_Osemiring__simprules_I3_J) ).
thf(113,axiom,
! [R: partia1833973666xt_a_b,X: a,Y: a,Z: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
=> ( ( mult_a_ring_ext_a_b @ R @ ( mult_a_ring_ext_a_b @ R @ X @ Y ) @ Z )
= ( mult_a_ring_ext_a_b @ R @ X @ ( mult_a_ring_ext_a_b @ R @ Y @ Z ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_semiring_Osemiring__simprules_I8_J) ).
thf(114,axiom,
( a_minus_a_b
= ( ^ [R2: partia1833973666xt_a_b,X2: a,Y5: a] : ( add_a_b @ R2 @ X2 @ ( a_inv_a_b @ R2 @ Y5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_a__minus__def) ).
thf(115,axiom,
! [M: partia1833973666xt_a_b,S2: set_a,X: a,Y: a] :
( ( locali425460998xt_a_b @ M @ S2 )
=> ( ( member_a @ X @ S2 )
=> ( ( member_a @ Y @ S2 )
=> ( member_a @ ( mult_a_ring_ext_a_b @ M @ X @ Y ) @ S2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_Localization__Mirabelle__afvchqjmgj_Osubmonoid_Om__closed) ).
thf(116,axiom,
! [R: partia1833973666xt_a_b,S2: set_a] :
( ( locali1648887798ac_a_b @ R @ S2 )
=> ( locali807230110ng_a_b @ R @ S2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_eq__obj__rng__of__frac_Oaxioms_I2_J) ).
thf(117,axiom,
! [R: partia1833973666xt_a_b,S2: set_a] :
( ( locali880295127ng_a_b @ R @ S2 )
=> ( locali425460998xt_a_b @ R @ S2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_mult__submonoid__of__rng_Oaxioms_I2_J) ).
thf(118,axiom,
! [R: partia1833973666xt_a_b,S2: set_a] :
( ( locali807230110ng_a_b @ R @ S2 )
=> ( locali880295127ng_a_b @ R @ S2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_mult__submonoid__of__crng_Oaxioms_I2_J) ).
thf(119,axiom,
! [M: partia1833973666xt_a_b,S2: set_a] :
( ( locali425460998xt_a_b @ M @ S2 )
=> ( locali425460998xt_a_b @ M @ S2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_Localization__Mirabelle__afvchqjmgj_Osubmonoid_Ois__submonoid) ).
thf(120,axiom,
! [Z: int] :
( ( add_pow_a_b_int @ r @ Z @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_add_Oint__pow__one) ).
thf(121,axiom,
! [X: a,I: int] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( add_pow_a_b_int @ r @ I @ X ) @ ( partia1066395285xt_a_b @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_add_Oint__pow__closed) ).
thf(122,axiom,
! [X: a,Y: a,I: int] :
( ( ( add_a_b @ r @ X @ Y )
= ( add_a_b @ r @ Y @ X ) )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ I @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) @ ( add_pow_a_b_int @ r @ I @ Y ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_add_Oint__pow__mult__distrib) ).
thf(123,axiom,
! [X: a,Y: a,I: int] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ I @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) @ ( add_pow_a_b_int @ r @ I @ Y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_add_Oint__pow__distrib) ).
thf(124,axiom,
! [A: a,B: a,K: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ ( add_pow_a_b_int @ r @ K @ B ) )
= ( add_pow_a_b_int @ r @ K @ ( mult_a_ring_ext_a_b @ r @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_add__pow__rdistr__int) ).
thf(125,axiom,
! [A: a,B: a,K: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( add_pow_a_b_int @ r @ K @ A ) @ B )
= ( add_pow_a_b_int @ r @ K @ ( mult_a_ring_ext_a_b @ r @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_add__pow__ldistr__int) ).
thf(126,axiom,
! [R: partia1833973666xt_a_b,X: a,Y: a,Z: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
=> ( ( mult_a_ring_ext_a_b @ R @ Z @ ( add_a_b @ R @ X @ Y ) )
= ( add_a_b @ R @ ( mult_a_ring_ext_a_b @ R @ Z @ X ) @ ( mult_a_ring_ext_a_b @ R @ Z @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_semiring_Or__distr) ).
thf(127,axiom,
! [R: partia1833973666xt_a_b,X: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( mult_a_ring_ext_a_b @ R @ X @ ( zero_a_b @ R ) )
= ( zero_a_b @ R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_semiring_Or__null) ).
thf(128,axiom,
! [R: partia1833973666xt_a_b,X: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( mult_a_ring_ext_a_b @ R @ ( zero_a_b @ R ) @ X )
= ( zero_a_b @ R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_semiring_Ol__null) ).
thf(129,axiom,
! [R: partia1833973666xt_a_b,X: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( add_a_b @ R @ ( zero_a_b @ R ) @ X )
= X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_semiring_Osemiring__simprules_I6_J) ).
thf(130,axiom,
! [R: partia1833973666xt_a_b,X: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( add_a_b @ R @ X @ ( zero_a_b @ R ) )
= X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_semiring_Osemiring__simprules_I11_J) ).
thf(131,axiom,
! [X: a,I: int] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ I @ ( a_inv_a_b @ r @ X ) )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_add_Oint__pow__inv) ).
thf(132,axiom,
locali425460998xt_a_b @ r @ s,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_submonoid__axioms) ).
thf(133,axiom,
( ( ^ [Y4: product_prod_a_a,Z2: product_prod_a_a] : ( Y4 = Z2 ) )
= ( ^ [S: product_prod_a_a,T3: product_prod_a_a] :
( ( ( product_fst_a_a @ S )
= ( product_fst_a_a @ T3 ) )
& ( ( product_snd_a_a @ S )
= ( product_snd_a_a @ T3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_prod__eq__iff) ).
thf(134,axiom,
locali807230110ng_a_b @ r @ s,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_mult__submonoid__of__crng__axioms) ).
thf(135,axiom,
locali880295127ng_a_b @ r @ s,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_mult__submonoid__of__rng__axioms) ).
thf(136,axiom,
! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( a_inv_a_b @ r @ X )
= ( zero_a_b @ r ) )
= ( X
= ( zero_a_b @ r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_add_Oinv__eq__1__iff) ).
thf(137,axiom,
! [X: a,A: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ X @ A )
= X )
= ( A
= ( zero_a_b @ r ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_add_Ol__cancel__one) ).
thf(138,axiom,
! [X: a,A: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( X
= ( add_a_b @ r @ X @ A ) )
= ( A
= ( zero_a_b @ r ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_add_Ol__cancel__one_H) ).
thf(139,axiom,
! [X: a,A: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ A @ X )
= X )
= ( A
= ( zero_a_b @ r ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_add_Or__cancel__one) ).
thf(140,axiom,
! [X: a,A: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( X
= ( add_a_b @ r @ A @ X ) )
= ( A
= ( zero_a_b @ r ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_add_Or__cancel__one_H) ).
thf(141,axiom,
! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( zero_a_b @ r ) @ X )
= X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_l__zero) ).
thf(142,axiom,
! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ X @ ( zero_a_b @ r ) )
= X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_r__zero) ).
thf(143,axiom,
! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( zero_a_b @ r ) @ X )
= ( zero_a_b @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_l__null) ).
thf(144,axiom,
! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ X @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_r__null) ).
thf(145,axiom,
! [X: a,Y: a] :
( ( member_a @ X @ s )
=> ( ( member_a @ Y @ s )
=> ( member_a @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_m__closed) ).
thf(146,axiom,
( ( a_inv_a_b @ r @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_local_Ominus__zero) ).
thf(147,axiom,
! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( a_inv_a_b @ r @ X ) @ ( partia1066395285xt_a_b @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_add_Oinv__closed) ).
thf(148,axiom,
! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ ( a_inv_a_b @ r @ X ) )
= X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_local_Ominus__minus) ).
thf(149,axiom,
member_a @ ( zero_a_b @ r ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_zero__closed) ).
thf(150,axiom,
~ ! [T2: a] :
( ( member_a @ T2 @ s )
=> ( ( mult_a_ring_ext_a_b @ r @ T2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
!= ( zero_a_b @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062t_H_O_A_092_060lbrakk_062t_H_A_092_060in_062_AS_059_At_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Ar_H_A_092_060ominus_062_As_H_A_092_060otimes_062_Afst_Ay_H_J_A_061_A_092_060zero_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(151,axiom,
~ ! [T: a] :
( ( member_a @ T @ s )
=> ( ( mult_a_ring_ext_a_b @ r @ T @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
!= ( zero_a_b @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062t_O_A_092_060lbrakk_062t_A_092_060in_062_AS_059_At_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_A_092_060ominus_062_As_A_092_060otimes_062_Afst_Ax_H_J_A_061_A_092_060zero_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(152,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ ( add_a_b @ r @ A @ B ) )
= ( a_minus_a_b @ r @ ( a_inv_a_b @ r @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_inv__add) ).
thf(153,axiom,
! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ X )
= ( zero_a_b @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_l__neg) ).
thf(154,axiom,
! [Y: a,X: a] :
( ( ( add_a_b @ r @ Y @ X )
= ( zero_a_b @ r ) )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ X )
= Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_minus__equality) ).
thf(155,axiom,
! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ X @ ( a_inv_a_b @ r @ X ) )
= ( zero_a_b @ r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_r__neg) ).
thf(156,axiom,
! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ X @ Y )
= ( zero_a_b @ r ) )
=> ( X
= ( a_inv_a_b @ r @ Y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_sum__zero__eq__neg) ).
thf(157,axiom,
locali1648887798ac_a_b @ r @ s,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_eq__obj__rng__of__frac__axioms) ).
thf(158,axiom,
! [X: a,Y: a,Z: a] :
( ( ( add_a_b @ r @ X @ Y )
= Z )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ Z )
= Y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_a__transpose__inv) ).
thf(159,axiom,
! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ Y ) @ ( a_inv_a_b @ r @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_add_Oinv__mult__group) ).
thf(160,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( A
= ( add_a_b @ r @ ( a_inv_a_b @ r @ B ) @ C ) )
= ( C
= ( add_a_b @ r @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add_Oinv__solve__left) ).
thf(161,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ B ) @ C )
= A )
= ( C
= ( add_a_b @ r @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_add_Oinv__solve__left_H) ).
thf(162,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( A
= ( add_a_b @ r @ B @ ( a_inv_a_b @ r @ C ) ) )
= ( B
= ( add_a_b @ r @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_add_Oinv__solve__right) ).
thf(163,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ B @ ( a_inv_a_b @ r @ C ) )
= A )
= ( B
= ( add_a_b @ r @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_add_Oinv__solve__right_H) ).
thf(164,axiom,
! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ ( a_inv_a_b @ r @ Y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_local_Ominus__add) ).
thf(165,axiom,
! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ ( add_a_b @ r @ X @ Y ) )
= Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_r__neg1) ).
thf(166,axiom,
! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ X @ ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ Y ) )
= Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_r__neg2) ).
thf(167,axiom,
! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( a_inv_a_b @ r @ X ) @ Y )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_l__minus) ).
thf(168,axiom,
! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ X @ ( a_inv_a_b @ r @ Y ) )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_r__minus) ).
thf(169,axiom,
! [X: a,Y: a] :
( ( ( add_a_b @ r @ X @ Y )
= ( zero_a_b @ r ) )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ Y @ X )
= ( zero_a_b @ r ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add_Oinv__comm) ).
thf(170,axiom,
! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ? [X3: a] :
( ( member_a @ X3 @ ( partia1066395285xt_a_b @ r ) )
& ( ( add_a_b @ r @ X3 @ X )
= ( zero_a_b @ r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_add_Ol__inv__ex) ).
thf(171,axiom,
! [U: a] :
( ( member_a @ U @ ( partia1066395285xt_a_b @ r ) )
=> ( ! [X3: a] :
( ( member_a @ X3 @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ U @ X3 )
= X3 ) )
=> ( U
= ( zero_a_b @ r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_add_Oone__unique) ).
thf(172,axiom,
! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ? [X3: a] :
( ( member_a @ X3 @ ( partia1066395285xt_a_b @ r ) )
& ( ( add_a_b @ r @ X @ X3 )
= ( zero_a_b @ r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_add_Or__inv__ex) ).
thf(173,axiom,
! [Y: a,X: a,Y3: a] :
( ( ( add_a_b @ r @ Y @ X )
= ( zero_a_b @ r ) )
=> ( ( ( add_a_b @ r @ X @ Y3 )
= ( zero_a_b @ r ) )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y3 @ ( partia1066395285xt_a_b @ r ) )
=> ( Y = Y3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_local_Ominus__unique) ).
thf(174,axiom,
! [Prod: product_prod_a_a,Prod2: product_prod_a_a] :
( ( ( ( product_fst_a_a @ Prod )
= ( product_fst_a_a @ Prod2 ) )
& ( ( product_snd_a_a @ Prod )
= ( product_snd_a_a @ Prod2 ) ) )
=> ( Prod = Prod2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_prod_Oexpand) ).
thf(175,axiom,
! [P: a > a > $o,P2: product_prod_a_a] :
( ( P @ ( product_snd_a_a @ P2 ) @ ( product_fst_a_a @ P2 ) )
=> ~ ! [X3: a,Y2: a] :
~ ( P @ Y2 @ X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_exE__realizer_H) ).
thf(176,axiom,
! [P2: product_prod_a_a,Q2: product_prod_a_a] :
( ( ( product_fst_a_a @ P2 )
= ( product_fst_a_a @ Q2 ) )
=> ( ( ( product_snd_a_a @ P2 )
= ( product_snd_a_a @ Q2 ) )
=> ( P2 = Q2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_prod__eqI) ).
thf(177,axiom,
! [X: a,Y: a] :
( ( a_minus_a_b @ r @ X @ Y )
= ( add_a_b @ r @ X @ ( a_inv_a_b @ r @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_minus__eq) ).
thf(178,axiom,
semiring_a_b @ r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_local_Osemiring__axioms) ).
thf(179,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ s,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_f8) ).
thf(180,axiom,
member_a @ t @ s,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_f6) ).
thf(181,axiom,
member_a @ t2 @ s,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_f4) ).
thf(182,axiom,
! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_semiring__simprules_I3_J) ).
thf(183,axiom,
! [X: a,Y: a,Z: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ Y @ X )
= ( add_a_b @ r @ Z @ X ) )
= ( Y = Z ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_local_Oadd_Oright__cancel) ).
thf(184,axiom,
! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( add_a_b @ r @ X @ Y ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_add_Om__closed) ).
thf(185,axiom,
! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( a_minus_a_b @ r @ X @ Y ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_minus__closed) ).
thf(186,axiom,
( ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
= ( zero_a_b @ r ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_f7) ).
thf(187,axiom,
( ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
= ( zero_a_b @ r ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_f5) ).
thf(188,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_f38) ).
thf(189,axiom,
member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_f39) ).
thf(190,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_f37) ).
thf(191,axiom,
( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_f31) ).
thf(192,axiom,
( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52__092_060open_062t_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_J_A_092_060ominus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_J_A_092_060ominus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_092_060close_062) ).
thf(193,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_f14) ).
thf(194,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50__092_060open_062t_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_J_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_J_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_092_060close_062) ).
thf(195,axiom,
( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_f33) ).
thf(196,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_f30) ).
thf(198,axiom,
! [A2: set_a] :
( ( collect_a
@ ^ [X2: a] : ( member_a @ X2 @ A2 ) )
= A2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(199,axiom,
! [A: a,P: a > $o] :
( ( member_a @ A @ ( collect_a @ P ) )
= ( P @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(200,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_f29) ).
thf(201,axiom,
( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ t ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_f26) ).
thf(202,axiom,
( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_f32) ).
thf(203,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_f25) ).
thf(204,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_f12) ).
thf(205,axiom,
( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39__092_060open_062t_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_J_A_092_060ominus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_061_At_H_A_092_060otimes_062_As_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_At_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_At_H_A_092_060otimes_062_As_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_At_A_092_060otimes_062_A_Is_A_092_060otimes_062_Afst_Ax_H_J_092_060close_062) ).
thf(206,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_f13) ).
thf(207,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_f36) ).
thf(208,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_f34) ).
thf(209,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_f23) ).
thf(210,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34__092_060open_062t_A_092_060otimes_062_As_A_092_060otimes_062_Asnd_Ax_H_A_092_060in_062_Acarrier_AR_092_060close_062) ).
thf(211,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_f9) ).
thf(212,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_f24) ).
thf(213,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_f16) ).
thf(214,axiom,
( ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30__092_060open_062t_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Ar_H_A_092_060ominus_062_As_H_A_092_060otimes_062_Afst_Ay_H_J_A_061_At_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_At_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Afst_Ay_H_J_092_060close_062) ).
thf(215,axiom,
( ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29__092_060open_062t_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_A_092_060ominus_062_As_A_092_060otimes_062_Afst_Ax_H_J_A_061_At_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_At_A_092_060otimes_062_A_Is_A_092_060otimes_062_Afst_Ax_H_J_092_060close_062) ).
thf(216,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_f35) ).
thf(217,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_f27) ).
thf(218,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_f10) ).
thf(219,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_f11) ).
thf(220,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_f28) ).
thf(221,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23__092_060open_062snd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060in_062_Acarrier_AR_092_060close_062) ).
thf(222,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_f15) ).
thf(223,axiom,
( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21__092_060open_062_092_060lbrakk_062snd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060in_062_Acarrier_AR_059_Asnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_A_092_060in_062_Acarrier_AR_059_At_A_092_060otimes_062_At_H_A_092_060in_062_Acarrier_AR_092_060rbrakk_062_A_092_060Longrightarrow_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060oplus_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_092_060close_062) ).
thf(224,axiom,
member_a @ ( product_fst_a_a @ x ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_f22) ).
thf(225,axiom,
( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_f40) ).
thf(226,axiom,
member_a @ ( product_snd_a_a @ y ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_f21) ).
thf(227,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ C @ A ) @ B )
= ( a_minus_a_b @ r @ C @ ( add_a_b @ r @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_right__inv__add) ).
thf(228,axiom,
! [A: a,B: a,C: a,D: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ D @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ A @ C ) @ B ) @ D )
= ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ ( add_a_b @ r @ A @ B ) @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_four__elem__comm) ).
thf(229,axiom,
! [X: a,Y: a,Z: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ Z @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ Z @ X ) @ ( mult_a_ring_ext_a_b @ r @ Z @ Y ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_r__distr) ).
thf(230,axiom,
! [X: a,Y: a,Z: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( add_a_b @ r @ X @ Y ) @ Z )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X @ Z ) @ ( mult_a_ring_ext_a_b @ r @ Y @ Z ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_l__distr) ).
thf(231,axiom,
member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_f42) ).
thf(232,axiom,
member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_f41) ).
thf(233,axiom,
member_a @ s2 @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_f19) ).
thf(234,axiom,
member_a @ s3 @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_f20) ).
thf(235,axiom,
! [X: a,Y: a,Z: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ X @ ( add_a_b @ r @ Y @ Z ) )
= ( add_a_b @ r @ Y @ ( add_a_b @ r @ X @ Z ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_add_Om__lcomm) ).
thf(236,axiom,
! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ X @ Y )
= ( add_a_b @ r @ Y @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_add_Om__comm) ).
thf(237,axiom,
! [X: a,Y: a,Z: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( add_a_b @ r @ X @ Y ) @ Z )
= ( add_a_b @ r @ X @ ( add_a_b @ r @ Y @ Z ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_add_Om__assoc) ).
thf(238,axiom,
! [X: a,Y: a,Z: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ X @ ( mult_a_ring_ext_a_b @ r @ Y @ Z ) )
= ( mult_a_ring_ext_a_b @ r @ Y @ ( mult_a_ring_ext_a_b @ r @ X @ Z ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_m__lcomm) ).
thf(239,axiom,
! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ X @ Y )
= ( mult_a_ring_ext_a_b @ r @ Y @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_m__comm) ).
thf(240,axiom,
! [X: a,Y: a,Z: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) @ Z )
= ( mult_a_ring_ext_a_b @ r @ X @ ( mult_a_ring_ext_a_b @ r @ Y @ Z ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_m__assoc) ).
thf(241,axiom,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( a_minus_a_b @ r @ C @ A )
= ( a_minus_a_b @ r @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_local_Oright__minus__eq) ).
thf(242,axiom,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( add_a_b @ r @ C @ A )
= ( add_a_b @ r @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_right__add__eq) ).
thf(243,axiom,
member_a @ t2 @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_f17) ).
thf(244,axiom,
member_a @ t @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_f18) ).
thf(245,conjecture,
( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(246,negated_conjecture,
( ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[245]) ).
thf(247,plain,
( ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[246]) ).
thf(248,plain,
( ( ord_less_eq_set_a
= ( ^ [A4: set_a,B4: set_a] :
! [X2: a] :
( ( member_a @ X2 @ A4 )
=> ( member_a @ X2 @ B4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(249,plain,
( ( ! [A2: set_a,B3: set_a,C: a] :
( ( ord_less_eq_set_a @ A2 @ B3 )
=> ( ( member_a @ C @ A2 )
=> ( member_a @ C @ B3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(250,plain,
( ( ! [A2: set_a,B3: set_a,X: a] :
( ( ord_less_eq_set_a @ A2 @ B3 )
=> ( ( member_a @ X @ A2 )
=> ( member_a @ X @ B3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(251,plain,
( ( ! [A2: set_a] :
( ( ? [X2: a] : ( member_a @ X2 @ A2 ) )
= ( A2 != bot_bot_set_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(252,plain,
( ( ! [A2: set_a] :
( ! [Y2: a] :
~ ( member_a @ Y2 @ A2 )
=> ( A2 = bot_bot_set_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(253,plain,
( ( ! [A2: set_a,A: a] :
( ( A2 = bot_bot_set_a )
=> ~ ( member_a @ A @ A2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(254,plain,
( ( ! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(255,plain,
( ( ! [A2: set_a] :
( ( minus_minus_set_a @ A2 @ A2 )
= bot_bot_set_a ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(256,plain,
( ( ! [A2: set_a] :
( ( minus_minus_set_a @ bot_bot_set_a @ A2 )
= bot_bot_set_a ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(257,plain,
( ( ! [A2: set_a] :
( ( minus_minus_set_a @ A2 @ bot_bot_set_a )
= A2 ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(258,plain,
( ( ! [A2: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A2 ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(259,plain,
( ( ! [A2: set_a] :
( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
= ( A2 = bot_bot_set_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(260,plain,
( ( ! [A2: set_a,B3: set_a] :
( ! [X3: a] :
( ( member_a @ X3 @ A2 )
=> ( member_a @ X3 @ B3 ) )
=> ( ord_less_eq_set_a @ A2 @ B3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(261,plain,
( ( ! [P: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ P ) )
= ( ! [X2: a] :
~ ( P @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(262,plain,
( ( ! [P: a > $o] :
( ( ( collect_a @ P )
= bot_bot_set_a )
= ( ! [X2: a] :
~ ( P @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(263,plain,
( ( ! [A2: set_a] :
( ( ! [X2: a] :
~ ( member_a @ X2 @ A2 ) )
= ( A2 = bot_bot_set_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(264,plain,
( ( ! [C: a] :
~ ( member_a @ C @ bot_bot_set_a ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(265,plain,
( ( ! [A2: set_a,B3: set_a] :
( ( ord_less_eq_set_a @ A2 @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ord_less_eq_set_a @ B3 @ ( partia1066395285xt_a_b @ r ) )
=> ( ord_less_eq_set_a @ ( set_add_a_b @ r @ A2 @ B3 ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(266,plain,
( ( ! [H: set_a,K2: set_a] :
( ( ord_less_eq_set_a @ H @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ord_less_eq_set_a @ K2 @ ( partia1066395285xt_a_b @ r ) )
=> ( ord_less_eq_set_a @ ( set_add_a_b @ r @ H @ K2 ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(267,plain,
( ( ! [H: set_a] :
( ( ord_less_eq_set_a @ H @ ( partia1066395285xt_a_b @ r ) )
=> ( ( H != bot_bot_set_a )
=> ( ! [X3: a] :
( ( member_a @ X3 @ H )
=> ( member_a @ ( a_inv_a_b @ r @ X3 ) @ H ) )
=> ( ! [X3: a] :
( ( member_a @ X3 @ H )
=> ! [Xa: a] :
( ( member_a @ Xa @ H )
=> ( member_a @ ( add_a_b @ r @ X3 @ Xa ) @ H ) ) )
=> ( member_a @ ( zero_a_b @ r ) @ H ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(268,plain,
( ( ! [M: partia1833973666xt_a_b,S2: set_a] :
( ( locali425460998xt_a_b @ M @ S2 )
=> ( ord_less_eq_set_a @ S2 @ ( partia1066395285xt_a_b @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(269,plain,
( ( ord_less_eq_set_a @ s @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(270,plain,
( ( ! [X: a,I: int,J: int] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ ( plus_plus_int @ I @ J ) @ X )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) @ ( add_pow_a_b_int @ r @ J @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(271,plain,
( ( ! [X: a,I: int] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ ( uminus_uminus_int @ I ) @ X )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(272,plain,
( ( ! [X: a,N: int,M2: int] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ ( minus_minus_int @ N @ M2 ) @ X )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ N @ X ) @ ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ M2 @ X ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(273,plain,
( ( ! [R: partia1833973666xt_a_b,X: a,Y: a,Z: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
=> ( ( mult_a_ring_ext_a_b @ R @ ( add_a_b @ R @ X @ Y ) @ Z )
= ( add_a_b @ R @ ( mult_a_ring_ext_a_b @ R @ X @ Z ) @ ( mult_a_ring_ext_a_b @ R @ Y @ Z ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(274,plain,
( ( ! [R: partia1833973666xt_a_b] :
( ( semiring_a_b @ R )
=> ( member_a @ ( zero_a_b @ R ) @ ( partia1066395285xt_a_b @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(275,plain,
( ( ! [R: partia1833973666xt_a_b,X: a,Y: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
=> ( member_a @ ( add_a_b @ R @ X @ Y ) @ ( partia1066395285xt_a_b @ R ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(276,plain,
( ( ! [R: partia1833973666xt_a_b,X: a,Y: a,Z: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
=> ( ( add_a_b @ R @ ( add_a_b @ R @ X @ Y ) @ Z )
= ( add_a_b @ R @ X @ ( add_a_b @ R @ Y @ Z ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(277,plain,
( ( ! [R: partia1833973666xt_a_b,X: a,Y: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
=> ( ( add_a_b @ R @ X @ Y )
= ( add_a_b @ R @ Y @ X ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(278,plain,
( ( ! [R: partia1833973666xt_a_b,X: a,Y: a,Z: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
=> ( ( add_a_b @ R @ X @ ( add_a_b @ R @ Y @ Z ) )
= ( add_a_b @ R @ Y @ ( add_a_b @ R @ X @ Z ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(279,plain,
( ( ! [R: partia1833973666xt_a_b,X: a,Y: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
=> ( member_a @ ( mult_a_ring_ext_a_b @ R @ X @ Y ) @ ( partia1066395285xt_a_b @ R ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(280,plain,
( ( ! [R: partia1833973666xt_a_b,X: a,Y: a,Z: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
=> ( ( mult_a_ring_ext_a_b @ R @ ( mult_a_ring_ext_a_b @ R @ X @ Y ) @ Z )
= ( mult_a_ring_ext_a_b @ R @ X @ ( mult_a_ring_ext_a_b @ R @ Y @ Z ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(281,plain,
( ( ! [R: partia1833973666xt_a_b,S2: set_a] :
( ( locali1648887798ac_a_b @ R @ S2 )
=> ( locali807230110ng_a_b @ R @ S2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(282,plain,
( ( ! [R: partia1833973666xt_a_b,S2: set_a] :
( ( locali880295127ng_a_b @ R @ S2 )
=> ( locali425460998xt_a_b @ R @ S2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(283,plain,
( ( ! [R: partia1833973666xt_a_b,S2: set_a] :
( ( locali807230110ng_a_b @ R @ S2 )
=> ( locali880295127ng_a_b @ R @ S2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(284,plain,
( ( ! [M: partia1833973666xt_a_b,S2: set_a] :
( ( locali425460998xt_a_b @ M @ S2 )
=> ( locali425460998xt_a_b @ M @ S2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(285,plain,
( ( ! [X: a,I: int] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( add_pow_a_b_int @ r @ I @ X ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(286,plain,
( ( ! [X: a,Y: a,I: int] :
( ( ( add_a_b @ r @ X @ Y )
= ( add_a_b @ r @ Y @ X ) )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ I @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) @ ( add_pow_a_b_int @ r @ I @ Y ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(287,plain,
( ( ! [X: a,Y: a,I: int] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ I @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) @ ( add_pow_a_b_int @ r @ I @ Y ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(288,plain,
( ( ! [A: a,B: a,K: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ ( add_pow_a_b_int @ r @ K @ B ) )
= ( add_pow_a_b_int @ r @ K @ ( mult_a_ring_ext_a_b @ r @ A @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(289,plain,
( ( ! [A: a,B: a,K: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( add_pow_a_b_int @ r @ K @ A ) @ B )
= ( add_pow_a_b_int @ r @ K @ ( mult_a_ring_ext_a_b @ r @ A @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(290,plain,
( ( ! [R: partia1833973666xt_a_b,X: a,Y: a,Z: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
=> ( ( mult_a_ring_ext_a_b @ R @ Z @ ( add_a_b @ R @ X @ Y ) )
= ( add_a_b @ R @ ( mult_a_ring_ext_a_b @ R @ Z @ X ) @ ( mult_a_ring_ext_a_b @ R @ Z @ Y ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(291,plain,
( ( ! [R: partia1833973666xt_a_b,X: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( mult_a_ring_ext_a_b @ R @ X @ ( zero_a_b @ R ) )
= ( zero_a_b @ R ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(292,plain,
( ( ! [R: partia1833973666xt_a_b,X: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( mult_a_ring_ext_a_b @ R @ ( zero_a_b @ R ) @ X )
= ( zero_a_b @ R ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(293,plain,
( ( ! [R: partia1833973666xt_a_b,X: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( add_a_b @ R @ ( zero_a_b @ R ) @ X )
= X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(294,plain,
( ( ! [R: partia1833973666xt_a_b,X: a] :
( ( semiring_a_b @ R )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
=> ( ( add_a_b @ R @ X @ ( zero_a_b @ R ) )
= X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(295,plain,
( ( ! [X: a,I: int] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ I @ ( a_inv_a_b @ r @ X ) )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(296,plain,
( ( ! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( a_inv_a_b @ r @ X )
= ( zero_a_b @ r ) )
= ( X
= ( zero_a_b @ r ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(297,plain,
( ( ! [X: a,A: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ X @ A )
= X )
= ( A
= ( zero_a_b @ r ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(298,plain,
( ( ! [X: a,A: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( X
= ( add_a_b @ r @ X @ A ) )
= ( A
= ( zero_a_b @ r ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(299,plain,
( ( ! [X: a,A: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ A @ X )
= X )
= ( A
= ( zero_a_b @ r ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(300,plain,
( ( ! [X: a,A: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( X
= ( add_a_b @ r @ A @ X ) )
= ( A
= ( zero_a_b @ r ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(301,plain,
( ( ! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( zero_a_b @ r ) @ X )
= X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(302,plain,
( ( ! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ X @ ( zero_a_b @ r ) )
= X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(303,plain,
( ( ! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( zero_a_b @ r ) @ X )
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(304,plain,
( ( ! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ X @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(305,plain,
( ( ! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( a_inv_a_b @ r @ X ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(306,plain,
( ( ! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ ( a_inv_a_b @ r @ X ) )
= X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(307,plain,
( ( member_a @ ( zero_a_b @ r ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(308,plain,
( ( ~ ! [T2: a] :
( ( member_a @ T2 @ s )
=> ( ( mult_a_ring_ext_a_b @ r @ T2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
!= ( zero_a_b @ r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(309,plain,
( ( ~ ! [T: a] :
( ( member_a @ T @ s )
=> ( ( mult_a_ring_ext_a_b @ r @ T @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
!= ( zero_a_b @ r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(310,plain,
( ( ! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ ( add_a_b @ r @ A @ B ) )
= ( a_minus_a_b @ r @ ( a_inv_a_b @ r @ A ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(311,plain,
( ( ! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ X )
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(312,plain,
( ( ! [Y: a,X: a] :
( ( ( add_a_b @ r @ Y @ X )
= ( zero_a_b @ r ) )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ X )
= Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(313,plain,
( ( ! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ X @ ( a_inv_a_b @ r @ X ) )
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(314,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ X @ Y )
= ( zero_a_b @ r ) )
=> ( X
= ( a_inv_a_b @ r @ Y ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(315,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( ( add_a_b @ r @ X @ Y )
= Z )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ Z )
= Y ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(316,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ Y ) @ ( a_inv_a_b @ r @ X ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(317,plain,
( ( ! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( A
= ( add_a_b @ r @ ( a_inv_a_b @ r @ B ) @ C ) )
= ( C
= ( add_a_b @ r @ B @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(318,plain,
( ( ! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ B ) @ C )
= A )
= ( C
= ( add_a_b @ r @ B @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(319,plain,
( ( ! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( A
= ( add_a_b @ r @ B @ ( a_inv_a_b @ r @ C ) ) )
= ( B
= ( add_a_b @ r @ A @ C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(320,plain,
( ( ! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ B @ ( a_inv_a_b @ r @ C ) )
= A )
= ( B
= ( add_a_b @ r @ A @ C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(321,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ ( a_inv_a_b @ r @ Y ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(322,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ ( add_a_b @ r @ X @ Y ) )
= Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(323,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ X @ ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ Y ) )
= Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(324,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( a_inv_a_b @ r @ X ) @ Y )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(325,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ X @ ( a_inv_a_b @ r @ Y ) )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(326,plain,
( ( ! [X: a,Y: a] :
( ( ( add_a_b @ r @ X @ Y )
= ( zero_a_b @ r ) )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ Y @ X )
= ( zero_a_b @ r ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(327,plain,
( ( ! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ? [X3: a] :
( ( member_a @ X3 @ ( partia1066395285xt_a_b @ r ) )
& ( ( add_a_b @ r @ X3 @ X )
= ( zero_a_b @ r ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(328,plain,
( ( ! [U: a] :
( ( member_a @ U @ ( partia1066395285xt_a_b @ r ) )
=> ( ! [X3: a] :
( ( member_a @ X3 @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ U @ X3 )
= X3 ) )
=> ( U
= ( zero_a_b @ r ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(329,plain,
( ( ! [X: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ? [X3: a] :
( ( member_a @ X3 @ ( partia1066395285xt_a_b @ r ) )
& ( ( add_a_b @ r @ X @ X3 )
= ( zero_a_b @ r ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(330,plain,
( ( ! [Y: a,X: a,Y3: a] :
( ( ( add_a_b @ r @ Y @ X )
= ( zero_a_b @ r ) )
=> ( ( ( add_a_b @ r @ X @ Y3 )
= ( zero_a_b @ r ) )
=> ( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y3 @ ( partia1066395285xt_a_b @ r ) )
=> ( Y = Y3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(331,plain,
( ( ! [A2: set_a] :
( ( collect_a
@ ^ [X2: a] : ( member_a @ X2 @ A2 ) )
= A2 ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(332,plain,
( ( ! [A: a,P: a > $o] :
( ( member_a @ A @ ( collect_a @ P ) )
= ( P @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(333,plain,
( ( ! [H: set_a,K2: set_a] :
( ( additi2104487374up_a_b @ H @ r )
=> ( ( additi2104487374up_a_b @ K2 @ r )
=> ( additi2104487374up_a_b @ ( set_add_a_b @ r @ H @ K2 ) @ r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(334,plain,
( ( ( partia1066395285xt_a_b @ r )
!= bot_bot_set_a )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(335,plain,
( ( a_minus_a_b
= ( ^ [R2: partia1833973666xt_a_b,X2: a,Y5: a] : ( add_a_b @ R2 @ X2 @ ( a_inv_a_b @ R2 @ Y5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(336,plain,
( ( ! [M: partia1833973666xt_a_b,S2: set_a,X: a,Y: a] :
( ( locali425460998xt_a_b @ M @ S2 )
=> ( ( member_a @ X @ S2 )
=> ( ( member_a @ Y @ S2 )
=> ( member_a @ ( mult_a_ring_ext_a_b @ M @ X @ Y ) @ S2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(337,plain,
( ( ! [Z: int] :
( ( add_pow_a_b_int @ r @ Z @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(338,plain,
( ( locali425460998xt_a_b @ r @ s )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(339,plain,
( ( ( ^ [Y4: product_prod_a_a,Z2: product_prod_a_a] : ( Y4 = Z2 ) )
= ( ^ [S: product_prod_a_a,T3: product_prod_a_a] :
( ( ( product_fst_a_a @ S )
= ( product_fst_a_a @ T3 ) )
& ( ( product_snd_a_a @ S )
= ( product_snd_a_a @ T3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(340,plain,
( ( locali807230110ng_a_b @ r @ s )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(341,plain,
( ( locali880295127ng_a_b @ r @ s )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(342,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ s )
=> ( ( member_a @ Y @ s )
=> ( member_a @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) @ s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(343,plain,
( ( ( a_inv_a_b @ r @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(344,plain,
( ( locali1648887798ac_a_b @ r @ s )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(345,plain,
( ( ! [Prod: product_prod_a_a,Prod2: product_prod_a_a] :
( ( ( ( product_fst_a_a @ Prod )
= ( product_fst_a_a @ Prod2 ) )
& ( ( product_snd_a_a @ Prod )
= ( product_snd_a_a @ Prod2 ) ) )
=> ( Prod = Prod2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(346,plain,
( ( ! [P: a > a > $o,P2: product_prod_a_a] :
( ( P @ ( product_snd_a_a @ P2 ) @ ( product_fst_a_a @ P2 ) )
=> ~ ! [X3: a,Y2: a] :
~ ( P @ Y2 @ X3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(347,plain,
( ( ! [P2: product_prod_a_a,Q2: product_prod_a_a] :
( ( ( product_fst_a_a @ P2 )
= ( product_fst_a_a @ Q2 ) )
=> ( ( ( product_snd_a_a @ P2 )
= ( product_snd_a_a @ Q2 ) )
=> ( P2 = Q2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(348,plain,
( ( ! [X: a,Y: a] :
( ( a_minus_a_b @ r @ X @ Y )
= ( add_a_b @ r @ X @ ( a_inv_a_b @ r @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(349,plain,
( ( semiring_a_b @ r )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(350,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ s )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(351,plain,
( ( member_a @ t @ s )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(352,plain,
( ( member_a @ t2 @ s )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(353,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(354,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ Y @ X )
= ( add_a_b @ r @ Z @ X ) )
= ( Y = Z ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(355,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( add_a_b @ r @ X @ Y ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(356,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( a_minus_a_b @ r @ X @ Y ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(357,plain,
( ( ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
= ( zero_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(358,plain,
( ( ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
= ( zero_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(359,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(360,plain,
( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(361,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(362,plain,
( ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(363,plain,
( ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(364,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(365,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(366,plain,
( ( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(367,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(368,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(369,plain,
( ( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ t ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(370,plain,
( ( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(371,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(372,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(373,plain,
( ( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(374,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(375,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(376,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(377,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(378,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(379,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(380,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(381,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(382,plain,
( ( ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(383,plain,
( ( ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(384,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(385,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(386,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(387,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(388,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(389,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(390,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(391,plain,
( ( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(392,plain,
( ( member_a @ ( product_fst_a_a @ x ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(393,plain,
( ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(394,plain,
( ( member_a @ ( product_snd_a_a @ y ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(395,plain,
( ( ! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ C @ A ) @ B )
= ( a_minus_a_b @ r @ C @ ( add_a_b @ r @ A @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(396,plain,
( ( ! [A: a,B: a,C: a,D: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ D @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ A @ C ) @ B ) @ D )
= ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ ( add_a_b @ r @ A @ B ) @ C ) @ D ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(397,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ Z @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ Z @ X ) @ ( mult_a_ring_ext_a_b @ r @ Z @ Y ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(398,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( add_a_b @ r @ X @ Y ) @ Z )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X @ Z ) @ ( mult_a_ring_ext_a_b @ r @ Y @ Z ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(399,plain,
( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(400,plain,
( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(401,plain,
( ( member_a @ s2 @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(402,plain,
( ( member_a @ s3 @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(403,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ X @ ( add_a_b @ r @ Y @ Z ) )
= ( add_a_b @ r @ Y @ ( add_a_b @ r @ X @ Z ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(404,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ X @ Y )
= ( add_a_b @ r @ Y @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(405,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( add_a_b @ r @ X @ Y ) @ Z )
= ( add_a_b @ r @ X @ ( add_a_b @ r @ Y @ Z ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(406,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ X @ ( mult_a_ring_ext_a_b @ r @ Y @ Z ) )
= ( mult_a_ring_ext_a_b @ r @ Y @ ( mult_a_ring_ext_a_b @ r @ X @ Z ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(407,plain,
( ( ! [X: a,Y: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ X @ Y )
= ( mult_a_ring_ext_a_b @ r @ Y @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(408,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) @ Z )
= ( mult_a_ring_ext_a_b @ r @ X @ ( mult_a_ring_ext_a_b @ r @ Y @ Z ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(409,plain,
( ( ! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( a_minus_a_b @ r @ C @ A )
= ( a_minus_a_b @ r @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(410,plain,
( ( ! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( add_a_b @ r @ C @ A )
= ( add_a_b @ r @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(411,plain,
( ( member_a @ t2 @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(412,plain,
( ( member_a @ t @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(413,plain,
( ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[247]) ).
thf(414,plain,
( ( ! [A2: set_a,B3: set_a] :
( ~ ( ord_less_eq_set_a @ A2 @ B3 )
| ! [C: a] :
( ~ ( member_a @ C @ A2 )
| ( member_a @ C @ B3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[249]) ).
thf(415,plain,
( ( ! [A2: set_a,B3: set_a] :
( ~ ( ord_less_eq_set_a @ A2 @ B3 )
| ! [X: a] :
( ~ ( member_a @ X @ A2 )
| ( member_a @ X @ B3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[250]) ).
thf(416,plain,
( ( ! [A2: set_a] :
( ( ? [X2: a] : ( member_a @ X2 @ A2 ) )
= ( A2 != bot_bot_set_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[251]) ).
thf(417,plain,
( ( ! [A2: set_a] :
( ( member_a @ ( sK1_Y2 @ A2 ) @ A2 )
| ( A2 = bot_bot_set_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[252]) ).
thf(418,plain,
( ( ! [A2: set_a] :
( ( A2 != bot_bot_set_a )
| ! [A: a] :
~ ( member_a @ A @ A2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[253]) ).
thf(419,plain,
( ( ! [A2: set_a,B3: set_a] :
( ( ( member_a @ ( sK2_X3 @ B3 @ A2 ) @ A2 )
& ~ ( member_a @ ( sK2_X3 @ B3 @ A2 ) @ B3 ) )
| ( ord_less_eq_set_a @ A2 @ B3 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[260]) ).
thf(420,plain,
( ( ! [A2: set_a] :
( ~ ( ord_less_eq_set_a @ A2 @ ( partia1066395285xt_a_b @ r ) )
| ! [B3: set_a] :
( ~ ( ord_less_eq_set_a @ B3 @ ( partia1066395285xt_a_b @ r ) )
| ( ord_less_eq_set_a @ ( set_add_a_b @ r @ A2 @ B3 ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[265]) ).
thf(421,plain,
( ( ! [H: set_a] :
( ~ ( ord_less_eq_set_a @ H @ ( partia1066395285xt_a_b @ r ) )
| ! [K2: set_a] :
( ~ ( ord_less_eq_set_a @ K2 @ ( partia1066395285xt_a_b @ r ) )
| ( ord_less_eq_set_a @ ( set_add_a_b @ r @ H @ K2 ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[266]) ).
thf(422,plain,
( ( ! [H: set_a] :
( ~ ( ord_less_eq_set_a @ H @ ( partia1066395285xt_a_b @ r ) )
| ( H = bot_bot_set_a )
| ( ( member_a @ ( sK5_X3 @ H ) @ H )
& ~ ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ H ) ) @ H ) )
| ( ( member_a @ ( sK3_X3 @ H ) @ H )
& ( member_a @ ( sK4_SY248 @ H ) @ H )
& ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ H ) @ ( sK4_SY248 @ H ) ) @ H ) )
| ( member_a @ ( zero_a_b @ r ) @ H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[267]) ).
thf(423,plain,
( ( ! [M: partia1833973666xt_a_b,S2: set_a] :
( ~ ( locali425460998xt_a_b @ M @ S2 )
| ( ord_less_eq_set_a @ S2 @ ( partia1066395285xt_a_b @ M ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[268]) ).
thf(424,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [I: int,J: int] :
( ( add_pow_a_b_int @ r @ ( plus_plus_int @ I @ J ) @ X )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) @ ( add_pow_a_b_int @ r @ J @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[270]) ).
thf(425,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [I: int] :
( ( add_pow_a_b_int @ r @ ( uminus_uminus_int @ I ) @ X )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[271]) ).
thf(426,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [N: int,M2: int] :
( ( add_pow_a_b_int @ r @ ( minus_minus_int @ N @ M2 ) @ X )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ N @ X ) @ ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ M2 @ X ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[272]) ).
thf(427,plain,
( ( ! [R: partia1833973666xt_a_b,X: a] :
( ~ ( semiring_a_b @ R )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
| ( ( mult_a_ring_ext_a_b @ R @ ( add_a_b @ R @ X @ Y ) @ Z )
= ( add_a_b @ R @ ( mult_a_ring_ext_a_b @ R @ X @ Z ) @ ( mult_a_ring_ext_a_b @ R @ Y @ Z ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[273]) ).
thf(428,plain,
( ( ! [R: partia1833973666xt_a_b] :
( ~ ( semiring_a_b @ R )
| ( member_a @ ( zero_a_b @ R ) @ ( partia1066395285xt_a_b @ R ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[274]) ).
thf(429,plain,
( ( ! [R: partia1833973666xt_a_b] :
( ~ ( semiring_a_b @ R )
| ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
| ( member_a @ ( add_a_b @ R @ X @ Y ) @ ( partia1066395285xt_a_b @ R ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[275]) ).
thf(430,plain,
( ( ! [R: partia1833973666xt_a_b,X: a] :
( ~ ( semiring_a_b @ R )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
| ( ( add_a_b @ R @ ( add_a_b @ R @ X @ Y ) @ Z )
= ( add_a_b @ R @ X @ ( add_a_b @ R @ Y @ Z ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[276]) ).
thf(431,plain,
( ( ! [R: partia1833973666xt_a_b] :
( ~ ( semiring_a_b @ R )
| ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
| ( ( add_a_b @ R @ X @ Y )
= ( add_a_b @ R @ Y @ X ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[277]) ).
thf(432,plain,
( ( ! [R: partia1833973666xt_a_b,X: a] :
( ~ ( semiring_a_b @ R )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
| ( ( add_a_b @ R @ X @ ( add_a_b @ R @ Y @ Z ) )
= ( add_a_b @ R @ Y @ ( add_a_b @ R @ X @ Z ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[278]) ).
thf(433,plain,
( ( ! [R: partia1833973666xt_a_b] :
( ~ ( semiring_a_b @ R )
| ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
| ( member_a @ ( mult_a_ring_ext_a_b @ R @ X @ Y ) @ ( partia1066395285xt_a_b @ R ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[279]) ).
thf(434,plain,
( ( ! [R: partia1833973666xt_a_b,X: a] :
( ~ ( semiring_a_b @ R )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
| ( ( mult_a_ring_ext_a_b @ R @ ( mult_a_ring_ext_a_b @ R @ X @ Y ) @ Z )
= ( mult_a_ring_ext_a_b @ R @ X @ ( mult_a_ring_ext_a_b @ R @ Y @ Z ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[280]) ).
thf(435,plain,
( ( ! [R: partia1833973666xt_a_b,S2: set_a] :
( ~ ( locali1648887798ac_a_b @ R @ S2 )
| ( locali807230110ng_a_b @ R @ S2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[281]) ).
thf(436,plain,
( ( ! [R: partia1833973666xt_a_b,S2: set_a] :
( ~ ( locali880295127ng_a_b @ R @ S2 )
| ( locali425460998xt_a_b @ R @ S2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[282]) ).
thf(437,plain,
( ( ! [R: partia1833973666xt_a_b,S2: set_a] :
( ~ ( locali807230110ng_a_b @ R @ S2 )
| ( locali880295127ng_a_b @ R @ S2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[283]) ).
thf(438,plain,
( ( ! [M: partia1833973666xt_a_b,S2: set_a] : $true )
= $true ),
inference(extcnf_combined,[status(esa)],[284]) ).
thf(439,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [I: int] : ( member_a @ ( add_pow_a_b_int @ r @ I @ X ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[285]) ).
thf(440,plain,
( ( ! [X: a,Y: a] :
( ( ( add_a_b @ r @ X @ Y )
!= ( add_a_b @ r @ Y @ X ) )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ! [I: int] :
( ( add_pow_a_b_int @ r @ I @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) @ ( add_pow_a_b_int @ r @ I @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[286]) ).
thf(441,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ! [I: int] :
( ( add_pow_a_b_int @ r @ I @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) @ ( add_pow_a_b_int @ r @ I @ Y ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[287]) ).
thf(442,plain,
( ( ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ! [B: a] :
( ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ! [K: int] :
( ( mult_a_ring_ext_a_b @ r @ A @ ( add_pow_a_b_int @ r @ K @ B ) )
= ( add_pow_a_b_int @ r @ K @ ( mult_a_ring_ext_a_b @ r @ A @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[288]) ).
thf(443,plain,
( ( ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ! [B: a] :
( ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ! [K: int] :
( ( mult_a_ring_ext_a_b @ r @ ( add_pow_a_b_int @ r @ K @ A ) @ B )
= ( add_pow_a_b_int @ r @ K @ ( mult_a_ring_ext_a_b @ r @ A @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[289]) ).
thf(444,plain,
( ( ! [R: partia1833973666xt_a_b,X: a] :
( ~ ( semiring_a_b @ R )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
| ( ( mult_a_ring_ext_a_b @ R @ Z @ ( add_a_b @ R @ X @ Y ) )
= ( add_a_b @ R @ ( mult_a_ring_ext_a_b @ R @ Z @ X ) @ ( mult_a_ring_ext_a_b @ R @ Z @ Y ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[290]) ).
thf(445,plain,
( ( ! [R: partia1833973666xt_a_b] :
( ~ ( semiring_a_b @ R )
| ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ( ( mult_a_ring_ext_a_b @ R @ X @ ( zero_a_b @ R ) )
= ( zero_a_b @ R ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[291]) ).
thf(446,plain,
( ( ! [R: partia1833973666xt_a_b] :
( ~ ( semiring_a_b @ R )
| ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ( ( mult_a_ring_ext_a_b @ R @ ( zero_a_b @ R ) @ X )
= ( zero_a_b @ R ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[292]) ).
thf(447,plain,
( ( ! [R: partia1833973666xt_a_b] :
( ~ ( semiring_a_b @ R )
| ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ( ( add_a_b @ R @ ( zero_a_b @ R ) @ X )
= X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[293]) ).
thf(448,plain,
( ( ! [R: partia1833973666xt_a_b] :
( ~ ( semiring_a_b @ R )
| ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ( ( add_a_b @ R @ X @ ( zero_a_b @ R ) )
= X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[294]) ).
thf(449,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [I: int] :
( ( add_pow_a_b_int @ r @ I @ ( a_inv_a_b @ r @ X ) )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[295]) ).
thf(450,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( a_inv_a_b @ r @ X )
= ( zero_a_b @ r ) )
= ( X
= ( zero_a_b @ r ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[296]) ).
thf(451,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ X @ A )
= X )
= ( A
= ( zero_a_b @ r ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[297]) ).
thf(452,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ( ( X
= ( add_a_b @ r @ X @ A ) )
= ( A
= ( zero_a_b @ r ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[298]) ).
thf(453,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ A @ X )
= X )
= ( A
= ( zero_a_b @ r ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[299]) ).
thf(454,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ( ( X
= ( add_a_b @ r @ A @ X ) )
= ( A
= ( zero_a_b @ r ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[300]) ).
thf(455,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( zero_a_b @ r ) @ X )
= X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[301]) ).
thf(456,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ X @ ( zero_a_b @ r ) )
= X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[302]) ).
thf(457,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( zero_a_b @ r ) @ X )
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[303]) ).
thf(458,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ X @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[304]) ).
thf(459,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( a_inv_a_b @ r @ X ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[305]) ).
thf(460,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( a_inv_a_b @ r @ X ) )
= X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[306]) ).
thf(461,plain,
( ( ( member_a @ sK6_T2 @ s )
& ( ( mult_a_ring_ext_a_b @ r @ sK6_T2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
= ( zero_a_b @ r ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[308]) ).
thf(462,plain,
( ( ( member_a @ sK7_T @ s )
& ( ( mult_a_ring_ext_a_b @ r @ sK7_T @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
= ( zero_a_b @ r ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[309]) ).
thf(463,plain,
( ( ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ! [B: a] :
( ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( add_a_b @ r @ A @ B ) )
= ( a_minus_a_b @ r @ ( a_inv_a_b @ r @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[310]) ).
thf(464,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ X )
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[311]) ).
thf(465,plain,
( ( ! [Y: a,X: a] :
( ( ( add_a_b @ r @ Y @ X )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ X )
= Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[312]) ).
thf(466,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ X @ ( a_inv_a_b @ r @ X ) )
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[313]) ).
thf(467,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ X @ Y )
!= ( zero_a_b @ r ) )
| ( X
= ( a_inv_a_b @ r @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[314]) ).
thf(468,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( ( add_a_b @ r @ X @ Y )
!= Z )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ Z )
= Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[315]) ).
thf(469,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ Y ) @ ( a_inv_a_b @ r @ X ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[316]) ).
thf(470,plain,
( ( ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ! [B: a] :
( ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ! [C: a] :
( ~ ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
| ( ( A
= ( add_a_b @ r @ ( a_inv_a_b @ r @ B ) @ C ) )
= ( C
= ( add_a_b @ r @ B @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[317]) ).
thf(471,plain,
( ( ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ! [B: a] :
( ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ! [C: a] :
( ~ ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ B ) @ C )
= A )
= ( C
= ( add_a_b @ r @ B @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[318]) ).
thf(472,plain,
( ( ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ! [B: a] :
( ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ! [C: a] :
( ~ ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
| ( ( A
= ( add_a_b @ r @ B @ ( a_inv_a_b @ r @ C ) ) )
= ( B
= ( add_a_b @ r @ A @ C ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[319]) ).
thf(473,plain,
( ( ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ! [B: a] :
( ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ! [C: a] :
( ~ ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ B @ ( a_inv_a_b @ r @ C ) )
= A )
= ( B
= ( add_a_b @ r @ A @ C ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[320]) ).
thf(474,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ ( a_inv_a_b @ r @ Y ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[321]) ).
thf(475,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ ( add_a_b @ r @ X @ Y ) )
= Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[322]) ).
thf(476,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ X @ ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ Y ) )
= Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[323]) ).
thf(477,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( a_inv_a_b @ r @ X ) @ Y )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[324]) ).
thf(478,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ X @ ( a_inv_a_b @ r @ Y ) )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[325]) ).
thf(479,plain,
( ( ! [X: a,Y: a] :
( ( ( add_a_b @ r @ X @ Y )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ Y @ X )
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[326]) ).
thf(480,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ ( sK8_X3 @ X ) @ X )
= ( zero_a_b @ r ) )
& ( member_a @ ( sK8_X3 @ X ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[327]) ).
thf(481,plain,
( ( ! [U: a] :
( ~ ( member_a @ U @ ( partia1066395285xt_a_b @ r ) )
| ( ( member_a @ ( sK9_X3 @ U ) @ ( partia1066395285xt_a_b @ r ) )
& ( ( add_a_b @ r @ U @ ( sK9_X3 @ U ) )
!= ( sK9_X3 @ U ) ) )
| ( U
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[328]) ).
thf(482,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ X @ ( sK10_X3 @ X ) )
= ( zero_a_b @ r ) )
& ( member_a @ ( sK10_X3 @ X ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[329]) ).
thf(483,plain,
( ( ! [Y: a,X: a] :
( ( ( add_a_b @ r @ Y @ X )
!= ( zero_a_b @ r ) )
| ! [Y3: a] :
( ( ( add_a_b @ r @ X @ Y3 )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ Y3 @ ( partia1066395285xt_a_b @ r ) )
| ( Y = Y3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[330]) ).
thf(484,plain,
( ( ! [H: set_a] :
( ~ ( additi2104487374up_a_b @ H @ r )
| ! [K2: set_a] :
( ~ ( additi2104487374up_a_b @ K2 @ r )
| ( additi2104487374up_a_b @ ( set_add_a_b @ r @ H @ K2 ) @ r ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[333]) ).
thf(485,plain,
( ( ( partia1066395285xt_a_b @ r )
!= bot_bot_set_a )
= $true ),
inference(extcnf_combined,[status(esa)],[334]) ).
thf(486,plain,
( ( ! [M: partia1833973666xt_a_b,S2: set_a] :
( ~ ( locali425460998xt_a_b @ M @ S2 )
| ! [X: a] :
( ~ ( member_a @ X @ S2 )
| ! [Y: a] :
( ~ ( member_a @ Y @ S2 )
| ( member_a @ ( mult_a_ring_ext_a_b @ M @ X @ Y ) @ S2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[336]) ).
thf(487,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ s )
| ! [Y: a] :
( ~ ( member_a @ Y @ s )
| ( member_a @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) @ s ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[342]) ).
thf(488,plain,
( ( ! [Prod: product_prod_a_a,Prod2: product_prod_a_a] :
( ( ( product_fst_a_a @ Prod )
!= ( product_fst_a_a @ Prod2 ) )
| ( ( product_snd_a_a @ Prod )
!= ( product_snd_a_a @ Prod2 ) )
| ( Prod = Prod2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[345]) ).
thf(489,plain,
( ( ! [P: a > a > $o] :
( ! [P2: product_prod_a_a] :
~ ( P @ ( product_snd_a_a @ P2 ) @ ( product_fst_a_a @ P2 ) )
| ( P @ ( sK12_SY249 @ P ) @ ( sK11_X3 @ P ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[346]) ).
thf(490,plain,
( ( ! [P2: product_prod_a_a,Q2: product_prod_a_a] :
( ( ( product_fst_a_a @ P2 )
!= ( product_fst_a_a @ Q2 ) )
| ( ( product_snd_a_a @ P2 )
!= ( product_snd_a_a @ Q2 ) )
| ( P2 = Q2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[347]) ).
thf(491,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[353]) ).
thf(492,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ Y @ X )
= ( add_a_b @ r @ Z @ X ) )
= ( Y = Z ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[354]) ).
thf(493,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( add_a_b @ r @ X @ Y ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[355]) ).
thf(494,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( a_minus_a_b @ r @ X @ Y ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[356]) ).
thf(495,plain,
( ( ~ ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[391]) ).
thf(496,plain,
( ( ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ! [B: a] :
( ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ! [C: a] :
( ~ ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ C @ A ) @ B )
= ( a_minus_a_b @ r @ C @ ( add_a_b @ r @ A @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[395]) ).
thf(497,plain,
( ( ! [A: a,B: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ! [C: a] :
( ~ ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
| ! [D: a] :
( ~ ( member_a @ D @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ A @ C ) @ B ) @ D )
= ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ ( add_a_b @ r @ A @ B ) @ C ) @ D ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[396]) ).
thf(498,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ Z @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ Z @ X ) @ ( mult_a_ring_ext_a_b @ r @ Z @ Y ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[397]) ).
thf(499,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( add_a_b @ r @ X @ Y ) @ Z )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X @ Z ) @ ( mult_a_ring_ext_a_b @ r @ Y @ Z ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[398]) ).
thf(500,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ X @ ( add_a_b @ r @ Y @ Z ) )
= ( add_a_b @ r @ Y @ ( add_a_b @ r @ X @ Z ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[403]) ).
thf(501,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ X @ Y )
= ( add_a_b @ r @ Y @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[404]) ).
thf(502,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( add_a_b @ r @ X @ Y ) @ Z )
= ( add_a_b @ r @ X @ ( add_a_b @ r @ Y @ Z ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[405]) ).
thf(503,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ X @ ( mult_a_ring_ext_a_b @ r @ Y @ Z ) )
= ( mult_a_ring_ext_a_b @ r @ Y @ ( mult_a_ring_ext_a_b @ r @ X @ Z ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[406]) ).
thf(504,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ X @ Y )
= ( mult_a_ring_ext_a_b @ r @ Y @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[407]) ).
thf(505,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) @ Z )
= ( mult_a_ring_ext_a_b @ r @ X @ ( mult_a_ring_ext_a_b @ r @ Y @ Z ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[408]) ).
thf(506,plain,
( ( ! [A: a,B: a] :
( ( A != B )
| ! [C: a] :
( ( a_minus_a_b @ r @ C @ A )
= ( a_minus_a_b @ r @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[409]) ).
thf(507,plain,
( ( ! [A: a,B: a] :
( ( A != B )
| ! [C: a] :
( ( add_a_b @ r @ C @ A )
= ( add_a_b @ r @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[410]) ).
thf(508,plain,
( ( member_a @ t @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(509,plain,
( ( member_a @ t2 @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(510,plain,
( ( ! [A: a,B: a] :
( ( A != B )
| ! [C: a] :
( ( add_a_b @ r @ C @ A )
= ( add_a_b @ r @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(511,plain,
( ( ! [A: a,B: a] :
( ( A != B )
| ! [C: a] :
( ( a_minus_a_b @ r @ C @ A )
= ( a_minus_a_b @ r @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[506]) ).
thf(512,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) @ Z )
= ( mult_a_ring_ext_a_b @ r @ X @ ( mult_a_ring_ext_a_b @ r @ Y @ Z ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(513,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ X @ Y )
= ( mult_a_ring_ext_a_b @ r @ Y @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(514,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ X @ ( mult_a_ring_ext_a_b @ r @ Y @ Z ) )
= ( mult_a_ring_ext_a_b @ r @ Y @ ( mult_a_ring_ext_a_b @ r @ X @ Z ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[503]) ).
thf(515,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( add_a_b @ r @ X @ Y ) @ Z )
= ( add_a_b @ r @ X @ ( add_a_b @ r @ Y @ Z ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(516,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ X @ Y )
= ( add_a_b @ r @ Y @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(517,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ X @ ( add_a_b @ r @ Y @ Z ) )
= ( add_a_b @ r @ Y @ ( add_a_b @ r @ X @ Z ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(518,plain,
( ( member_a @ s3 @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(519,plain,
( ( member_a @ s2 @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(520,plain,
( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(521,plain,
( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(522,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( add_a_b @ r @ X @ Y ) @ Z )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X @ Z ) @ ( mult_a_ring_ext_a_b @ r @ Y @ Z ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(523,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ Z @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ Z @ X ) @ ( mult_a_ring_ext_a_b @ r @ Z @ Y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(524,plain,
( ( ! [A: a,B: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ! [C: a] :
( ~ ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
| ! [D: a] :
( ~ ( member_a @ D @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ A @ C ) @ B ) @ D )
= ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ ( add_a_b @ r @ A @ B ) @ C ) @ D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(525,plain,
( ( ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ! [B: a] :
( ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ! [C: a] :
( ~ ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ C @ A ) @ B )
= ( a_minus_a_b @ r @ C @ ( add_a_b @ r @ A @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[496]) ).
thf(526,plain,
( ( member_a @ ( product_snd_a_a @ y ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(527,plain,
( ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(528,plain,
( ( member_a @ ( product_fst_a_a @ x ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(529,plain,
( ( ~ ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(530,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(531,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(532,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(533,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(534,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(535,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(536,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(537,plain,
( ( ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(538,plain,
( ( ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(539,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(540,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(541,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(542,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(543,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(544,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(545,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(546,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(547,plain,
( ( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(548,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(549,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(550,plain,
( ( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(551,plain,
( ( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ t ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(552,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(553,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(554,plain,
( ( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(555,plain,
( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(556,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(557,plain,
( ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(558,plain,
( ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(559,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(560,plain,
( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(561,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(562,plain,
( ( ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
= ( zero_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(563,plain,
( ( ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
= ( zero_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(564,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( a_minus_a_b @ r @ X @ Y ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[494]) ).
thf(565,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( add_a_b @ r @ X @ Y ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(566,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ Y @ X )
= ( add_a_b @ r @ Z @ X ) )
= ( Y = Z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(567,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(568,plain,
( ( member_a @ t2 @ s )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(569,plain,
( ( member_a @ t @ s )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(570,plain,
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ s )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(571,plain,
( ( semiring_a_b @ r )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(572,plain,
( ( ! [X: a,Y: a] :
( ( a_minus_a_b @ r @ X @ Y )
= ( add_a_b @ r @ X @ ( a_inv_a_b @ r @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(573,plain,
( ( ! [P2: product_prod_a_a,Q2: product_prod_a_a] :
( ( ( product_fst_a_a @ P2 )
!= ( product_fst_a_a @ Q2 ) )
| ( ( product_snd_a_a @ P2 )
!= ( product_snd_a_a @ Q2 ) )
| ( P2 = Q2 ) ) )
= $true ),
inference(copy,[status(thm)],[490]) ).
thf(574,plain,
( ( ! [P: a > a > $o] :
( ! [P2: product_prod_a_a] :
~ ( P @ ( product_snd_a_a @ P2 ) @ ( product_fst_a_a @ P2 ) )
| ( P @ ( sK12_SY249 @ P ) @ ( sK11_X3 @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[489]) ).
thf(575,plain,
( ( ! [Prod: product_prod_a_a,Prod2: product_prod_a_a] :
( ( ( product_fst_a_a @ Prod )
!= ( product_fst_a_a @ Prod2 ) )
| ( ( product_snd_a_a @ Prod )
!= ( product_snd_a_a @ Prod2 ) )
| ( Prod = Prod2 ) ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(576,plain,
( ( locali1648887798ac_a_b @ r @ s )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(577,plain,
( ( ( a_inv_a_b @ r @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(578,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ s )
| ! [Y: a] :
( ~ ( member_a @ Y @ s )
| ( member_a @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) @ s ) ) ) )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(579,plain,
( ( locali880295127ng_a_b @ r @ s )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(580,plain,
( ( locali807230110ng_a_b @ r @ s )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(581,plain,
( ( ( ^ [Y4: product_prod_a_a,Z2: product_prod_a_a] : ( Y4 = Z2 ) )
= ( ^ [S: product_prod_a_a,T3: product_prod_a_a] :
( ( ( product_fst_a_a @ S )
= ( product_fst_a_a @ T3 ) )
& ( ( product_snd_a_a @ S )
= ( product_snd_a_a @ T3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[339]) ).
thf(582,plain,
( ( locali425460998xt_a_b @ r @ s )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(583,plain,
( ( ! [Z: int] :
( ( add_pow_a_b_int @ r @ Z @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) ) )
= $true ),
inference(copy,[status(thm)],[337]) ).
thf(584,plain,
( ( ! [M: partia1833973666xt_a_b,S2: set_a] :
( ~ ( locali425460998xt_a_b @ M @ S2 )
| ! [X: a] :
( ~ ( member_a @ X @ S2 )
| ! [Y: a] :
( ~ ( member_a @ Y @ S2 )
| ( member_a @ ( mult_a_ring_ext_a_b @ M @ X @ Y ) @ S2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(585,plain,
( ( a_minus_a_b
= ( ^ [R2: partia1833973666xt_a_b,X2: a,Y5: a] : ( add_a_b @ R2 @ X2 @ ( a_inv_a_b @ R2 @ Y5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(586,plain,
( ( ( partia1066395285xt_a_b @ r )
!= bot_bot_set_a )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(587,plain,
( ( ! [H: set_a] :
( ~ ( additi2104487374up_a_b @ H @ r )
| ! [K2: set_a] :
( ~ ( additi2104487374up_a_b @ K2 @ r )
| ( additi2104487374up_a_b @ ( set_add_a_b @ r @ H @ K2 ) @ r ) ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(588,plain,
( ( ! [A: a,P: a > $o] :
( ( member_a @ A @ ( collect_a @ P ) )
= ( P @ A ) ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(589,plain,
( ( ! [A2: set_a] :
( ( collect_a
@ ^ [X2: a] : ( member_a @ X2 @ A2 ) )
= A2 ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(590,plain,
( ( ! [Y: a,X: a] :
( ( ( add_a_b @ r @ Y @ X )
!= ( zero_a_b @ r ) )
| ! [Y3: a] :
( ( ( add_a_b @ r @ X @ Y3 )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ Y3 @ ( partia1066395285xt_a_b @ r ) )
| ( Y = Y3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(591,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ X @ ( sK10_X3 @ X ) )
= ( zero_a_b @ r ) )
& ( member_a @ ( sK10_X3 @ X ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(592,plain,
( ( ! [U: a] :
( ~ ( member_a @ U @ ( partia1066395285xt_a_b @ r ) )
| ( ( member_a @ ( sK9_X3 @ U ) @ ( partia1066395285xt_a_b @ r ) )
& ( ( add_a_b @ r @ U @ ( sK9_X3 @ U ) )
!= ( sK9_X3 @ U ) ) )
| ( U
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(593,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ ( sK8_X3 @ X ) @ X )
= ( zero_a_b @ r ) )
& ( member_a @ ( sK8_X3 @ X ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(594,plain,
( ( ! [X: a,Y: a] :
( ( ( add_a_b @ r @ X @ Y )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ Y @ X )
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(595,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ X @ ( a_inv_a_b @ r @ Y ) )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(596,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( a_inv_a_b @ r @ X ) @ Y )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ X @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(597,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ X @ ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ Y ) )
= Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[476]) ).
thf(598,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ ( add_a_b @ r @ X @ Y ) )
= Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(599,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ ( a_inv_a_b @ r @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(600,plain,
( ( ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ! [B: a] :
( ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ! [C: a] :
( ~ ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ B @ ( a_inv_a_b @ r @ C ) )
= A )
= ( B
= ( add_a_b @ r @ A @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(601,plain,
( ( ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ! [B: a] :
( ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ! [C: a] :
( ~ ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
| ( ( A
= ( add_a_b @ r @ B @ ( a_inv_a_b @ r @ C ) ) )
= ( B
= ( add_a_b @ r @ A @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(602,plain,
( ( ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ! [B: a] :
( ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ! [C: a] :
( ~ ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ B ) @ C )
= A )
= ( C
= ( add_a_b @ r @ B @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(603,plain,
( ( ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ! [B: a] :
( ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ! [C: a] :
( ~ ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
| ( ( A
= ( add_a_b @ r @ ( a_inv_a_b @ r @ B ) @ C ) )
= ( C
= ( add_a_b @ r @ B @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(604,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ Y ) @ ( a_inv_a_b @ r @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(605,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( ( add_a_b @ r @ X @ Y )
!= Z )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ Z )
= Y ) ) )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(606,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ X @ Y )
!= ( zero_a_b @ r ) )
| ( X
= ( a_inv_a_b @ r @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(607,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ X @ ( a_inv_a_b @ r @ X ) )
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(608,plain,
( ( ! [Y: a,X: a] :
( ( ( add_a_b @ r @ Y @ X )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ X )
= Y ) ) )
= $true ),
inference(copy,[status(thm)],[465]) ).
thf(609,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ X ) @ X )
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(610,plain,
( ( ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ! [B: a] :
( ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( add_a_b @ r @ A @ B ) )
= ( a_minus_a_b @ r @ ( a_inv_a_b @ r @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(611,plain,
( ( ( member_a @ sK7_T @ s )
& ( ( mult_a_ring_ext_a_b @ r @ sK7_T @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
= ( zero_a_b @ r ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(612,plain,
( ( ( member_a @ sK6_T2 @ s )
& ( ( mult_a_ring_ext_a_b @ r @ sK6_T2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
= ( zero_a_b @ r ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(613,plain,
( ( member_a @ ( zero_a_b @ r ) @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[307]) ).
thf(614,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( a_inv_a_b @ r @ X ) )
= X ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(615,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( a_inv_a_b @ r @ X ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(616,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ X @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(617,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( zero_a_b @ r ) @ X )
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(618,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ X @ ( zero_a_b @ r ) )
= X ) ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(619,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( zero_a_b @ r ) @ X )
= X ) ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(620,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ( ( X
= ( add_a_b @ r @ A @ X ) )
= ( A
= ( zero_a_b @ r ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[454]) ).
thf(621,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ A @ X )
= X )
= ( A
= ( zero_a_b @ r ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(622,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ( ( X
= ( add_a_b @ r @ X @ A ) )
= ( A
= ( zero_a_b @ r ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(623,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ X @ A )
= X )
= ( A
= ( zero_a_b @ r ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(624,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( a_inv_a_b @ r @ X )
= ( zero_a_b @ r ) )
= ( X
= ( zero_a_b @ r ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(625,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [I: int] :
( ( add_pow_a_b_int @ r @ I @ ( a_inv_a_b @ r @ X ) )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(626,plain,
( ( ! [R: partia1833973666xt_a_b] :
( ~ ( semiring_a_b @ R )
| ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ( ( add_a_b @ R @ X @ ( zero_a_b @ R ) )
= X ) ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(627,plain,
( ( ! [R: partia1833973666xt_a_b] :
( ~ ( semiring_a_b @ R )
| ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ( ( add_a_b @ R @ ( zero_a_b @ R ) @ X )
= X ) ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(628,plain,
( ( ! [R: partia1833973666xt_a_b] :
( ~ ( semiring_a_b @ R )
| ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ( ( mult_a_ring_ext_a_b @ R @ ( zero_a_b @ R ) @ X )
= ( zero_a_b @ R ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[446]) ).
thf(629,plain,
( ( ! [R: partia1833973666xt_a_b] :
( ~ ( semiring_a_b @ R )
| ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ( ( mult_a_ring_ext_a_b @ R @ X @ ( zero_a_b @ R ) )
= ( zero_a_b @ R ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(630,plain,
( ( ! [R: partia1833973666xt_a_b,X: a] :
( ~ ( semiring_a_b @ R )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
| ( ( mult_a_ring_ext_a_b @ R @ Z @ ( add_a_b @ R @ X @ Y ) )
= ( add_a_b @ R @ ( mult_a_ring_ext_a_b @ R @ Z @ X ) @ ( mult_a_ring_ext_a_b @ R @ Z @ Y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(631,plain,
( ( ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ! [B: a] :
( ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ! [K: int] :
( ( mult_a_ring_ext_a_b @ r @ ( add_pow_a_b_int @ r @ K @ A ) @ B )
= ( add_pow_a_b_int @ r @ K @ ( mult_a_ring_ext_a_b @ r @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(632,plain,
( ( ! [A: a] :
( ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ! [B: a] :
( ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ! [K: int] :
( ( mult_a_ring_ext_a_b @ r @ A @ ( add_pow_a_b_int @ r @ K @ B ) )
= ( add_pow_a_b_int @ r @ K @ ( mult_a_ring_ext_a_b @ r @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(633,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ! [I: int] :
( ( add_pow_a_b_int @ r @ I @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) @ ( add_pow_a_b_int @ r @ I @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(634,plain,
( ( ! [X: a,Y: a] :
( ( ( add_a_b @ r @ X @ Y )
!= ( add_a_b @ r @ Y @ X ) )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ r ) )
| ! [I: int] :
( ( add_pow_a_b_int @ r @ I @ ( add_a_b @ r @ X @ Y ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) @ ( add_pow_a_b_int @ r @ I @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(635,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [I: int] : ( member_a @ ( add_pow_a_b_int @ r @ I @ X ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(636,plain,
( ( ! [M: partia1833973666xt_a_b,S2: set_a] : $true )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(637,plain,
( ( ! [R: partia1833973666xt_a_b,S2: set_a] :
( ~ ( locali807230110ng_a_b @ R @ S2 )
| ( locali880295127ng_a_b @ R @ S2 ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(638,plain,
( ( ! [R: partia1833973666xt_a_b,S2: set_a] :
( ~ ( locali880295127ng_a_b @ R @ S2 )
| ( locali425460998xt_a_b @ R @ S2 ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(639,plain,
( ( ! [R: partia1833973666xt_a_b,S2: set_a] :
( ~ ( locali1648887798ac_a_b @ R @ S2 )
| ( locali807230110ng_a_b @ R @ S2 ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(640,plain,
( ( ! [R: partia1833973666xt_a_b,X: a] :
( ~ ( semiring_a_b @ R )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
| ( ( mult_a_ring_ext_a_b @ R @ ( mult_a_ring_ext_a_b @ R @ X @ Y ) @ Z )
= ( mult_a_ring_ext_a_b @ R @ X @ ( mult_a_ring_ext_a_b @ R @ Y @ Z ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(641,plain,
( ( ! [R: partia1833973666xt_a_b] :
( ~ ( semiring_a_b @ R )
| ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
| ( member_a @ ( mult_a_ring_ext_a_b @ R @ X @ Y ) @ ( partia1066395285xt_a_b @ R ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(642,plain,
( ( ! [R: partia1833973666xt_a_b,X: a] :
( ~ ( semiring_a_b @ R )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
| ( ( add_a_b @ R @ X @ ( add_a_b @ R @ Y @ Z ) )
= ( add_a_b @ R @ Y @ ( add_a_b @ R @ X @ Z ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(643,plain,
( ( ! [R: partia1833973666xt_a_b] :
( ~ ( semiring_a_b @ R )
| ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
| ( ( add_a_b @ R @ X @ Y )
= ( add_a_b @ R @ Y @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(644,plain,
( ( ! [R: partia1833973666xt_a_b,X: a] :
( ~ ( semiring_a_b @ R )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
| ( ( add_a_b @ R @ ( add_a_b @ R @ X @ Y ) @ Z )
= ( add_a_b @ R @ X @ ( add_a_b @ R @ Y @ Z ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(645,plain,
( ( ! [R: partia1833973666xt_a_b] :
( ~ ( semiring_a_b @ R )
| ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
| ( member_a @ ( add_a_b @ R @ X @ Y ) @ ( partia1066395285xt_a_b @ R ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(646,plain,
( ( ! [R: partia1833973666xt_a_b] :
( ~ ( semiring_a_b @ R )
| ( member_a @ ( zero_a_b @ R ) @ ( partia1066395285xt_a_b @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(647,plain,
( ( ! [R: partia1833973666xt_a_b,X: a] :
( ~ ( semiring_a_b @ R )
| ~ ( member_a @ X @ ( partia1066395285xt_a_b @ R ) )
| ! [Y: a] :
( ~ ( member_a @ Y @ ( partia1066395285xt_a_b @ R ) )
| ! [Z: a] :
( ~ ( member_a @ Z @ ( partia1066395285xt_a_b @ R ) )
| ( ( mult_a_ring_ext_a_b @ R @ ( add_a_b @ R @ X @ Y ) @ Z )
= ( add_a_b @ R @ ( mult_a_ring_ext_a_b @ R @ X @ Z ) @ ( mult_a_ring_ext_a_b @ R @ Y @ Z ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(648,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [N: int,M2: int] :
( ( add_pow_a_b_int @ r @ ( minus_minus_int @ N @ M2 ) @ X )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ N @ X ) @ ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ M2 @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(649,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [I: int] :
( ( add_pow_a_b_int @ r @ ( uminus_uminus_int @ I ) @ X )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(650,plain,
( ( ! [X: a] :
( ~ ( member_a @ X @ ( partia1066395285xt_a_b @ r ) )
| ! [I: int,J: int] :
( ( add_pow_a_b_int @ r @ ( plus_plus_int @ I @ J ) @ X )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ I @ X ) @ ( add_pow_a_b_int @ r @ J @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(651,plain,
( ( ord_less_eq_set_a @ s @ ( partia1066395285xt_a_b @ r ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(652,plain,
( ( ! [M: partia1833973666xt_a_b,S2: set_a] :
( ~ ( locali425460998xt_a_b @ M @ S2 )
| ( ord_less_eq_set_a @ S2 @ ( partia1066395285xt_a_b @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(653,plain,
( ( ! [H: set_a] :
( ~ ( ord_less_eq_set_a @ H @ ( partia1066395285xt_a_b @ r ) )
| ( H = bot_bot_set_a )
| ( ( member_a @ ( sK5_X3 @ H ) @ H )
& ~ ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ H ) ) @ H ) )
| ( ( member_a @ ( sK3_X3 @ H ) @ H )
& ( member_a @ ( sK4_SY248 @ H ) @ H )
& ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ H ) @ ( sK4_SY248 @ H ) ) @ H ) )
| ( member_a @ ( zero_a_b @ r ) @ H ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(654,plain,
( ( ! [H: set_a] :
( ~ ( ord_less_eq_set_a @ H @ ( partia1066395285xt_a_b @ r ) )
| ! [K2: set_a] :
( ~ ( ord_less_eq_set_a @ K2 @ ( partia1066395285xt_a_b @ r ) )
| ( ord_less_eq_set_a @ ( set_add_a_b @ r @ H @ K2 ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(655,plain,
( ( ! [A2: set_a] :
( ~ ( ord_less_eq_set_a @ A2 @ ( partia1066395285xt_a_b @ r ) )
| ! [B3: set_a] :
( ~ ( ord_less_eq_set_a @ B3 @ ( partia1066395285xt_a_b @ r ) )
| ( ord_less_eq_set_a @ ( set_add_a_b @ r @ A2 @ B3 ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(656,plain,
( ( ! [C: a] :
~ ( member_a @ C @ bot_bot_set_a ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(657,plain,
( ( ! [A2: set_a] :
( ( ! [X2: a] :
~ ( member_a @ X2 @ A2 ) )
= ( A2 = bot_bot_set_a ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(658,plain,
( ( ! [P: a > $o] :
( ( ( collect_a @ P )
= bot_bot_set_a )
= ( ! [X2: a] :
~ ( P @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(659,plain,
( ( ! [P: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ P ) )
= ( ! [X2: a] :
~ ( P @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(660,plain,
( ( ! [A2: set_a,B3: set_a] :
( ( ( member_a @ ( sK2_X3 @ B3 @ A2 ) @ A2 )
& ~ ( member_a @ ( sK2_X3 @ B3 @ A2 ) @ B3 ) )
| ( ord_less_eq_set_a @ A2 @ B3 ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(661,plain,
( ( ! [A2: set_a] :
( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
= ( A2 = bot_bot_set_a ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(662,plain,
( ( ! [A2: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A2 ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(663,plain,
( ( ! [A2: set_a] :
( ( minus_minus_set_a @ A2 @ bot_bot_set_a )
= A2 ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(664,plain,
( ( ! [A2: set_a] :
( ( minus_minus_set_a @ bot_bot_set_a @ A2 )
= bot_bot_set_a ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(665,plain,
( ( ! [A2: set_a] :
( ( minus_minus_set_a @ A2 @ A2 )
= bot_bot_set_a ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(666,plain,
( ( ! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(667,plain,
( ( ! [A2: set_a] :
( ( A2 != bot_bot_set_a )
| ! [A: a] :
~ ( member_a @ A @ A2 ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(668,plain,
( ( ! [A2: set_a] :
( ( member_a @ ( sK1_Y2 @ A2 ) @ A2 )
| ( A2 = bot_bot_set_a ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(669,plain,
( ( ! [A2: set_a] :
( ( ? [X2: a] : ( member_a @ X2 @ A2 ) )
= ( A2 != bot_bot_set_a ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(670,plain,
( ( ! [A2: set_a,B3: set_a] :
( ~ ( ord_less_eq_set_a @ A2 @ B3 )
| ! [X: a] :
( ~ ( member_a @ X @ A2 )
| ( member_a @ X @ B3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(671,plain,
( ( ! [A2: set_a,B3: set_a] :
( ~ ( ord_less_eq_set_a @ A2 @ B3 )
| ! [C: a] :
( ~ ( member_a @ C @ A2 )
| ( member_a @ C @ B3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(672,plain,
( ( ord_less_eq_set_a
= ( ^ [A4: set_a,B4: set_a] :
! [X2: a] :
( ( member_a @ X2 @ A4 )
=> ( member_a @ X2 @ B4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(673,plain,
( ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(674,plain,
( ( ~ ( ~ ( member_a @ sK7_T @ s )
| ( ( mult_a_ring_ext_a_b @ r @ sK7_T @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
!= ( zero_a_b @ r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[611]) ).
thf(675,plain,
( ( ~ ( ~ ( member_a @ sK6_T2 @ s )
| ( ( mult_a_ring_ext_a_b @ r @ sK6_T2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
!= ( zero_a_b @ r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[612]) ).
thf(676,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( ~ ( member_a @ ( sK2_X3 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member_a @ ( sK2_X3 @ SX1 @ SX0 ) @ SX1 ) )
| ( ord_less_eq_set_a @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(677,plain,
( ( ! [SX0: set_a] :
( ( ~ ! [SX1: a] :
~ ( member_a @ SX1 @ SX0 ) )
= ( SX0 != bot_bot_set_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[669]) ).
thf(678,plain,
( ( ord_less_eq_set_a
= ( ^ [SX0: set_a,SX1: set_a] :
! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ( member_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[672]) ).
thf(679,plain,
( ( ! [SX0: a] :
( ~ ( member_a @ SX0 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( ( ( add_a_b @ r @ ( sK8_X3 @ SX0 ) @ SX0 )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( sK8_X3 @ SX0 ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[593]) ).
thf(680,plain,
( ( ( ^ [SX0: product_prod_a_a,SX1: product_prod_a_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: product_prod_a_a,SX1: product_prod_a_a] :
~ ( ( ( product_fst_a_a @ SX0 )
!= ( product_fst_a_a @ SX1 ) )
| ( ( product_snd_a_a @ SX0 )
!= ( product_snd_a_a @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581]) ).
thf(681,plain,
( ( ! [SX0: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ ( partia1066395285xt_a_b @ r ) )
| ( SX0 = bot_bot_set_a )
| ~ ( ~ ( member_a @ ( sK5_X3 @ SX0 ) @ SX0 )
| ~ ~ ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SX0 ) ) @ SX0 ) )
| ~ ( ~ ( member_a @ ( sK3_X3 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( member_a @ ( sK4_SY248 @ SX0 ) @ SX0 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SX0 ) @ ( sK4_SY248 @ SX0 ) ) @ SX0 ) ) )
| ( member_a @ ( zero_a_b @ r ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[653]) ).
thf(682,plain,
( ( ! [SX0: a] :
( ~ ( member_a @ SX0 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( ~ ( member_a @ ( sK9_X3 @ SX0 ) @ ( partia1066395285xt_a_b @ r ) )
| ~ ( ( ( add_a_b @ r @ SX0 @ ( sK9_X3 @ SX0 ) )
!= ( sK9_X3 @ SX0 ) ) ) )
| ( SX0
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[592]) ).
thf(683,plain,
( ( ! [SX0: a] :
( ~ ( member_a @ SX0 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( ( ( add_a_b @ r @ SX0 @ ( sK10_X3 @ SX0 ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( sK10_X3 @ SX0 ) @ ( partia1066395285xt_a_b @ r ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[591]) ).
thf(684,plain,
! [SV1: a] :
( ( ! [SY250: a] :
( ( SV1 != SY250 )
| ! [SY251: a] :
( ( add_a_b @ r @ SY251 @ SV1 )
= ( add_a_b @ r @ SY251 @ SY250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(685,plain,
! [SV2: a] :
( ( ! [SY252: a] :
( ( SV2 != SY252 )
| ! [SY253: a] :
( ( a_minus_a_b @ r @ SY253 @ SV2 )
= ( a_minus_a_b @ r @ SY253 @ SY252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(686,plain,
! [SV3: a] :
( ( ~ ( member_a @ SV3 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY254: a] :
( ~ ( member_a @ SY254 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY255: a] :
( ~ ( member_a @ SY255 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV3 @ SY254 ) @ SY255 )
= ( mult_a_ring_ext_a_b @ r @ SV3 @ ( mult_a_ring_ext_a_b @ r @ SY254 @ SY255 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(687,plain,
! [SV4: a] :
( ( ~ ( member_a @ SV4 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY256: a] :
( ~ ( member_a @ SY256 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SV4 @ SY256 )
= ( mult_a_ring_ext_a_b @ r @ SY256 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(688,plain,
! [SV5: a] :
( ( ~ ( member_a @ SV5 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY257: a] :
( ~ ( member_a @ SY257 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY258: a] :
( ~ ( member_a @ SY258 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SV5 @ ( mult_a_ring_ext_a_b @ r @ SY257 @ SY258 ) )
= ( mult_a_ring_ext_a_b @ r @ SY257 @ ( mult_a_ring_ext_a_b @ r @ SV5 @ SY258 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(689,plain,
! [SV6: a] :
( ( ~ ( member_a @ SV6 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY259: a] :
( ~ ( member_a @ SY259 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY260: a] :
( ~ ( member_a @ SY260 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( add_a_b @ r @ SV6 @ SY259 ) @ SY260 )
= ( add_a_b @ r @ SV6 @ ( add_a_b @ r @ SY259 @ SY260 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(690,plain,
! [SV7: a] :
( ( ~ ( member_a @ SV7 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY261: a] :
( ~ ( member_a @ SY261 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV7 @ SY261 )
= ( add_a_b @ r @ SY261 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(691,plain,
! [SV8: a] :
( ( ~ ( member_a @ SV8 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY262: a] :
( ~ ( member_a @ SY262 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY263: a] :
( ~ ( member_a @ SY263 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV8 @ ( add_a_b @ r @ SY262 @ SY263 ) )
= ( add_a_b @ r @ SY262 @ ( add_a_b @ r @ SV8 @ SY263 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(692,plain,
! [SV9: a] :
( ( ~ ( member_a @ SV9 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY264: a] :
( ~ ( member_a @ SY264 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY265: a] :
( ~ ( member_a @ SY265 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( add_a_b @ r @ SV9 @ SY264 ) @ SY265 )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV9 @ SY265 ) @ ( mult_a_ring_ext_a_b @ r @ SY264 @ SY265 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(693,plain,
! [SV10: a] :
( ( ~ ( member_a @ SV10 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY266: a] :
( ~ ( member_a @ SY266 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY267: a] :
( ~ ( member_a @ SY267 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SY267 @ ( add_a_b @ r @ SV10 @ SY266 ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SY267 @ SV10 ) @ ( mult_a_ring_ext_a_b @ r @ SY267 @ SY266 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(694,plain,
! [SV11: a] :
( ( ! [SY268: a] :
( ~ ( member_a @ SV11 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SY268 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY269: a] :
( ~ ( member_a @ SY269 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY270: a] :
( ~ ( member_a @ SY270 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ SV11 @ SY269 ) @ SY268 ) @ SY270 )
= ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ ( add_a_b @ r @ SV11 @ SY268 ) @ SY269 ) @ SY270 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(695,plain,
! [SV12: a] :
( ( ~ ( member_a @ SV12 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY271: a] :
( ~ ( member_a @ SY271 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY272: a] :
( ~ ( member_a @ SY272 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ SY272 @ SV12 ) @ SY271 )
= ( a_minus_a_b @ r @ SY272 @ ( add_a_b @ r @ SV12 @ SY271 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(696,plain,
( ( ( ~ ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ~ ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(697,plain,
! [SV13: a] :
( ( ~ ( member_a @ SV13 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY273: a] :
( ~ ( member_a @ SY273 @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( a_minus_a_b @ r @ SV13 @ SY273 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(698,plain,
! [SV14: a] :
( ( ~ ( member_a @ SV14 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY274: a] :
( ~ ( member_a @ SY274 @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( add_a_b @ r @ SV14 @ SY274 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(699,plain,
! [SV15: a] :
( ( ~ ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY275: a] :
( ~ ( member_a @ SY275 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY276: a] :
( ~ ( member_a @ SY276 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SY275 @ SV15 )
= ( add_a_b @ r @ SY276 @ SV15 ) )
= ( SY275 = SY276 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(700,plain,
! [SV16: a] :
( ( ~ ( member_a @ SV16 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY277: a] :
( ~ ( member_a @ SY277 @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( mult_a_ring_ext_a_b @ r @ SV16 @ SY277 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(701,plain,
! [SV17: a] :
( ( ! [SY278: a] :
( ( a_minus_a_b @ r @ SV17 @ SY278 )
= ( add_a_b @ r @ SV17 @ ( a_inv_a_b @ r @ SY278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(702,plain,
! [SV18: product_prod_a_a] :
( ( ! [SY279: product_prod_a_a] :
( ( ( product_fst_a_a @ SV18 )
!= ( product_fst_a_a @ SY279 ) )
| ( ( product_snd_a_a @ SV18 )
!= ( product_snd_a_a @ SY279 ) )
| ( SV18 = SY279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(703,plain,
! [SV19: a > a > $o] :
( ( ! [SY280: product_prod_a_a] :
~ ( SV19 @ ( product_snd_a_a @ SY280 ) @ ( product_fst_a_a @ SY280 ) )
| ( SV19 @ ( sK12_SY249 @ SV19 ) @ ( sK11_X3 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(704,plain,
! [SV20: product_prod_a_a] :
( ( ! [SY281: product_prod_a_a] :
( ( ( product_fst_a_a @ SV20 )
!= ( product_fst_a_a @ SY281 ) )
| ( ( product_snd_a_a @ SV20 )
!= ( product_snd_a_a @ SY281 ) )
| ( SV20 = SY281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(705,plain,
! [SV21: a] :
( ( ~ ( member_a @ SV21 @ s )
| ! [SY282: a] :
( ~ ( member_a @ SY282 @ s )
| ( member_a @ ( mult_a_ring_ext_a_b @ r @ SV21 @ SY282 ) @ s ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(706,plain,
! [SV22: int] :
( ( ( add_pow_a_b_int @ r @ SV22 @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(707,plain,
! [SV23: partia1833973666xt_a_b] :
( ( ! [SY283: set_a] :
( ~ ( locali425460998xt_a_b @ SV23 @ SY283 )
| ! [SY284: a] :
( ~ ( member_a @ SY284 @ SY283 )
| ! [SY285: a] :
( ~ ( member_a @ SY285 @ SY283 )
| ( member_a @ ( mult_a_ring_ext_a_b @ SV23 @ SY284 @ SY285 ) @ SY283 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(708,plain,
( ( ! [SV24: partia1833973666xt_a_b] :
( ( a_minus_a_b @ SV24 )
= ( ^ [SY286: a,SY287: a] : ( add_a_b @ SV24 @ SY286 @ ( a_inv_a_b @ SV24 @ SY287 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[585]) ).
thf(709,plain,
( ( a_minus_a_b
= ( ^ [R2: partia1833973666xt_a_b,X2: a,Y5: a] : ( add_a_b @ R2 @ X2 @ ( a_inv_a_b @ R2 @ Y5 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[585]) ).
thf(710,plain,
( ( ( partia1066395285xt_a_b @ r )
= bot_bot_set_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(711,plain,
! [SV25: set_a] :
( ( ~ ( additi2104487374up_a_b @ SV25 @ r )
| ! [SY288: set_a] :
( ~ ( additi2104487374up_a_b @ SY288 @ r )
| ( additi2104487374up_a_b @ ( set_add_a_b @ r @ SV25 @ SY288 ) @ r ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(712,plain,
! [SV26: a] :
( ( ! [SY289: a > $o] :
( ( member_a @ SV26 @ ( collect_a @ SY289 ) )
= ( SY289 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(713,plain,
! [SV27: set_a] :
( ( ( collect_a
@ ^ [SY290: a] : ( member_a @ SY290 @ SV27 ) )
= SV27 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(714,plain,
! [SV28: a] :
( ( ! [SY291: a] :
( ( ( add_a_b @ r @ SV28 @ SY291 )
!= ( zero_a_b @ r ) )
| ! [SY292: a] :
( ( ( add_a_b @ r @ SY291 @ SY292 )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ SY291 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV28 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SY292 @ ( partia1066395285xt_a_b @ r ) )
| ( SV28 = SY292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(715,plain,
! [SV29: a] :
( ( ! [SY293: a] :
( ( ( add_a_b @ r @ SV29 @ SY293 )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ SV29 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SY293 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SY293 @ SV29 )
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(716,plain,
! [SV30: a] :
( ( ~ ( member_a @ SV30 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY294: a] :
( ~ ( member_a @ SY294 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SV30 @ ( a_inv_a_b @ r @ SY294 ) )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV30 @ SY294 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(717,plain,
! [SV31: a] :
( ( ~ ( member_a @ SV31 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY295: a] :
( ~ ( member_a @ SY295 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( a_inv_a_b @ r @ SV31 ) @ SY295 )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV31 @ SY295 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(718,plain,
! [SV32: a] :
( ( ~ ( member_a @ SV32 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY296: a] :
( ~ ( member_a @ SY296 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV32 @ ( add_a_b @ r @ ( a_inv_a_b @ r @ SV32 ) @ SY296 ) )
= SY296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(719,plain,
! [SV33: a] :
( ( ~ ( member_a @ SV33 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY297: a] :
( ~ ( member_a @ SY297 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV33 ) @ ( add_a_b @ r @ SV33 @ SY297 ) )
= SY297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(720,plain,
! [SV34: a] :
( ( ~ ( member_a @ SV34 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY298: a] :
( ~ ( member_a @ SY298 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( add_a_b @ r @ SV34 @ SY298 ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV34 ) @ ( a_inv_a_b @ r @ SY298 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(721,plain,
! [SV35: a] :
( ( ~ ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY299: a] :
( ~ ( member_a @ SY299 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY300: a] :
( ~ ( member_a @ SY300 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SY299 @ ( a_inv_a_b @ r @ SY300 ) )
= SV35 )
= ( SY299
= ( add_a_b @ r @ SV35 @ SY300 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(722,plain,
! [SV36: a] :
( ( ~ ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY301: a] :
( ~ ( member_a @ SY301 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY302: a] :
( ~ ( member_a @ SY302 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV36
= ( add_a_b @ r @ SY301 @ ( a_inv_a_b @ r @ SY302 ) ) )
= ( SY301
= ( add_a_b @ r @ SV36 @ SY302 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(723,plain,
! [SV37: a] :
( ( ~ ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY303: a] :
( ~ ( member_a @ SY303 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY304: a] :
( ~ ( member_a @ SY304 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SY303 ) @ SY304 )
= SV37 )
= ( SY304
= ( add_a_b @ r @ SY303 @ SV37 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(724,plain,
! [SV38: a] :
( ( ~ ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY305: a] :
( ~ ( member_a @ SY305 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY306: a] :
( ~ ( member_a @ SY306 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SY305 ) @ SY306 ) )
= ( SY306
= ( add_a_b @ r @ SY305 @ SV38 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(725,plain,
! [SV39: a] :
( ( ~ ( member_a @ SV39 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY307: a] :
( ~ ( member_a @ SY307 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( add_a_b @ r @ SV39 @ SY307 ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SY307 ) @ ( a_inv_a_b @ r @ SV39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(726,plain,
! [SV40: a] :
( ( ! [SY308: a,SY309: a] :
( ( ( add_a_b @ r @ SV40 @ SY308 )
!= SY309 )
| ~ ( member_a @ SV40 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SY308 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SY309 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV40 ) @ SY309 )
= SY308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(727,plain,
! [SV41: a] :
( ( ~ ( member_a @ SV41 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY310: a] :
( ~ ( member_a @ SY310 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV41 @ SY310 )
!= ( zero_a_b @ r ) )
| ( SV41
= ( a_inv_a_b @ r @ SY310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(728,plain,
! [SV42: a] :
( ( ~ ( member_a @ SV42 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV42 @ ( a_inv_a_b @ r @ SV42 ) )
= ( zero_a_b @ r ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(729,plain,
! [SV43: a] :
( ( ! [SY311: a] :
( ( ( add_a_b @ r @ SV43 @ SY311 )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ SY311 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV43 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ SY311 )
= SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(730,plain,
! [SV44: a] :
( ( ~ ( member_a @ SV44 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV44 ) @ SV44 )
= ( zero_a_b @ r ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(731,plain,
! [SV45: a] :
( ( ~ ( member_a @ SV45 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY312: a] :
( ~ ( member_a @ SY312 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( add_a_b @ r @ SV45 @ SY312 ) )
= ( a_minus_a_b @ r @ ( a_inv_a_b @ r @ SV45 ) @ SY312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(732,plain,
! [SV46: a] :
( ( ~ ( member_a @ SV46 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( a_inv_a_b @ r @ SV46 ) )
= SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(733,plain,
! [SV47: a] :
( ( ~ ( member_a @ SV47 @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( a_inv_a_b @ r @ SV47 ) @ ( partia1066395285xt_a_b @ r ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(734,plain,
! [SV48: a] :
( ( ~ ( member_a @ SV48 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SV48 @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(735,plain,
! [SV49: a] :
( ( ~ ( member_a @ SV49 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( zero_a_b @ r ) @ SV49 )
= ( zero_a_b @ r ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(736,plain,
! [SV50: a] :
( ( ~ ( member_a @ SV50 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV50 @ ( zero_a_b @ r ) )
= SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(737,plain,
! [SV51: a] :
( ( ~ ( member_a @ SV51 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( zero_a_b @ r ) @ SV51 )
= SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(738,plain,
! [SV52: a] :
( ( ~ ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY313: a] :
( ~ ( member_a @ SY313 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV52
= ( add_a_b @ r @ SY313 @ SV52 ) )
= ( SY313
= ( zero_a_b @ r ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(739,plain,
! [SV53: a] :
( ( ~ ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY314: a] :
( ~ ( member_a @ SY314 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SY314 @ SV53 )
= SV53 )
= ( SY314
= ( zero_a_b @ r ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(740,plain,
! [SV54: a] :
( ( ~ ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY315: a] :
( ~ ( member_a @ SY315 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV54
= ( add_a_b @ r @ SV54 @ SY315 ) )
= ( SY315
= ( zero_a_b @ r ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(741,plain,
! [SV55: a] :
( ( ~ ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY316: a] :
( ~ ( member_a @ SY316 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SV55 @ SY316 )
= SV55 )
= ( SY316
= ( zero_a_b @ r ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(742,plain,
! [SV56: a] :
( ( ~ ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( a_inv_a_b @ r @ SV56 )
= ( zero_a_b @ r ) )
= ( SV56
= ( zero_a_b @ r ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(743,plain,
! [SV57: a] :
( ( ~ ( member_a @ SV57 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY317: int] :
( ( add_pow_a_b_int @ r @ SY317 @ ( a_inv_a_b @ r @ SV57 ) )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ SY317 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(744,plain,
! [SV58: partia1833973666xt_a_b] :
( ( ~ ( semiring_a_b @ SV58 )
| ! [SY318: a] :
( ~ ( member_a @ SY318 @ ( partia1066395285xt_a_b @ SV58 ) )
| ( ( add_a_b @ SV58 @ SY318 @ ( zero_a_b @ SV58 ) )
= SY318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(745,plain,
! [SV59: partia1833973666xt_a_b] :
( ( ~ ( semiring_a_b @ SV59 )
| ! [SY319: a] :
( ~ ( member_a @ SY319 @ ( partia1066395285xt_a_b @ SV59 ) )
| ( ( add_a_b @ SV59 @ ( zero_a_b @ SV59 ) @ SY319 )
= SY319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(746,plain,
! [SV60: partia1833973666xt_a_b] :
( ( ~ ( semiring_a_b @ SV60 )
| ! [SY320: a] :
( ~ ( member_a @ SY320 @ ( partia1066395285xt_a_b @ SV60 ) )
| ( ( mult_a_ring_ext_a_b @ SV60 @ ( zero_a_b @ SV60 ) @ SY320 )
= ( zero_a_b @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(747,plain,
! [SV61: partia1833973666xt_a_b] :
( ( ~ ( semiring_a_b @ SV61 )
| ! [SY321: a] :
( ~ ( member_a @ SY321 @ ( partia1066395285xt_a_b @ SV61 ) )
| ( ( mult_a_ring_ext_a_b @ SV61 @ SY321 @ ( zero_a_b @ SV61 ) )
= ( zero_a_b @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(748,plain,
! [SV62: partia1833973666xt_a_b] :
( ( ! [SY322: a] :
( ~ ( semiring_a_b @ SV62 )
| ~ ( member_a @ SY322 @ ( partia1066395285xt_a_b @ SV62 ) )
| ! [SY323: a] :
( ~ ( member_a @ SY323 @ ( partia1066395285xt_a_b @ SV62 ) )
| ! [SY324: a] :
( ~ ( member_a @ SY324 @ ( partia1066395285xt_a_b @ SV62 ) )
| ( ( mult_a_ring_ext_a_b @ SV62 @ SY324 @ ( add_a_b @ SV62 @ SY322 @ SY323 ) )
= ( add_a_b @ SV62 @ ( mult_a_ring_ext_a_b @ SV62 @ SY324 @ SY322 ) @ ( mult_a_ring_ext_a_b @ SV62 @ SY324 @ SY323 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(749,plain,
! [SV63: a] :
( ( ~ ( member_a @ SV63 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY325: a] :
( ~ ( member_a @ SY325 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY326: int] :
( ( mult_a_ring_ext_a_b @ r @ ( add_pow_a_b_int @ r @ SY326 @ SV63 ) @ SY325 )
= ( add_pow_a_b_int @ r @ SY326 @ ( mult_a_ring_ext_a_b @ r @ SV63 @ SY325 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(750,plain,
! [SV64: a] :
( ( ~ ( member_a @ SV64 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY327: a] :
( ~ ( member_a @ SY327 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY328: int] :
( ( mult_a_ring_ext_a_b @ r @ SV64 @ ( add_pow_a_b_int @ r @ SY328 @ SY327 ) )
= ( add_pow_a_b_int @ r @ SY328 @ ( mult_a_ring_ext_a_b @ r @ SV64 @ SY327 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(751,plain,
! [SV65: a] :
( ( ~ ( member_a @ SV65 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY329: a] :
( ~ ( member_a @ SY329 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY330: int] :
( ( add_pow_a_b_int @ r @ SY330 @ ( add_a_b @ r @ SV65 @ SY329 ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY330 @ SV65 ) @ ( add_pow_a_b_int @ r @ SY330 @ SY329 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(752,plain,
! [SV66: a] :
( ( ! [SY331: a] :
( ( ( add_a_b @ r @ SV66 @ SY331 )
!= ( add_a_b @ r @ SY331 @ SV66 ) )
| ~ ( member_a @ SV66 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SY331 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY332: int] :
( ( add_pow_a_b_int @ r @ SY332 @ ( add_a_b @ r @ SV66 @ SY331 ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY332 @ SV66 ) @ ( add_pow_a_b_int @ r @ SY332 @ SY331 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(753,plain,
! [SV67: a] :
( ( ~ ( member_a @ SV67 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY333: int] : ( member_a @ ( add_pow_a_b_int @ r @ SY333 @ SV67 ) @ ( partia1066395285xt_a_b @ r ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(754,plain,
( ( ! [S2: set_a] : $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(755,plain,
! [SV69: partia1833973666xt_a_b] :
( ( ! [SY335: set_a] :
( ~ ( locali807230110ng_a_b @ SV69 @ SY335 )
| ( locali880295127ng_a_b @ SV69 @ SY335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(756,plain,
! [SV70: partia1833973666xt_a_b] :
( ( ! [SY336: set_a] :
( ~ ( locali880295127ng_a_b @ SV70 @ SY336 )
| ( locali425460998xt_a_b @ SV70 @ SY336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(757,plain,
! [SV71: partia1833973666xt_a_b] :
( ( ! [SY337: set_a] :
( ~ ( locali1648887798ac_a_b @ SV71 @ SY337 )
| ( locali807230110ng_a_b @ SV71 @ SY337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(758,plain,
! [SV72: partia1833973666xt_a_b] :
( ( ! [SY338: a] :
( ~ ( semiring_a_b @ SV72 )
| ~ ( member_a @ SY338 @ ( partia1066395285xt_a_b @ SV72 ) )
| ! [SY339: a] :
( ~ ( member_a @ SY339 @ ( partia1066395285xt_a_b @ SV72 ) )
| ! [SY340: a] :
( ~ ( member_a @ SY340 @ ( partia1066395285xt_a_b @ SV72 ) )
| ( ( mult_a_ring_ext_a_b @ SV72 @ ( mult_a_ring_ext_a_b @ SV72 @ SY338 @ SY339 ) @ SY340 )
= ( mult_a_ring_ext_a_b @ SV72 @ SY338 @ ( mult_a_ring_ext_a_b @ SV72 @ SY339 @ SY340 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(759,plain,
! [SV73: partia1833973666xt_a_b] :
( ( ~ ( semiring_a_b @ SV73 )
| ! [SY341: a] :
( ~ ( member_a @ SY341 @ ( partia1066395285xt_a_b @ SV73 ) )
| ! [SY342: a] :
( ~ ( member_a @ SY342 @ ( partia1066395285xt_a_b @ SV73 ) )
| ( member_a @ ( mult_a_ring_ext_a_b @ SV73 @ SY341 @ SY342 ) @ ( partia1066395285xt_a_b @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(760,plain,
! [SV74: partia1833973666xt_a_b] :
( ( ! [SY343: a] :
( ~ ( semiring_a_b @ SV74 )
| ~ ( member_a @ SY343 @ ( partia1066395285xt_a_b @ SV74 ) )
| ! [SY344: a] :
( ~ ( member_a @ SY344 @ ( partia1066395285xt_a_b @ SV74 ) )
| ! [SY345: a] :
( ~ ( member_a @ SY345 @ ( partia1066395285xt_a_b @ SV74 ) )
| ( ( add_a_b @ SV74 @ SY343 @ ( add_a_b @ SV74 @ SY344 @ SY345 ) )
= ( add_a_b @ SV74 @ SY344 @ ( add_a_b @ SV74 @ SY343 @ SY345 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(761,plain,
! [SV75: partia1833973666xt_a_b] :
( ( ~ ( semiring_a_b @ SV75 )
| ! [SY346: a] :
( ~ ( member_a @ SY346 @ ( partia1066395285xt_a_b @ SV75 ) )
| ! [SY347: a] :
( ~ ( member_a @ SY347 @ ( partia1066395285xt_a_b @ SV75 ) )
| ( ( add_a_b @ SV75 @ SY346 @ SY347 )
= ( add_a_b @ SV75 @ SY347 @ SY346 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(762,plain,
! [SV76: partia1833973666xt_a_b] :
( ( ! [SY348: a] :
( ~ ( semiring_a_b @ SV76 )
| ~ ( member_a @ SY348 @ ( partia1066395285xt_a_b @ SV76 ) )
| ! [SY349: a] :
( ~ ( member_a @ SY349 @ ( partia1066395285xt_a_b @ SV76 ) )
| ! [SY350: a] :
( ~ ( member_a @ SY350 @ ( partia1066395285xt_a_b @ SV76 ) )
| ( ( add_a_b @ SV76 @ ( add_a_b @ SV76 @ SY348 @ SY349 ) @ SY350 )
= ( add_a_b @ SV76 @ SY348 @ ( add_a_b @ SV76 @ SY349 @ SY350 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(763,plain,
! [SV77: partia1833973666xt_a_b] :
( ( ~ ( semiring_a_b @ SV77 )
| ! [SY351: a] :
( ~ ( member_a @ SY351 @ ( partia1066395285xt_a_b @ SV77 ) )
| ! [SY352: a] :
( ~ ( member_a @ SY352 @ ( partia1066395285xt_a_b @ SV77 ) )
| ( member_a @ ( add_a_b @ SV77 @ SY351 @ SY352 ) @ ( partia1066395285xt_a_b @ SV77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(764,plain,
! [SV78: partia1833973666xt_a_b] :
( ( ~ ( semiring_a_b @ SV78 )
| ( member_a @ ( zero_a_b @ SV78 ) @ ( partia1066395285xt_a_b @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(765,plain,
! [SV79: partia1833973666xt_a_b] :
( ( ! [SY353: a] :
( ~ ( semiring_a_b @ SV79 )
| ~ ( member_a @ SY353 @ ( partia1066395285xt_a_b @ SV79 ) )
| ! [SY354: a] :
( ~ ( member_a @ SY354 @ ( partia1066395285xt_a_b @ SV79 ) )
| ! [SY355: a] :
( ~ ( member_a @ SY355 @ ( partia1066395285xt_a_b @ SV79 ) )
| ( ( mult_a_ring_ext_a_b @ SV79 @ ( add_a_b @ SV79 @ SY353 @ SY354 ) @ SY355 )
= ( add_a_b @ SV79 @ ( mult_a_ring_ext_a_b @ SV79 @ SY353 @ SY355 ) @ ( mult_a_ring_ext_a_b @ SV79 @ SY354 @ SY355 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(766,plain,
! [SV80: a] :
( ( ~ ( member_a @ SV80 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY356: int,SY357: int] :
( ( add_pow_a_b_int @ r @ ( minus_minus_int @ SY356 @ SY357 ) @ SV80 )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY356 @ SV80 ) @ ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ SY357 @ SV80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(767,plain,
! [SV81: a] :
( ( ~ ( member_a @ SV81 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY358: int] :
( ( add_pow_a_b_int @ r @ ( uminus_uminus_int @ SY358 ) @ SV81 )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ SY358 @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(768,plain,
! [SV82: a] :
( ( ~ ( member_a @ SV82 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY359: int,SY360: int] :
( ( add_pow_a_b_int @ r @ ( plus_plus_int @ SY359 @ SY360 ) @ SV82 )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY359 @ SV82 ) @ ( add_pow_a_b_int @ r @ SY360 @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(769,plain,
! [SV83: partia1833973666xt_a_b] :
( ( ! [SY361: set_a] :
( ~ ( locali425460998xt_a_b @ SV83 @ SY361 )
| ( ord_less_eq_set_a @ SY361 @ ( partia1066395285xt_a_b @ SV83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(770,plain,
! [SV84: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV84 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY362: set_a] :
( ~ ( ord_less_eq_set_a @ SY362 @ ( partia1066395285xt_a_b @ r ) )
| ( ord_less_eq_set_a @ ( set_add_a_b @ r @ SV84 @ SY362 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(771,plain,
! [SV85: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV85 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY363: set_a] :
( ~ ( ord_less_eq_set_a @ SY363 @ ( partia1066395285xt_a_b @ r ) )
| ( ord_less_eq_set_a @ ( set_add_a_b @ r @ SV85 @ SY363 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(772,plain,
! [SV86: a] :
( ( ~ ( member_a @ SV86 @ bot_bot_set_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(773,plain,
! [SV87: set_a] :
( ( ( ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 ) )
= ( SV87 = bot_bot_set_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(774,plain,
! [SV88: a > $o] :
( ( ( ( collect_a @ SV88 )
= bot_bot_set_a )
= ( ! [SY365: a] :
~ ( SV88 @ SY365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(775,plain,
! [SV89: a > $o] :
( ( ( bot_bot_set_a
= ( collect_a @ SV89 ) )
= ( ! [SY366: a] :
~ ( SV89 @ SY366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(776,plain,
! [SV90: set_a] :
( ( ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
= ( SV90 = bot_bot_set_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(777,plain,
! [SV91: set_a] :
( ( ord_less_eq_set_a @ bot_bot_set_a @ SV91 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(778,plain,
! [SV92: set_a] :
( ( ( minus_minus_set_a @ SV92 @ bot_bot_set_a )
= SV92 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(779,plain,
! [SV93: set_a] :
( ( ( minus_minus_set_a @ bot_bot_set_a @ SV93 )
= bot_bot_set_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(780,plain,
! [SV94: set_a] :
( ( ( minus_minus_set_a @ SV94 @ SV94 )
= bot_bot_set_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(781,plain,
! [SV95: a] :
( ( ~ ( member_a @ SV95 @ bot_bot_set_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(782,plain,
! [SV96: set_a] :
( ( ( SV96 != bot_bot_set_a )
| ! [SY367: a] :
~ ( member_a @ SY367 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(783,plain,
! [SV97: set_a] :
( ( ( member_a @ ( sK1_Y2 @ SV97 ) @ SV97 )
| ( SV97 = bot_bot_set_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(784,plain,
! [SV98: set_a] :
( ( ! [SY368: set_a] :
( ~ ( ord_less_eq_set_a @ SV98 @ SY368 )
| ! [SY369: a] :
( ~ ( member_a @ SY369 @ SV98 )
| ( member_a @ SY369 @ SY368 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(785,plain,
! [SV99: set_a] :
( ( ! [SY370: set_a] :
( ~ ( ord_less_eq_set_a @ SV99 @ SY370 )
| ! [SY371: a] :
( ~ ( member_a @ SY371 @ SV99 )
| ( member_a @ SY371 @ SY370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(786,plain,
( ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(787,plain,
( ( ~ ( member_a @ sK7_T @ s )
| ( ( mult_a_ring_ext_a_b @ r @ sK7_T @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
!= ( zero_a_b @ r ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(788,plain,
( ( ~ ( member_a @ sK6_T2 @ s )
| ( ( mult_a_ring_ext_a_b @ r @ sK6_T2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
!= ( zero_a_b @ r ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(789,plain,
! [SV100: set_a] :
( ( ! [SY372: set_a] :
( ~ ( ~ ( member_a @ ( sK2_X3 @ SY372 @ SV100 ) @ SV100 )
| ~ ~ ( member_a @ ( sK2_X3 @ SY372 @ SV100 ) @ SY372 ) )
| ( ord_less_eq_set_a @ SV100 @ SY372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(790,plain,
! [SV101: set_a] :
( ( ( ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 ) )
= ( SV101 != bot_bot_set_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(791,plain,
( ( ! [SV102: set_a] :
( ( ord_less_eq_set_a @ SV102 )
= ( ^ [SY374: set_a] :
! [SY375: a] :
( ~ ( member_a @ SY375 @ SV102 )
| ( member_a @ SY375 @ SY374 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[678]) ).
thf(792,plain,
( ( ord_less_eq_set_a
= ( ^ [SX0: set_a,SX1: set_a] :
! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ( member_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[678]) ).
thf(793,plain,
! [SV103: a] :
( ( ~ ( member_a @ SV103 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( ( ( add_a_b @ r @ ( sK8_X3 @ SV103 ) @ SV103 )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( sK8_X3 @ SV103 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(794,plain,
( ( ! [SV104: product_prod_a_a] :
( ( ^ [SY376: product_prod_a_a] : ( SV104 = SY376 ) )
= ( ^ [SY377: product_prod_a_a] :
~ ( ( ( product_fst_a_a @ SV104 )
!= ( product_fst_a_a @ SY377 ) )
| ( ( product_snd_a_a @ SV104 )
!= ( product_snd_a_a @ SY377 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[680]) ).
thf(795,plain,
( ( ( ^ [SX0: product_prod_a_a,SX1: product_prod_a_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: product_prod_a_a,SX1: product_prod_a_a] :
~ ( ( ( product_fst_a_a @ SX0 )
!= ( product_fst_a_a @ SX1 ) )
| ( ( product_snd_a_a @ SX0 )
!= ( product_snd_a_a @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[680]) ).
thf(796,plain,
! [SV105: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
| ( SV105 = bot_bot_set_a )
| ~ ( ~ ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 ) )
| ~ ( ~ ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 )
| ~ ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) )
| ( member_a @ ( zero_a_b @ r ) @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(797,plain,
! [SV106: a] :
( ( ~ ( member_a @ SV106 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( ~ ( member_a @ ( sK9_X3 @ SV106 ) @ ( partia1066395285xt_a_b @ r ) )
| ~ ( ( ( add_a_b @ r @ SV106 @ ( sK9_X3 @ SV106 ) )
!= ( sK9_X3 @ SV106 ) ) ) )
| ( SV106
= ( zero_a_b @ r ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(798,plain,
! [SV107: a] :
( ( ~ ( member_a @ SV107 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( ( ( add_a_b @ r @ SV107 @ ( sK10_X3 @ SV107 ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( sK10_X3 @ SV107 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(799,plain,
! [SV108: a,SV1: a] :
( ( ( SV1 != SV108 )
| ! [SY378: a] :
( ( add_a_b @ r @ SY378 @ SV1 )
= ( add_a_b @ r @ SY378 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(800,plain,
! [SV109: a,SV2: a] :
( ( ( SV2 != SV109 )
| ! [SY379: a] :
( ( a_minus_a_b @ r @ SY379 @ SV2 )
= ( a_minus_a_b @ r @ SY379 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(801,plain,
! [SV3: a] :
( ( ( ~ ( member_a @ SV3 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY254: a] :
( ~ ( member_a @ SY254 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY255: a] :
( ~ ( member_a @ SY255 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV3 @ SY254 ) @ SY255 )
= ( mult_a_ring_ext_a_b @ r @ SV3 @ ( mult_a_ring_ext_a_b @ r @ SY254 @ SY255 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[686]) ).
thf(802,plain,
! [SV4: a] :
( ( ( ~ ( member_a @ SV4 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY256: a] :
( ~ ( member_a @ SY256 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SV4 @ SY256 )
= ( mult_a_ring_ext_a_b @ r @ SY256 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(803,plain,
! [SV5: a] :
( ( ( ~ ( member_a @ SV5 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY257: a] :
( ~ ( member_a @ SY257 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY258: a] :
( ~ ( member_a @ SY258 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SV5 @ ( mult_a_ring_ext_a_b @ r @ SY257 @ SY258 ) )
= ( mult_a_ring_ext_a_b @ r @ SY257 @ ( mult_a_ring_ext_a_b @ r @ SV5 @ SY258 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[688]) ).
thf(804,plain,
! [SV6: a] :
( ( ( ~ ( member_a @ SV6 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY259: a] :
( ~ ( member_a @ SY259 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY260: a] :
( ~ ( member_a @ SY260 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( add_a_b @ r @ SV6 @ SY259 ) @ SY260 )
= ( add_a_b @ r @ SV6 @ ( add_a_b @ r @ SY259 @ SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(805,plain,
! [SV7: a] :
( ( ( ~ ( member_a @ SV7 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY261: a] :
( ~ ( member_a @ SY261 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV7 @ SY261 )
= ( add_a_b @ r @ SY261 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[690]) ).
thf(806,plain,
! [SV8: a] :
( ( ( ~ ( member_a @ SV8 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY262: a] :
( ~ ( member_a @ SY262 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY263: a] :
( ~ ( member_a @ SY263 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV8 @ ( add_a_b @ r @ SY262 @ SY263 ) )
= ( add_a_b @ r @ SY262 @ ( add_a_b @ r @ SV8 @ SY263 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(807,plain,
! [SV9: a] :
( ( ( ~ ( member_a @ SV9 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY264: a] :
( ~ ( member_a @ SY264 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY265: a] :
( ~ ( member_a @ SY265 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( add_a_b @ r @ SV9 @ SY264 ) @ SY265 )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV9 @ SY265 ) @ ( mult_a_ring_ext_a_b @ r @ SY264 @ SY265 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[692]) ).
thf(808,plain,
! [SV10: a] :
( ( ( ~ ( member_a @ SV10 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY266: a] :
( ~ ( member_a @ SY266 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY267: a] :
( ~ ( member_a @ SY267 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SY267 @ ( add_a_b @ r @ SV10 @ SY266 ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SY267 @ SV10 ) @ ( mult_a_ring_ext_a_b @ r @ SY267 @ SY266 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[693]) ).
thf(809,plain,
! [SV110: a,SV11: a] :
( ( ~ ( member_a @ SV11 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV110 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY380: a] :
( ~ ( member_a @ SY380 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY381: a] :
( ~ ( member_a @ SY381 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ SV11 @ SY380 ) @ SV110 ) @ SY381 )
= ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ ( add_a_b @ r @ SV11 @ SV110 ) @ SY380 ) @ SY381 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(810,plain,
! [SV12: a] :
( ( ( ~ ( member_a @ SV12 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY271: a] :
( ~ ( member_a @ SY271 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY272: a] :
( ~ ( member_a @ SY272 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ SY272 @ SV12 ) @ SY271 )
= ( a_minus_a_b @ r @ SY272 @ ( add_a_b @ r @ SV12 @ SY271 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[695]) ).
thf(811,plain,
( ( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ~ ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[696]) ).
thf(812,plain,
! [SV13: a] :
( ( ( ~ ( member_a @ SV13 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY273: a] :
( ~ ( member_a @ SY273 @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( a_minus_a_b @ r @ SV13 @ SY273 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(813,plain,
! [SV14: a] :
( ( ( ~ ( member_a @ SV14 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY274: a] :
( ~ ( member_a @ SY274 @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( add_a_b @ r @ SV14 @ SY274 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[698]) ).
thf(814,plain,
! [SV15: a] :
( ( ( ~ ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY275: a] :
( ~ ( member_a @ SY275 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY276: a] :
( ~ ( member_a @ SY276 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SY275 @ SV15 )
= ( add_a_b @ r @ SY276 @ SV15 ) )
= ( SY275 = SY276 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[699]) ).
thf(815,plain,
! [SV16: a] :
( ( ( ~ ( member_a @ SV16 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY277: a] :
( ~ ( member_a @ SY277 @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( mult_a_ring_ext_a_b @ r @ SV16 @ SY277 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[700]) ).
thf(816,plain,
! [SV111: a,SV17: a] :
( ( ( a_minus_a_b @ r @ SV17 @ SV111 )
= ( add_a_b @ r @ SV17 @ ( a_inv_a_b @ r @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(817,plain,
! [SV112: product_prod_a_a,SV18: product_prod_a_a] :
( ( ( ( product_fst_a_a @ SV18 )
!= ( product_fst_a_a @ SV112 ) )
| ( ( product_snd_a_a @ SV18 )
!= ( product_snd_a_a @ SV112 ) )
| ( SV18 = SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(818,plain,
! [SV19: a > a > $o] :
( ( ( ! [SY280: product_prod_a_a] :
~ ( SV19 @ ( product_snd_a_a @ SY280 ) @ ( product_fst_a_a @ SY280 ) ) )
= $true )
| ( ( SV19 @ ( sK12_SY249 @ SV19 ) @ ( sK11_X3 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[703]) ).
thf(819,plain,
! [SV113: product_prod_a_a,SV20: product_prod_a_a] :
( ( ( ( product_fst_a_a @ SV20 )
!= ( product_fst_a_a @ SV113 ) )
| ( ( product_snd_a_a @ SV20 )
!= ( product_snd_a_a @ SV113 ) )
| ( SV20 = SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(820,plain,
! [SV21: a] :
( ( ( ~ ( member_a @ SV21 @ s ) )
= $true )
| ( ( ! [SY282: a] :
( ~ ( member_a @ SY282 @ s )
| ( member_a @ ( mult_a_ring_ext_a_b @ r @ SV21 @ SY282 ) @ s ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[705]) ).
thf(821,plain,
! [SV114: set_a,SV23: partia1833973666xt_a_b] :
( ( ~ ( locali425460998xt_a_b @ SV23 @ SV114 )
| ! [SY382: a] :
( ~ ( member_a @ SY382 @ SV114 )
| ! [SY383: a] :
( ~ ( member_a @ SY383 @ SV114 )
| ( member_a @ ( mult_a_ring_ext_a_b @ SV23 @ SY382 @ SY383 ) @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(822,plain,
! [SV115: partia1833973666xt_a_b] :
( ( ( a_minus_a_b @ SV115 )
= ( ^ [SY384: a,SY385: a] : ( add_a_b @ SV115 @ SY384 @ ( a_inv_a_b @ SV115 @ SY385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(823,plain,
! [SV25: set_a] :
( ( ( ~ ( additi2104487374up_a_b @ SV25 @ r ) )
= $true )
| ( ( ! [SY288: set_a] :
( ~ ( additi2104487374up_a_b @ SY288 @ r )
| ( additi2104487374up_a_b @ ( set_add_a_b @ r @ SV25 @ SY288 ) @ r ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[711]) ).
thf(824,plain,
! [SV116: a > $o,SV26: a] :
( ( ( member_a @ SV26 @ ( collect_a @ SV116 ) )
= ( SV116 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(825,plain,
! [SV117: a,SV28: a] :
( ( ( ( add_a_b @ r @ SV28 @ SV117 )
!= ( zero_a_b @ r ) )
| ! [SY386: a] :
( ( ( add_a_b @ r @ SV117 @ SY386 )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ SV117 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV28 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SY386 @ ( partia1066395285xt_a_b @ r ) )
| ( SV28 = SY386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(826,plain,
! [SV118: a,SV29: a] :
( ( ( ( add_a_b @ r @ SV29 @ SV118 )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ SV29 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV118 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV118 @ SV29 )
= ( zero_a_b @ r ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(827,plain,
! [SV30: a] :
( ( ( ~ ( member_a @ SV30 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY294: a] :
( ~ ( member_a @ SY294 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SV30 @ ( a_inv_a_b @ r @ SY294 ) )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV30 @ SY294 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[716]) ).
thf(828,plain,
! [SV31: a] :
( ( ( ~ ( member_a @ SV31 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY295: a] :
( ~ ( member_a @ SY295 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( a_inv_a_b @ r @ SV31 ) @ SY295 )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV31 @ SY295 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[717]) ).
thf(829,plain,
! [SV32: a] :
( ( ( ~ ( member_a @ SV32 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY296: a] :
( ~ ( member_a @ SY296 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV32 @ ( add_a_b @ r @ ( a_inv_a_b @ r @ SV32 ) @ SY296 ) )
= SY296 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[718]) ).
thf(830,plain,
! [SV33: a] :
( ( ( ~ ( member_a @ SV33 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY297: a] :
( ~ ( member_a @ SY297 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV33 ) @ ( add_a_b @ r @ SV33 @ SY297 ) )
= SY297 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(831,plain,
! [SV34: a] :
( ( ( ~ ( member_a @ SV34 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY298: a] :
( ~ ( member_a @ SY298 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( add_a_b @ r @ SV34 @ SY298 ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV34 ) @ ( a_inv_a_b @ r @ SY298 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[720]) ).
thf(832,plain,
! [SV35: a] :
( ( ( ~ ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY299: a] :
( ~ ( member_a @ SY299 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY300: a] :
( ~ ( member_a @ SY300 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SY299 @ ( a_inv_a_b @ r @ SY300 ) )
= SV35 )
= ( SY299
= ( add_a_b @ r @ SV35 @ SY300 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(833,plain,
! [SV36: a] :
( ( ( ~ ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY301: a] :
( ~ ( member_a @ SY301 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY302: a] :
( ~ ( member_a @ SY302 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV36
= ( add_a_b @ r @ SY301 @ ( a_inv_a_b @ r @ SY302 ) ) )
= ( SY301
= ( add_a_b @ r @ SV36 @ SY302 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(834,plain,
! [SV37: a] :
( ( ( ~ ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY303: a] :
( ~ ( member_a @ SY303 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY304: a] :
( ~ ( member_a @ SY304 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SY303 ) @ SY304 )
= SV37 )
= ( SY304
= ( add_a_b @ r @ SY303 @ SV37 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[723]) ).
thf(835,plain,
! [SV38: a] :
( ( ( ~ ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY305: a] :
( ~ ( member_a @ SY305 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY306: a] :
( ~ ( member_a @ SY306 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SY305 ) @ SY306 ) )
= ( SY306
= ( add_a_b @ r @ SY305 @ SV38 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[724]) ).
thf(836,plain,
! [SV39: a] :
( ( ( ~ ( member_a @ SV39 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY307: a] :
( ~ ( member_a @ SY307 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( add_a_b @ r @ SV39 @ SY307 ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SY307 ) @ ( a_inv_a_b @ r @ SV39 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[725]) ).
thf(837,plain,
! [SV119: a,SV40: a] :
( ( ! [SY387: a] :
( ( ( add_a_b @ r @ SV40 @ SV119 )
!= SY387 )
| ~ ( member_a @ SV40 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV119 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SY387 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV40 ) @ SY387 )
= SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(838,plain,
! [SV41: a] :
( ( ( ~ ( member_a @ SV41 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY310: a] :
( ~ ( member_a @ SY310 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV41 @ SY310 )
!= ( zero_a_b @ r ) )
| ( SV41
= ( a_inv_a_b @ r @ SY310 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(839,plain,
! [SV42: a] :
( ( ( ~ ( member_a @ SV42 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( add_a_b @ r @ SV42 @ ( a_inv_a_b @ r @ SV42 ) )
= ( zero_a_b @ r ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[728]) ).
thf(840,plain,
! [SV120: a,SV43: a] :
( ( ( ( add_a_b @ r @ SV43 @ SV120 )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ SV120 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV43 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ SV120 )
= SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(841,plain,
! [SV44: a] :
( ( ( ~ ( member_a @ SV44 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV44 ) @ SV44 )
= ( zero_a_b @ r ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(842,plain,
! [SV45: a] :
( ( ( ~ ( member_a @ SV45 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY312: a] :
( ~ ( member_a @ SY312 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( add_a_b @ r @ SV45 @ SY312 ) )
= ( a_minus_a_b @ r @ ( a_inv_a_b @ r @ SV45 ) @ SY312 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(843,plain,
! [SV46: a] :
( ( ( ~ ( member_a @ SV46 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( a_inv_a_b @ r @ ( a_inv_a_b @ r @ SV46 ) )
= SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(844,plain,
! [SV47: a] :
( ( ( ~ ( member_a @ SV47 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( member_a @ ( a_inv_a_b @ r @ SV47 ) @ ( partia1066395285xt_a_b @ r ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(845,plain,
! [SV48: a] :
( ( ( ~ ( member_a @ SV48 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( mult_a_ring_ext_a_b @ r @ SV48 @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(846,plain,
! [SV49: a] :
( ( ( ~ ( member_a @ SV49 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( mult_a_ring_ext_a_b @ r @ ( zero_a_b @ r ) @ SV49 )
= ( zero_a_b @ r ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(847,plain,
! [SV50: a] :
( ( ( ~ ( member_a @ SV50 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( add_a_b @ r @ SV50 @ ( zero_a_b @ r ) )
= SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(848,plain,
! [SV51: a] :
( ( ( ~ ( member_a @ SV51 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( add_a_b @ r @ ( zero_a_b @ r ) @ SV51 )
= SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(849,plain,
! [SV52: a] :
( ( ( ~ ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY313: a] :
( ~ ( member_a @ SY313 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV52
= ( add_a_b @ r @ SY313 @ SV52 ) )
= ( SY313
= ( zero_a_b @ r ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[738]) ).
thf(850,plain,
! [SV53: a] :
( ( ( ~ ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY314: a] :
( ~ ( member_a @ SY314 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SY314 @ SV53 )
= SV53 )
= ( SY314
= ( zero_a_b @ r ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[739]) ).
thf(851,plain,
! [SV54: a] :
( ( ( ~ ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY315: a] :
( ~ ( member_a @ SY315 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV54
= ( add_a_b @ r @ SV54 @ SY315 ) )
= ( SY315
= ( zero_a_b @ r ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[740]) ).
thf(852,plain,
! [SV55: a] :
( ( ( ~ ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY316: a] :
( ~ ( member_a @ SY316 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SV55 @ SY316 )
= SV55 )
= ( SY316
= ( zero_a_b @ r ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[741]) ).
thf(853,plain,
! [SV56: a] :
( ( ( ~ ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( ( a_inv_a_b @ r @ SV56 )
= ( zero_a_b @ r ) )
= ( SV56
= ( zero_a_b @ r ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(854,plain,
! [SV57: a] :
( ( ( ~ ( member_a @ SV57 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY317: int] :
( ( add_pow_a_b_int @ r @ SY317 @ ( a_inv_a_b @ r @ SV57 ) )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ SY317 @ SV57 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(855,plain,
! [SV58: partia1833973666xt_a_b] :
( ( ( ~ ( semiring_a_b @ SV58 ) )
= $true )
| ( ( ! [SY318: a] :
( ~ ( member_a @ SY318 @ ( partia1066395285xt_a_b @ SV58 ) )
| ( ( add_a_b @ SV58 @ SY318 @ ( zero_a_b @ SV58 ) )
= SY318 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(856,plain,
! [SV59: partia1833973666xt_a_b] :
( ( ( ~ ( semiring_a_b @ SV59 ) )
= $true )
| ( ( ! [SY319: a] :
( ~ ( member_a @ SY319 @ ( partia1066395285xt_a_b @ SV59 ) )
| ( ( add_a_b @ SV59 @ ( zero_a_b @ SV59 ) @ SY319 )
= SY319 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(857,plain,
! [SV60: partia1833973666xt_a_b] :
( ( ( ~ ( semiring_a_b @ SV60 ) )
= $true )
| ( ( ! [SY320: a] :
( ~ ( member_a @ SY320 @ ( partia1066395285xt_a_b @ SV60 ) )
| ( ( mult_a_ring_ext_a_b @ SV60 @ ( zero_a_b @ SV60 ) @ SY320 )
= ( zero_a_b @ SV60 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(858,plain,
! [SV61: partia1833973666xt_a_b] :
( ( ( ~ ( semiring_a_b @ SV61 ) )
= $true )
| ( ( ! [SY321: a] :
( ~ ( member_a @ SY321 @ ( partia1066395285xt_a_b @ SV61 ) )
| ( ( mult_a_ring_ext_a_b @ SV61 @ SY321 @ ( zero_a_b @ SV61 ) )
= ( zero_a_b @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[747]) ).
thf(859,plain,
! [SV121: a,SV62: partia1833973666xt_a_b] :
( ( ~ ( semiring_a_b @ SV62 )
| ~ ( member_a @ SV121 @ ( partia1066395285xt_a_b @ SV62 ) )
| ! [SY388: a] :
( ~ ( member_a @ SY388 @ ( partia1066395285xt_a_b @ SV62 ) )
| ! [SY389: a] :
( ~ ( member_a @ SY389 @ ( partia1066395285xt_a_b @ SV62 ) )
| ( ( mult_a_ring_ext_a_b @ SV62 @ SY389 @ ( add_a_b @ SV62 @ SV121 @ SY388 ) )
= ( add_a_b @ SV62 @ ( mult_a_ring_ext_a_b @ SV62 @ SY389 @ SV121 ) @ ( mult_a_ring_ext_a_b @ SV62 @ SY389 @ SY388 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(860,plain,
! [SV63: a] :
( ( ( ~ ( member_a @ SV63 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY325: a] :
( ~ ( member_a @ SY325 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY326: int] :
( ( mult_a_ring_ext_a_b @ r @ ( add_pow_a_b_int @ r @ SY326 @ SV63 ) @ SY325 )
= ( add_pow_a_b_int @ r @ SY326 @ ( mult_a_ring_ext_a_b @ r @ SV63 @ SY325 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[749]) ).
thf(861,plain,
! [SV64: a] :
( ( ( ~ ( member_a @ SV64 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY327: a] :
( ~ ( member_a @ SY327 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY328: int] :
( ( mult_a_ring_ext_a_b @ r @ SV64 @ ( add_pow_a_b_int @ r @ SY328 @ SY327 ) )
= ( add_pow_a_b_int @ r @ SY328 @ ( mult_a_ring_ext_a_b @ r @ SV64 @ SY327 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(862,plain,
! [SV65: a] :
( ( ( ~ ( member_a @ SV65 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY329: a] :
( ~ ( member_a @ SY329 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY330: int] :
( ( add_pow_a_b_int @ r @ SY330 @ ( add_a_b @ r @ SV65 @ SY329 ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY330 @ SV65 ) @ ( add_pow_a_b_int @ r @ SY330 @ SY329 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(863,plain,
! [SV122: a,SV66: a] :
( ( ( ( add_a_b @ r @ SV66 @ SV122 )
!= ( add_a_b @ r @ SV122 @ SV66 ) )
| ~ ( member_a @ SV66 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV122 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY390: int] :
( ( add_pow_a_b_int @ r @ SY390 @ ( add_a_b @ r @ SV66 @ SV122 ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY390 @ SV66 ) @ ( add_pow_a_b_int @ r @ SY390 @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(864,plain,
! [SV67: a] :
( ( ( ~ ( member_a @ SV67 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY333: int] : ( member_a @ ( add_pow_a_b_int @ r @ SY333 @ SV67 ) @ ( partia1066395285xt_a_b @ r ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(865,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(866,plain,
! [SV124: set_a,SV69: partia1833973666xt_a_b] :
( ( ~ ( locali807230110ng_a_b @ SV69 @ SV124 )
| ( locali880295127ng_a_b @ SV69 @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(867,plain,
! [SV125: set_a,SV70: partia1833973666xt_a_b] :
( ( ~ ( locali880295127ng_a_b @ SV70 @ SV125 )
| ( locali425460998xt_a_b @ SV70 @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(868,plain,
! [SV126: set_a,SV71: partia1833973666xt_a_b] :
( ( ~ ( locali1648887798ac_a_b @ SV71 @ SV126 )
| ( locali807230110ng_a_b @ SV71 @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(869,plain,
! [SV127: a,SV72: partia1833973666xt_a_b] :
( ( ~ ( semiring_a_b @ SV72 )
| ~ ( member_a @ SV127 @ ( partia1066395285xt_a_b @ SV72 ) )
| ! [SY391: a] :
( ~ ( member_a @ SY391 @ ( partia1066395285xt_a_b @ SV72 ) )
| ! [SY392: a] :
( ~ ( member_a @ SY392 @ ( partia1066395285xt_a_b @ SV72 ) )
| ( ( mult_a_ring_ext_a_b @ SV72 @ ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ SY391 ) @ SY392 )
= ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ ( mult_a_ring_ext_a_b @ SV72 @ SY391 @ SY392 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(870,plain,
! [SV73: partia1833973666xt_a_b] :
( ( ( ~ ( semiring_a_b @ SV73 ) )
= $true )
| ( ( ! [SY341: a] :
( ~ ( member_a @ SY341 @ ( partia1066395285xt_a_b @ SV73 ) )
| ! [SY342: a] :
( ~ ( member_a @ SY342 @ ( partia1066395285xt_a_b @ SV73 ) )
| ( member_a @ ( mult_a_ring_ext_a_b @ SV73 @ SY341 @ SY342 ) @ ( partia1066395285xt_a_b @ SV73 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[759]) ).
thf(871,plain,
! [SV128: a,SV74: partia1833973666xt_a_b] :
( ( ~ ( semiring_a_b @ SV74 )
| ~ ( member_a @ SV128 @ ( partia1066395285xt_a_b @ SV74 ) )
| ! [SY393: a] :
( ~ ( member_a @ SY393 @ ( partia1066395285xt_a_b @ SV74 ) )
| ! [SY394: a] :
( ~ ( member_a @ SY394 @ ( partia1066395285xt_a_b @ SV74 ) )
| ( ( add_a_b @ SV74 @ SV128 @ ( add_a_b @ SV74 @ SY393 @ SY394 ) )
= ( add_a_b @ SV74 @ SY393 @ ( add_a_b @ SV74 @ SV128 @ SY394 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(872,plain,
! [SV75: partia1833973666xt_a_b] :
( ( ( ~ ( semiring_a_b @ SV75 ) )
= $true )
| ( ( ! [SY346: a] :
( ~ ( member_a @ SY346 @ ( partia1066395285xt_a_b @ SV75 ) )
| ! [SY347: a] :
( ~ ( member_a @ SY347 @ ( partia1066395285xt_a_b @ SV75 ) )
| ( ( add_a_b @ SV75 @ SY346 @ SY347 )
= ( add_a_b @ SV75 @ SY347 @ SY346 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(873,plain,
! [SV129: a,SV76: partia1833973666xt_a_b] :
( ( ~ ( semiring_a_b @ SV76 )
| ~ ( member_a @ SV129 @ ( partia1066395285xt_a_b @ SV76 ) )
| ! [SY395: a] :
( ~ ( member_a @ SY395 @ ( partia1066395285xt_a_b @ SV76 ) )
| ! [SY396: a] :
( ~ ( member_a @ SY396 @ ( partia1066395285xt_a_b @ SV76 ) )
| ( ( add_a_b @ SV76 @ ( add_a_b @ SV76 @ SV129 @ SY395 ) @ SY396 )
= ( add_a_b @ SV76 @ SV129 @ ( add_a_b @ SV76 @ SY395 @ SY396 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(874,plain,
! [SV77: partia1833973666xt_a_b] :
( ( ( ~ ( semiring_a_b @ SV77 ) )
= $true )
| ( ( ! [SY351: a] :
( ~ ( member_a @ SY351 @ ( partia1066395285xt_a_b @ SV77 ) )
| ! [SY352: a] :
( ~ ( member_a @ SY352 @ ( partia1066395285xt_a_b @ SV77 ) )
| ( member_a @ ( add_a_b @ SV77 @ SY351 @ SY352 ) @ ( partia1066395285xt_a_b @ SV77 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(875,plain,
! [SV78: partia1833973666xt_a_b] :
( ( ( ~ ( semiring_a_b @ SV78 ) )
= $true )
| ( ( member_a @ ( zero_a_b @ SV78 ) @ ( partia1066395285xt_a_b @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(876,plain,
! [SV130: a,SV79: partia1833973666xt_a_b] :
( ( ~ ( semiring_a_b @ SV79 )
| ~ ( member_a @ SV130 @ ( partia1066395285xt_a_b @ SV79 ) )
| ! [SY397: a] :
( ~ ( member_a @ SY397 @ ( partia1066395285xt_a_b @ SV79 ) )
| ! [SY398: a] :
( ~ ( member_a @ SY398 @ ( partia1066395285xt_a_b @ SV79 ) )
| ( ( mult_a_ring_ext_a_b @ SV79 @ ( add_a_b @ SV79 @ SV130 @ SY397 ) @ SY398 )
= ( add_a_b @ SV79 @ ( mult_a_ring_ext_a_b @ SV79 @ SV130 @ SY398 ) @ ( mult_a_ring_ext_a_b @ SV79 @ SY397 @ SY398 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(877,plain,
! [SV80: a] :
( ( ( ~ ( member_a @ SV80 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY356: int,SY357: int] :
( ( add_pow_a_b_int @ r @ ( minus_minus_int @ SY356 @ SY357 ) @ SV80 )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY356 @ SV80 ) @ ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ SY357 @ SV80 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(878,plain,
! [SV81: a] :
( ( ( ~ ( member_a @ SV81 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY358: int] :
( ( add_pow_a_b_int @ r @ ( uminus_uminus_int @ SY358 ) @ SV81 )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ SY358 @ SV81 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(879,plain,
! [SV82: a] :
( ( ( ~ ( member_a @ SV82 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY359: int,SY360: int] :
( ( add_pow_a_b_int @ r @ ( plus_plus_int @ SY359 @ SY360 ) @ SV82 )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY359 @ SV82 ) @ ( add_pow_a_b_int @ r @ SY360 @ SV82 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(880,plain,
! [SV131: set_a,SV83: partia1833973666xt_a_b] :
( ( ~ ( locali425460998xt_a_b @ SV83 @ SV131 )
| ( ord_less_eq_set_a @ SV131 @ ( partia1066395285xt_a_b @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(881,plain,
! [SV84: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV84 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY362: set_a] :
( ~ ( ord_less_eq_set_a @ SY362 @ ( partia1066395285xt_a_b @ r ) )
| ( ord_less_eq_set_a @ ( set_add_a_b @ r @ SV84 @ SY362 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(882,plain,
! [SV85: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV85 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY363: set_a] :
( ~ ( ord_less_eq_set_a @ SY363 @ ( partia1066395285xt_a_b @ r ) )
| ( ord_less_eq_set_a @ ( set_add_a_b @ r @ SV85 @ SY363 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(883,plain,
! [SV86: a] :
( ( member_a @ SV86 @ bot_bot_set_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(884,plain,
! [SV87: set_a] :
( ( ~ ( ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 )
| ( SV87 = bot_bot_set_a ) )
| ~ ( ~ ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 )
| ( SV87 != bot_bot_set_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[773]) ).
thf(885,plain,
! [SV87: set_a] :
( ( ( ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 ) )
= ( SV87 = bot_bot_set_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[773]) ).
thf(886,plain,
! [SV88: a > $o] :
( ( ~ ( ( ( collect_a @ SV88 )
= bot_bot_set_a )
| ! [SY365: a] :
~ ( SV88 @ SY365 ) )
| ~ ( ( ( collect_a @ SV88 )
!= bot_bot_set_a )
| ~ ! [SY365: a] :
~ ( SV88 @ SY365 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[774]) ).
thf(887,plain,
! [SV88: a > $o] :
( ( ( ( collect_a @ SV88 )
= bot_bot_set_a )
= ( ! [SY365: a] :
~ ( SV88 @ SY365 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[774]) ).
thf(888,plain,
! [SV89: a > $o] :
( ( ~ ( ( bot_bot_set_a
= ( collect_a @ SV89 ) )
| ! [SY366: a] :
~ ( SV89 @ SY366 ) )
| ~ ( ( bot_bot_set_a
!= ( collect_a @ SV89 ) )
| ~ ! [SY366: a] :
~ ( SV89 @ SY366 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[775]) ).
thf(889,plain,
! [SV89: a > $o] :
( ( ( bot_bot_set_a
= ( collect_a @ SV89 ) )
= ( ! [SY366: a] :
~ ( SV89 @ SY366 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[775]) ).
thf(890,plain,
! [SV90: set_a] :
( ( ~ ( ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
| ( SV90 = bot_bot_set_a ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
| ( SV90 != bot_bot_set_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[776]) ).
thf(891,plain,
! [SV90: set_a] :
( ( ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
= ( SV90 = bot_bot_set_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[776]) ).
thf(892,plain,
! [SV95: a] :
( ( member_a @ SV95 @ bot_bot_set_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(893,plain,
! [SV96: set_a] :
( ( ( SV96 != bot_bot_set_a )
= $true )
| ( ( ! [SY367: a] :
~ ( member_a @ SY367 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[782]) ).
thf(894,plain,
! [SV97: set_a] :
( ( ( member_a @ ( sK1_Y2 @ SV97 ) @ SV97 )
= $true )
| ( ( SV97 = bot_bot_set_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[783]) ).
thf(895,plain,
! [SV132: set_a,SV98: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV98 @ SV132 )
| ! [SY399: a] :
( ~ ( member_a @ SY399 @ SV98 )
| ( member_a @ SY399 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(896,plain,
! [SV133: set_a,SV99: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV99 @ SV133 )
| ! [SY400: a] :
( ~ ( member_a @ SY400 @ SV99 )
| ( member_a @ SY400 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(897,plain,
( ( ~ ( member_a @ sK7_T @ s ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[787]) ).
thf(898,plain,
( ( ( mult_a_ring_ext_a_b @ r @ sK7_T @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
!= ( zero_a_b @ r ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[787]) ).
thf(899,plain,
( ( ~ ( member_a @ sK6_T2 @ s ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[788]) ).
thf(900,plain,
( ( ( mult_a_ring_ext_a_b @ r @ sK6_T2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
!= ( zero_a_b @ r ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[788]) ).
thf(901,plain,
! [SV100: set_a,SV134: set_a] :
( ( ~ ( ~ ( member_a @ ( sK2_X3 @ SV134 @ SV100 ) @ SV100 )
| ~ ~ ( member_a @ ( sK2_X3 @ SV134 @ SV100 ) @ SV134 ) )
| ( ord_less_eq_set_a @ SV100 @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(902,plain,
! [SV101: set_a] :
( ( ~ ( ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 )
| ( SV101 != bot_bot_set_a ) )
| ~ ( ~ ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 )
| ~ ( ( SV101 != bot_bot_set_a ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[790]) ).
thf(903,plain,
! [SV101: set_a] :
( ( ( ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 ) )
= ( SV101 != bot_bot_set_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[790]) ).
thf(904,plain,
! [SV135: set_a] :
( ( ( ord_less_eq_set_a @ SV135 )
= ( ^ [SY401: set_a] :
! [SY402: a] :
( ~ ( member_a @ SY402 @ SV135 )
| ( member_a @ SY402 @ SY401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(905,plain,
! [SV103: a] :
( ( ( ~ ( member_a @ SV103 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ~ ( ( ( add_a_b @ r @ ( sK8_X3 @ SV103 ) @ SV103 )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( sK8_X3 @ SV103 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[793]) ).
thf(906,plain,
! [SV136: product_prod_a_a] :
( ( ( ^ [SY403: product_prod_a_a] : ( SV136 = SY403 ) )
= ( ^ [SY404: product_prod_a_a] :
~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SY404 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SY404 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(907,plain,
! [SV105: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( SV105 = bot_bot_set_a )
| ~ ( ~ ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 ) )
| ~ ( ~ ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 )
| ~ ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) )
| ( member_a @ ( zero_a_b @ r ) @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(908,plain,
! [SV106: a] :
( ( ( ~ ( member_a @ SV106 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ~ ( ~ ( member_a @ ( sK9_X3 @ SV106 ) @ ( partia1066395285xt_a_b @ r ) )
| ~ ( ( ( add_a_b @ r @ SV106 @ ( sK9_X3 @ SV106 ) )
!= ( sK9_X3 @ SV106 ) ) ) )
| ( SV106
= ( zero_a_b @ r ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[797]) ).
thf(909,plain,
! [SV107: a] :
( ( ( ~ ( member_a @ SV107 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ~ ( ( ( add_a_b @ r @ SV107 @ ( sK10_X3 @ SV107 ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( sK10_X3 @ SV107 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(910,plain,
! [SV108: a,SV1: a] :
( ( ( SV1 != SV108 )
= $true )
| ( ( ! [SY378: a] :
( ( add_a_b @ r @ SY378 @ SV1 )
= ( add_a_b @ r @ SY378 @ SV108 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(911,plain,
! [SV109: a,SV2: a] :
( ( ( SV2 != SV109 )
= $true )
| ( ( ! [SY379: a] :
( ( a_minus_a_b @ r @ SY379 @ SV2 )
= ( a_minus_a_b @ r @ SY379 @ SV109 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[800]) ).
thf(912,plain,
! [SV3: a] :
( ( ( member_a @ SV3 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY254: a] :
( ~ ( member_a @ SY254 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY255: a] :
( ~ ( member_a @ SY255 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV3 @ SY254 ) @ SY255 )
= ( mult_a_ring_ext_a_b @ r @ SV3 @ ( mult_a_ring_ext_a_b @ r @ SY254 @ SY255 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[801]) ).
thf(913,plain,
! [SV4: a] :
( ( ( member_a @ SV4 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY256: a] :
( ~ ( member_a @ SY256 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SV4 @ SY256 )
= ( mult_a_ring_ext_a_b @ r @ SY256 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(914,plain,
! [SV5: a] :
( ( ( member_a @ SV5 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY257: a] :
( ~ ( member_a @ SY257 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY258: a] :
( ~ ( member_a @ SY258 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SV5 @ ( mult_a_ring_ext_a_b @ r @ SY257 @ SY258 ) )
= ( mult_a_ring_ext_a_b @ r @ SY257 @ ( mult_a_ring_ext_a_b @ r @ SV5 @ SY258 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(915,plain,
! [SV6: a] :
( ( ( member_a @ SV6 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY259: a] :
( ~ ( member_a @ SY259 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY260: a] :
( ~ ( member_a @ SY260 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( add_a_b @ r @ SV6 @ SY259 ) @ SY260 )
= ( add_a_b @ r @ SV6 @ ( add_a_b @ r @ SY259 @ SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(916,plain,
! [SV7: a] :
( ( ( member_a @ SV7 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY261: a] :
( ~ ( member_a @ SY261 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV7 @ SY261 )
= ( add_a_b @ r @ SY261 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(917,plain,
! [SV8: a] :
( ( ( member_a @ SV8 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY262: a] :
( ~ ( member_a @ SY262 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY263: a] :
( ~ ( member_a @ SY263 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV8 @ ( add_a_b @ r @ SY262 @ SY263 ) )
= ( add_a_b @ r @ SY262 @ ( add_a_b @ r @ SV8 @ SY263 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(918,plain,
! [SV9: a] :
( ( ( member_a @ SV9 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY264: a] :
( ~ ( member_a @ SY264 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY265: a] :
( ~ ( member_a @ SY265 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( add_a_b @ r @ SV9 @ SY264 ) @ SY265 )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV9 @ SY265 ) @ ( mult_a_ring_ext_a_b @ r @ SY264 @ SY265 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(919,plain,
! [SV10: a] :
( ( ( member_a @ SV10 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY266: a] :
( ~ ( member_a @ SY266 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY267: a] :
( ~ ( member_a @ SY267 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SY267 @ ( add_a_b @ r @ SV10 @ SY266 ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SY267 @ SV10 ) @ ( mult_a_ring_ext_a_b @ r @ SY267 @ SY266 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(920,plain,
! [SV110: a,SV11: a] :
( ( ( ~ ( member_a @ SV11 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ~ ( member_a @ SV110 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY380: a] :
( ~ ( member_a @ SY380 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY381: a] :
( ~ ( member_a @ SY381 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ SV11 @ SY380 ) @ SV110 ) @ SY381 )
= ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ ( add_a_b @ r @ SV11 @ SV110 ) @ SY380 ) @ SY381 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[809]) ).
thf(921,plain,
! [SV12: a] :
( ( ( member_a @ SV12 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY271: a] :
( ~ ( member_a @ SY271 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY272: a] :
( ~ ( member_a @ SY272 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ SY272 @ SV12 ) @ SY271 )
= ( a_minus_a_b @ r @ SY272 @ ( add_a_b @ r @ SV12 @ SY271 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(922,plain,
( ( ( ~ ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ~ ( member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ) )
= $true )
| ( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[811]) ).
thf(923,plain,
! [SV13: a] :
( ( ( member_a @ SV13 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY273: a] :
( ~ ( member_a @ SY273 @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( a_minus_a_b @ r @ SV13 @ SY273 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(924,plain,
! [SV14: a] :
( ( ( member_a @ SV14 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY274: a] :
( ~ ( member_a @ SY274 @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( add_a_b @ r @ SV14 @ SY274 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(925,plain,
! [SV15: a] :
( ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY275: a] :
( ~ ( member_a @ SY275 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY276: a] :
( ~ ( member_a @ SY276 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SY275 @ SV15 )
= ( add_a_b @ r @ SY276 @ SV15 ) )
= ( SY275 = SY276 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(926,plain,
! [SV16: a] :
( ( ( member_a @ SV16 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY277: a] :
( ~ ( member_a @ SY277 @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( mult_a_ring_ext_a_b @ r @ SV16 @ SY277 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(927,plain,
! [SV112: product_prod_a_a,SV18: product_prod_a_a] :
( ( ( ( product_fst_a_a @ SV18 )
!= ( product_fst_a_a @ SV112 ) )
= $true )
| ( ( ( ( product_snd_a_a @ SV18 )
!= ( product_snd_a_a @ SV112 ) )
| ( SV18 = SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[817]) ).
thf(928,plain,
! [SV137: product_prod_a_a,SV19: a > a > $o] :
( ( ( ~ ( SV19 @ ( product_snd_a_a @ SV137 ) @ ( product_fst_a_a @ SV137 ) ) )
= $true )
| ( ( SV19 @ ( sK12_SY249 @ SV19 ) @ ( sK11_X3 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(929,plain,
! [SV113: product_prod_a_a,SV20: product_prod_a_a] :
( ( ( ( ( product_fst_a_a @ SV20 )
!= ( product_fst_a_a @ SV113 ) )
| ( ( product_snd_a_a @ SV20 )
!= ( product_snd_a_a @ SV113 ) ) )
= $true )
| ( ( SV20 = SV113 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[819]) ).
thf(930,plain,
! [SV21: a] :
( ( ( member_a @ SV21 @ s )
= $false )
| ( ( ! [SY282: a] :
( ~ ( member_a @ SY282 @ s )
| ( member_a @ ( mult_a_ring_ext_a_b @ r @ SV21 @ SY282 ) @ s ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(931,plain,
! [SV114: set_a,SV23: partia1833973666xt_a_b] :
( ( ( ~ ( locali425460998xt_a_b @ SV23 @ SV114 ) )
= $true )
| ( ( ! [SY382: a] :
( ~ ( member_a @ SY382 @ SV114 )
| ! [SY383: a] :
( ~ ( member_a @ SY383 @ SV114 )
| ( member_a @ ( mult_a_ring_ext_a_b @ SV23 @ SY382 @ SY383 ) @ SV114 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(932,plain,
! [SV115: partia1833973666xt_a_b] :
( ( ! [SV138: a] :
( ( a_minus_a_b @ SV115 @ SV138 )
= ( ^ [SY405: a] : ( add_a_b @ SV115 @ SV138 @ ( a_inv_a_b @ SV115 @ SY405 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[822]) ).
thf(933,plain,
! [SV115: partia1833973666xt_a_b] :
( ( ( a_minus_a_b @ SV115 )
= ( ^ [SY384: a,SY385: a] : ( add_a_b @ SV115 @ SY384 @ ( a_inv_a_b @ SV115 @ SY385 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[822]) ).
thf(934,plain,
! [SV25: set_a] :
( ( ( additi2104487374up_a_b @ SV25 @ r )
= $false )
| ( ( ! [SY288: set_a] :
( ~ ( additi2104487374up_a_b @ SY288 @ r )
| ( additi2104487374up_a_b @ ( set_add_a_b @ r @ SV25 @ SY288 ) @ r ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(935,plain,
! [SV116: a > $o,SV26: a] :
( ( ~ ( ( member_a @ SV26 @ ( collect_a @ SV116 ) )
| ( SV116 @ SV26 ) )
| ~ ( ~ ( member_a @ SV26 @ ( collect_a @ SV116 ) )
| ~ ( SV116 @ SV26 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[824]) ).
thf(936,plain,
! [SV116: a > $o,SV26: a] :
( ( ( member_a @ SV26 @ ( collect_a @ SV116 ) )
= ( SV116 @ SV26 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[824]) ).
thf(937,plain,
! [SV117: a,SV28: a] :
( ( ( ( add_a_b @ r @ SV28 @ SV117 )
!= ( zero_a_b @ r ) )
= $true )
| ( ( ! [SY386: a] :
( ( ( add_a_b @ r @ SV117 @ SY386 )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ SV117 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV28 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SY386 @ ( partia1066395285xt_a_b @ r ) )
| ( SV28 = SY386 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[825]) ).
thf(938,plain,
! [SV118: a,SV29: a] :
( ( ( ( add_a_b @ r @ SV29 @ SV118 )
!= ( zero_a_b @ r ) )
= $true )
| ( ( ~ ( member_a @ SV29 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV118 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV118 @ SV29 )
= ( zero_a_b @ r ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(939,plain,
! [SV30: a] :
( ( ( member_a @ SV30 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY294: a] :
( ~ ( member_a @ SY294 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SV30 @ ( a_inv_a_b @ r @ SY294 ) )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV30 @ SY294 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(940,plain,
! [SV31: a] :
( ( ( member_a @ SV31 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY295: a] :
( ~ ( member_a @ SY295 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( a_inv_a_b @ r @ SV31 ) @ SY295 )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV31 @ SY295 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(941,plain,
! [SV32: a] :
( ( ( member_a @ SV32 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY296: a] :
( ~ ( member_a @ SY296 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV32 @ ( add_a_b @ r @ ( a_inv_a_b @ r @ SV32 ) @ SY296 ) )
= SY296 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[829]) ).
thf(942,plain,
! [SV33: a] :
( ( ( member_a @ SV33 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY297: a] :
( ~ ( member_a @ SY297 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV33 ) @ ( add_a_b @ r @ SV33 @ SY297 ) )
= SY297 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(943,plain,
! [SV34: a] :
( ( ( member_a @ SV34 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY298: a] :
( ~ ( member_a @ SY298 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( add_a_b @ r @ SV34 @ SY298 ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV34 ) @ ( a_inv_a_b @ r @ SY298 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(944,plain,
! [SV35: a] :
( ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY299: a] :
( ~ ( member_a @ SY299 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY300: a] :
( ~ ( member_a @ SY300 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SY299 @ ( a_inv_a_b @ r @ SY300 ) )
= SV35 )
= ( SY299
= ( add_a_b @ r @ SV35 @ SY300 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(945,plain,
! [SV36: a] :
( ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY301: a] :
( ~ ( member_a @ SY301 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY302: a] :
( ~ ( member_a @ SY302 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV36
= ( add_a_b @ r @ SY301 @ ( a_inv_a_b @ r @ SY302 ) ) )
= ( SY301
= ( add_a_b @ r @ SV36 @ SY302 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(946,plain,
! [SV37: a] :
( ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY303: a] :
( ~ ( member_a @ SY303 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY304: a] :
( ~ ( member_a @ SY304 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SY303 ) @ SY304 )
= SV37 )
= ( SY304
= ( add_a_b @ r @ SY303 @ SV37 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(947,plain,
! [SV38: a] :
( ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY305: a] :
( ~ ( member_a @ SY305 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY306: a] :
( ~ ( member_a @ SY306 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SY305 ) @ SY306 ) )
= ( SY306
= ( add_a_b @ r @ SY305 @ SV38 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[835]) ).
thf(948,plain,
! [SV39: a] :
( ( ( member_a @ SV39 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY307: a] :
( ~ ( member_a @ SY307 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( add_a_b @ r @ SV39 @ SY307 ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SY307 ) @ ( a_inv_a_b @ r @ SV39 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(949,plain,
! [SV139: a,SV119: a,SV40: a] :
( ( ( ( add_a_b @ r @ SV40 @ SV119 )
!= SV139 )
| ~ ( member_a @ SV40 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV119 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV139 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV40 ) @ SV139 )
= SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(950,plain,
! [SV41: a] :
( ( ( member_a @ SV41 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY310: a] :
( ~ ( member_a @ SY310 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV41 @ SY310 )
!= ( zero_a_b @ r ) )
| ( SV41
= ( a_inv_a_b @ r @ SY310 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(951,plain,
! [SV42: a] :
( ( ( member_a @ SV42 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV42 @ ( a_inv_a_b @ r @ SV42 ) )
= ( zero_a_b @ r ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[839]) ).
thf(952,plain,
! [SV120: a,SV43: a] :
( ( ( ( add_a_b @ r @ SV43 @ SV120 )
!= ( zero_a_b @ r ) )
= $true )
| ( ( ~ ( member_a @ SV120 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV43 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ SV120 )
= SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(953,plain,
! [SV44: a] :
( ( ( member_a @ SV44 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV44 ) @ SV44 )
= ( zero_a_b @ r ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(954,plain,
! [SV45: a] :
( ( ( member_a @ SV45 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY312: a] :
( ~ ( member_a @ SY312 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( add_a_b @ r @ SV45 @ SY312 ) )
= ( a_minus_a_b @ r @ ( a_inv_a_b @ r @ SV45 ) @ SY312 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(955,plain,
! [SV46: a] :
( ( ( member_a @ SV46 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( a_inv_a_b @ r @ ( a_inv_a_b @ r @ SV46 ) )
= SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(956,plain,
! [SV47: a] :
( ( ( member_a @ SV47 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ ( a_inv_a_b @ r @ SV47 ) @ ( partia1066395285xt_a_b @ r ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(957,plain,
! [SV48: a] :
( ( ( member_a @ SV48 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( mult_a_ring_ext_a_b @ r @ SV48 @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(958,plain,
! [SV49: a] :
( ( ( member_a @ SV49 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( mult_a_ring_ext_a_b @ r @ ( zero_a_b @ r ) @ SV49 )
= ( zero_a_b @ r ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(959,plain,
! [SV50: a] :
( ( ( member_a @ SV50 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV50 @ ( zero_a_b @ r ) )
= SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(960,plain,
! [SV51: a] :
( ( ( member_a @ SV51 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ ( zero_a_b @ r ) @ SV51 )
= SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(961,plain,
! [SV52: a] :
( ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY313: a] :
( ~ ( member_a @ SY313 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV52
= ( add_a_b @ r @ SY313 @ SV52 ) )
= ( SY313
= ( zero_a_b @ r ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[849]) ).
thf(962,plain,
! [SV53: a] :
( ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY314: a] :
( ~ ( member_a @ SY314 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SY314 @ SV53 )
= SV53 )
= ( SY314
= ( zero_a_b @ r ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(963,plain,
! [SV54: a] :
( ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY315: a] :
( ~ ( member_a @ SY315 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV54
= ( add_a_b @ r @ SV54 @ SY315 ) )
= ( SY315
= ( zero_a_b @ r ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(964,plain,
! [SV55: a] :
( ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY316: a] :
( ~ ( member_a @ SY316 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SV55 @ SY316 )
= SV55 )
= ( SY316
= ( zero_a_b @ r ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(965,plain,
! [SV56: a] :
( ( ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( ( a_inv_a_b @ r @ SV56 )
= ( zero_a_b @ r ) )
= ( SV56
= ( zero_a_b @ r ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[853]) ).
thf(966,plain,
! [SV57: a] :
( ( ( member_a @ SV57 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY317: int] :
( ( add_pow_a_b_int @ r @ SY317 @ ( a_inv_a_b @ r @ SV57 ) )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ SY317 @ SV57 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(967,plain,
! [SV58: partia1833973666xt_a_b] :
( ( ( semiring_a_b @ SV58 )
= $false )
| ( ( ! [SY318: a] :
( ~ ( member_a @ SY318 @ ( partia1066395285xt_a_b @ SV58 ) )
| ( ( add_a_b @ SV58 @ SY318 @ ( zero_a_b @ SV58 ) )
= SY318 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[855]) ).
thf(968,plain,
! [SV59: partia1833973666xt_a_b] :
( ( ( semiring_a_b @ SV59 )
= $false )
| ( ( ! [SY319: a] :
( ~ ( member_a @ SY319 @ ( partia1066395285xt_a_b @ SV59 ) )
| ( ( add_a_b @ SV59 @ ( zero_a_b @ SV59 ) @ SY319 )
= SY319 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(969,plain,
! [SV60: partia1833973666xt_a_b] :
( ( ( semiring_a_b @ SV60 )
= $false )
| ( ( ! [SY320: a] :
( ~ ( member_a @ SY320 @ ( partia1066395285xt_a_b @ SV60 ) )
| ( ( mult_a_ring_ext_a_b @ SV60 @ ( zero_a_b @ SV60 ) @ SY320 )
= ( zero_a_b @ SV60 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(970,plain,
! [SV61: partia1833973666xt_a_b] :
( ( ( semiring_a_b @ SV61 )
= $false )
| ( ( ! [SY321: a] :
( ~ ( member_a @ SY321 @ ( partia1066395285xt_a_b @ SV61 ) )
| ( ( mult_a_ring_ext_a_b @ SV61 @ SY321 @ ( zero_a_b @ SV61 ) )
= ( zero_a_b @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(971,plain,
! [SV121: a,SV62: partia1833973666xt_a_b] :
( ( ( ~ ( semiring_a_b @ SV62 ) )
= $true )
| ( ( ~ ( member_a @ SV121 @ ( partia1066395285xt_a_b @ SV62 ) )
| ! [SY388: a] :
( ~ ( member_a @ SY388 @ ( partia1066395285xt_a_b @ SV62 ) )
| ! [SY389: a] :
( ~ ( member_a @ SY389 @ ( partia1066395285xt_a_b @ SV62 ) )
| ( ( mult_a_ring_ext_a_b @ SV62 @ SY389 @ ( add_a_b @ SV62 @ SV121 @ SY388 ) )
= ( add_a_b @ SV62 @ ( mult_a_ring_ext_a_b @ SV62 @ SY389 @ SV121 ) @ ( mult_a_ring_ext_a_b @ SV62 @ SY389 @ SY388 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(972,plain,
! [SV63: a] :
( ( ( member_a @ SV63 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY325: a] :
( ~ ( member_a @ SY325 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY326: int] :
( ( mult_a_ring_ext_a_b @ r @ ( add_pow_a_b_int @ r @ SY326 @ SV63 ) @ SY325 )
= ( add_pow_a_b_int @ r @ SY326 @ ( mult_a_ring_ext_a_b @ r @ SV63 @ SY325 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(973,plain,
! [SV64: a] :
( ( ( member_a @ SV64 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY327: a] :
( ~ ( member_a @ SY327 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY328: int] :
( ( mult_a_ring_ext_a_b @ r @ SV64 @ ( add_pow_a_b_int @ r @ SY328 @ SY327 ) )
= ( add_pow_a_b_int @ r @ SY328 @ ( mult_a_ring_ext_a_b @ r @ SV64 @ SY327 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(974,plain,
! [SV65: a] :
( ( ( member_a @ SV65 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY329: a] :
( ~ ( member_a @ SY329 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY330: int] :
( ( add_pow_a_b_int @ r @ SY330 @ ( add_a_b @ r @ SV65 @ SY329 ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY330 @ SV65 ) @ ( add_pow_a_b_int @ r @ SY330 @ SY329 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[862]) ).
thf(975,plain,
! [SV122: a,SV66: a] :
( ( ( ( add_a_b @ r @ SV66 @ SV122 )
!= ( add_a_b @ r @ SV122 @ SV66 ) )
= $true )
| ( ( ~ ( member_a @ SV66 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV122 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY390: int] :
( ( add_pow_a_b_int @ r @ SY390 @ ( add_a_b @ r @ SV66 @ SV122 ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY390 @ SV66 ) @ ( add_pow_a_b_int @ r @ SY390 @ SV122 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(976,plain,
! [SV67: a] :
( ( ( member_a @ SV67 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY333: int] : ( member_a @ ( add_pow_a_b_int @ r @ SY333 @ SV67 ) @ ( partia1066395285xt_a_b @ r ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(977,plain,
! [SV124: set_a,SV69: partia1833973666xt_a_b] :
( ( ( ~ ( locali807230110ng_a_b @ SV69 @ SV124 ) )
= $true )
| ( ( locali880295127ng_a_b @ SV69 @ SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(978,plain,
! [SV125: set_a,SV70: partia1833973666xt_a_b] :
( ( ( ~ ( locali880295127ng_a_b @ SV70 @ SV125 ) )
= $true )
| ( ( locali425460998xt_a_b @ SV70 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(979,plain,
! [SV126: set_a,SV71: partia1833973666xt_a_b] :
( ( ( ~ ( locali1648887798ac_a_b @ SV71 @ SV126 ) )
= $true )
| ( ( locali807230110ng_a_b @ SV71 @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[868]) ).
thf(980,plain,
! [SV127: a,SV72: partia1833973666xt_a_b] :
( ( ( ~ ( semiring_a_b @ SV72 ) )
= $true )
| ( ( ~ ( member_a @ SV127 @ ( partia1066395285xt_a_b @ SV72 ) )
| ! [SY391: a] :
( ~ ( member_a @ SY391 @ ( partia1066395285xt_a_b @ SV72 ) )
| ! [SY392: a] :
( ~ ( member_a @ SY392 @ ( partia1066395285xt_a_b @ SV72 ) )
| ( ( mult_a_ring_ext_a_b @ SV72 @ ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ SY391 ) @ SY392 )
= ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ ( mult_a_ring_ext_a_b @ SV72 @ SY391 @ SY392 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[869]) ).
thf(981,plain,
! [SV73: partia1833973666xt_a_b] :
( ( ( semiring_a_b @ SV73 )
= $false )
| ( ( ! [SY341: a] :
( ~ ( member_a @ SY341 @ ( partia1066395285xt_a_b @ SV73 ) )
| ! [SY342: a] :
( ~ ( member_a @ SY342 @ ( partia1066395285xt_a_b @ SV73 ) )
| ( member_a @ ( mult_a_ring_ext_a_b @ SV73 @ SY341 @ SY342 ) @ ( partia1066395285xt_a_b @ SV73 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(982,plain,
! [SV128: a,SV74: partia1833973666xt_a_b] :
( ( ( ~ ( semiring_a_b @ SV74 ) )
= $true )
| ( ( ~ ( member_a @ SV128 @ ( partia1066395285xt_a_b @ SV74 ) )
| ! [SY393: a] :
( ~ ( member_a @ SY393 @ ( partia1066395285xt_a_b @ SV74 ) )
| ! [SY394: a] :
( ~ ( member_a @ SY394 @ ( partia1066395285xt_a_b @ SV74 ) )
| ( ( add_a_b @ SV74 @ SV128 @ ( add_a_b @ SV74 @ SY393 @ SY394 ) )
= ( add_a_b @ SV74 @ SY393 @ ( add_a_b @ SV74 @ SV128 @ SY394 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(983,plain,
! [SV75: partia1833973666xt_a_b] :
( ( ( semiring_a_b @ SV75 )
= $false )
| ( ( ! [SY346: a] :
( ~ ( member_a @ SY346 @ ( partia1066395285xt_a_b @ SV75 ) )
| ! [SY347: a] :
( ~ ( member_a @ SY347 @ ( partia1066395285xt_a_b @ SV75 ) )
| ( ( add_a_b @ SV75 @ SY346 @ SY347 )
= ( add_a_b @ SV75 @ SY347 @ SY346 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(984,plain,
! [SV129: a,SV76: partia1833973666xt_a_b] :
( ( ( ~ ( semiring_a_b @ SV76 ) )
= $true )
| ( ( ~ ( member_a @ SV129 @ ( partia1066395285xt_a_b @ SV76 ) )
| ! [SY395: a] :
( ~ ( member_a @ SY395 @ ( partia1066395285xt_a_b @ SV76 ) )
| ! [SY396: a] :
( ~ ( member_a @ SY396 @ ( partia1066395285xt_a_b @ SV76 ) )
| ( ( add_a_b @ SV76 @ ( add_a_b @ SV76 @ SV129 @ SY395 ) @ SY396 )
= ( add_a_b @ SV76 @ SV129 @ ( add_a_b @ SV76 @ SY395 @ SY396 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(985,plain,
! [SV77: partia1833973666xt_a_b] :
( ( ( semiring_a_b @ SV77 )
= $false )
| ( ( ! [SY351: a] :
( ~ ( member_a @ SY351 @ ( partia1066395285xt_a_b @ SV77 ) )
| ! [SY352: a] :
( ~ ( member_a @ SY352 @ ( partia1066395285xt_a_b @ SV77 ) )
| ( member_a @ ( add_a_b @ SV77 @ SY351 @ SY352 ) @ ( partia1066395285xt_a_b @ SV77 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(986,plain,
! [SV78: partia1833973666xt_a_b] :
( ( ( semiring_a_b @ SV78 )
= $false )
| ( ( member_a @ ( zero_a_b @ SV78 ) @ ( partia1066395285xt_a_b @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[875]) ).
thf(987,plain,
! [SV130: a,SV79: partia1833973666xt_a_b] :
( ( ( ~ ( semiring_a_b @ SV79 ) )
= $true )
| ( ( ~ ( member_a @ SV130 @ ( partia1066395285xt_a_b @ SV79 ) )
| ! [SY397: a] :
( ~ ( member_a @ SY397 @ ( partia1066395285xt_a_b @ SV79 ) )
| ! [SY398: a] :
( ~ ( member_a @ SY398 @ ( partia1066395285xt_a_b @ SV79 ) )
| ( ( mult_a_ring_ext_a_b @ SV79 @ ( add_a_b @ SV79 @ SV130 @ SY397 ) @ SY398 )
= ( add_a_b @ SV79 @ ( mult_a_ring_ext_a_b @ SV79 @ SV130 @ SY398 ) @ ( mult_a_ring_ext_a_b @ SV79 @ SY397 @ SY398 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[876]) ).
thf(988,plain,
! [SV80: a] :
( ( ( member_a @ SV80 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY356: int,SY357: int] :
( ( add_pow_a_b_int @ r @ ( minus_minus_int @ SY356 @ SY357 ) @ SV80 )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY356 @ SV80 ) @ ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ SY357 @ SV80 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(989,plain,
! [SV81: a] :
( ( ( member_a @ SV81 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY358: int] :
( ( add_pow_a_b_int @ r @ ( uminus_uminus_int @ SY358 ) @ SV81 )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ SY358 @ SV81 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(990,plain,
! [SV82: a] :
( ( ( member_a @ SV82 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY359: int,SY360: int] :
( ( add_pow_a_b_int @ r @ ( plus_plus_int @ SY359 @ SY360 ) @ SV82 )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY359 @ SV82 ) @ ( add_pow_a_b_int @ r @ SY360 @ SV82 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(991,plain,
! [SV131: set_a,SV83: partia1833973666xt_a_b] :
( ( ( ~ ( locali425460998xt_a_b @ SV83 @ SV131 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV131 @ ( partia1066395285xt_a_b @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(992,plain,
! [SV84: set_a] :
( ( ( ord_less_eq_set_a @ SV84 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY362: set_a] :
( ~ ( ord_less_eq_set_a @ SY362 @ ( partia1066395285xt_a_b @ r ) )
| ( ord_less_eq_set_a @ ( set_add_a_b @ r @ SV84 @ SY362 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(993,plain,
! [SV85: set_a] :
( ( ( ord_less_eq_set_a @ SV85 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY363: set_a] :
( ~ ( ord_less_eq_set_a @ SY363 @ ( partia1066395285xt_a_b @ r ) )
| ( ord_less_eq_set_a @ ( set_add_a_b @ r @ SV85 @ SY363 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(994,plain,
! [SV87: set_a] :
( ( ( ~ ( ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 )
| ( SV87 = bot_bot_set_a ) ) )
= $true )
| ( ( ~ ( ~ ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 )
| ( SV87 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(995,plain,
! [SV88: a > $o] :
( ( ( ~ ( ( ( collect_a @ SV88 )
= bot_bot_set_a )
| ! [SY365: a] :
~ ( SV88 @ SY365 ) ) )
= $true )
| ( ( ~ ( ( ( collect_a @ SV88 )
!= bot_bot_set_a )
| ~ ! [SY365: a] :
~ ( SV88 @ SY365 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(996,plain,
! [SV89: a > $o] :
( ( ( ~ ( ( bot_bot_set_a
= ( collect_a @ SV89 ) )
| ! [SY366: a] :
~ ( SV89 @ SY366 ) ) )
= $true )
| ( ( ~ ( ( bot_bot_set_a
!= ( collect_a @ SV89 ) )
| ~ ! [SY366: a] :
~ ( SV89 @ SY366 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(997,plain,
! [SV90: set_a] :
( ( ( ~ ( ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
| ( SV90 = bot_bot_set_a ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
| ( SV90 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(998,plain,
! [SV96: set_a] :
( ( ( SV96 = bot_bot_set_a )
= $false )
| ( ( ! [SY367: a] :
~ ( member_a @ SY367 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(999,plain,
! [SV132: set_a,SV98: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV98 @ SV132 ) )
= $true )
| ( ( ! [SY399: a] :
( ~ ( member_a @ SY399 @ SV98 )
| ( member_a @ SY399 @ SV132 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[895]) ).
thf(1000,plain,
! [SV133: set_a,SV99: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV99 @ SV133 ) )
= $true )
| ( ( ! [SY400: a] :
( ~ ( member_a @ SY400 @ SV99 )
| ( member_a @ SY400 @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[896]) ).
thf(1001,plain,
( ( member_a @ sK7_T @ s )
= $true ),
inference(extcnf_not_neg,[status(thm)],[897]) ).
thf(1002,plain,
( ( ( mult_a_ring_ext_a_b @ r @ sK7_T @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
= ( zero_a_b @ r ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[898]) ).
thf(1003,plain,
( ( member_a @ sK6_T2 @ s )
= $true ),
inference(extcnf_not_neg,[status(thm)],[899]) ).
thf(1004,plain,
( ( ( mult_a_ring_ext_a_b @ r @ sK6_T2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
= ( zero_a_b @ r ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[900]) ).
thf(1005,plain,
! [SV100: set_a,SV134: set_a] :
( ( ( ~ ( ~ ( member_a @ ( sK2_X3 @ SV134 @ SV100 ) @ SV100 )
| ~ ~ ( member_a @ ( sK2_X3 @ SV134 @ SV100 ) @ SV134 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV100 @ SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[901]) ).
thf(1006,plain,
! [SV101: set_a] :
( ( ( ~ ( ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 )
| ( SV101 != bot_bot_set_a ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 )
| ~ ( ( SV101 != bot_bot_set_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[902]) ).
thf(1007,plain,
! [SV135: set_a] :
( ( ! [SV140: set_a] :
( ( ord_less_eq_set_a @ SV135 @ SV140 )
= ( ! [SY406: a] :
( ~ ( member_a @ SY406 @ SV135 )
| ( member_a @ SY406 @ SV140 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[904]) ).
thf(1008,plain,
! [SV135: set_a] :
( ( ( ord_less_eq_set_a @ SV135 )
= ( ^ [SY401: set_a] :
! [SY402: a] :
( ~ ( member_a @ SY402 @ SV135 )
| ( member_a @ SY402 @ SY401 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[904]) ).
thf(1009,plain,
! [SV103: a] :
( ( ( member_a @ SV103 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ~ ( ( ( add_a_b @ r @ ( sK8_X3 @ SV103 ) @ SV103 )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( sK8_X3 @ SV103 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(1010,plain,
! [SV136: product_prod_a_a] :
( ( ! [SV141: product_prod_a_a] :
( ( SV136 = SV141 )
= ( ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV141 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV141 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[906]) ).
thf(1011,plain,
! [SV136: product_prod_a_a] :
( ( ( ^ [SY403: product_prod_a_a] : ( SV136 = SY403 ) )
= ( ^ [SY404: product_prod_a_a] :
~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SY404 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SY404 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[906]) ).
thf(1012,plain,
! [SV105: set_a] :
( ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( SV105 = bot_bot_set_a )
| ~ ( ~ ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 ) )
| ~ ( ~ ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 )
| ~ ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) )
| ( member_a @ ( zero_a_b @ r ) @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(1013,plain,
! [SV106: a] :
( ( ( member_a @ SV106 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ~ ( ~ ( member_a @ ( sK9_X3 @ SV106 ) @ ( partia1066395285xt_a_b @ r ) )
| ~ ( ( ( add_a_b @ r @ SV106 @ ( sK9_X3 @ SV106 ) )
!= ( sK9_X3 @ SV106 ) ) ) )
| ( SV106
= ( zero_a_b @ r ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(1014,plain,
! [SV107: a] :
( ( ( member_a @ SV107 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ~ ( ( ( add_a_b @ r @ SV107 @ ( sK10_X3 @ SV107 ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( sK10_X3 @ SV107 ) @ ( partia1066395285xt_a_b @ r ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(1015,plain,
! [SV108: a,SV1: a] :
( ( ( SV1 = SV108 )
= $false )
| ( ( ! [SY378: a] :
( ( add_a_b @ r @ SY378 @ SV1 )
= ( add_a_b @ r @ SY378 @ SV108 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(1016,plain,
! [SV109: a,SV2: a] :
( ( ( SV2 = SV109 )
= $false )
| ( ( ! [SY379: a] :
( ( a_minus_a_b @ r @ SY379 @ SV2 )
= ( a_minus_a_b @ r @ SY379 @ SV109 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(1017,plain,
! [SV3: a,SV142: a] :
( ( ( ~ ( member_a @ SV142 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY407: a] :
( ~ ( member_a @ SY407 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV3 @ SV142 ) @ SY407 )
= ( mult_a_ring_ext_a_b @ r @ SV3 @ ( mult_a_ring_ext_a_b @ r @ SV142 @ SY407 ) ) ) ) )
= $true )
| ( ( member_a @ SV3 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1018,plain,
! [SV4: a,SV143: a] :
( ( ( ~ ( member_a @ SV143 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SV4 @ SV143 )
= ( mult_a_ring_ext_a_b @ r @ SV143 @ SV4 ) ) )
= $true )
| ( ( member_a @ SV4 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1019,plain,
! [SV5: a,SV144: a] :
( ( ( ~ ( member_a @ SV144 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY408: a] :
( ~ ( member_a @ SY408 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SV5 @ ( mult_a_ring_ext_a_b @ r @ SV144 @ SY408 ) )
= ( mult_a_ring_ext_a_b @ r @ SV144 @ ( mult_a_ring_ext_a_b @ r @ SV5 @ SY408 ) ) ) ) )
= $true )
| ( ( member_a @ SV5 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1020,plain,
! [SV6: a,SV145: a] :
( ( ( ~ ( member_a @ SV145 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY409: a] :
( ~ ( member_a @ SY409 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( add_a_b @ r @ SV6 @ SV145 ) @ SY409 )
= ( add_a_b @ r @ SV6 @ ( add_a_b @ r @ SV145 @ SY409 ) ) ) ) )
= $true )
| ( ( member_a @ SV6 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1021,plain,
! [SV7: a,SV146: a] :
( ( ( ~ ( member_a @ SV146 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV7 @ SV146 )
= ( add_a_b @ r @ SV146 @ SV7 ) ) )
= $true )
| ( ( member_a @ SV7 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1022,plain,
! [SV8: a,SV147: a] :
( ( ( ~ ( member_a @ SV147 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY410: a] :
( ~ ( member_a @ SY410 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV8 @ ( add_a_b @ r @ SV147 @ SY410 ) )
= ( add_a_b @ r @ SV147 @ ( add_a_b @ r @ SV8 @ SY410 ) ) ) ) )
= $true )
| ( ( member_a @ SV8 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1023,plain,
! [SV9: a,SV148: a] :
( ( ( ~ ( member_a @ SV148 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY411: a] :
( ~ ( member_a @ SY411 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( add_a_b @ r @ SV9 @ SV148 ) @ SY411 )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV9 @ SY411 ) @ ( mult_a_ring_ext_a_b @ r @ SV148 @ SY411 ) ) ) ) )
= $true )
| ( ( member_a @ SV9 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1024,plain,
! [SV10: a,SV149: a] :
( ( ( ~ ( member_a @ SV149 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY412: a] :
( ~ ( member_a @ SY412 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SY412 @ ( add_a_b @ r @ SV10 @ SV149 ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SY412 @ SV10 ) @ ( mult_a_ring_ext_a_b @ r @ SY412 @ SV149 ) ) ) ) )
= $true )
| ( ( member_a @ SV10 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1025,plain,
! [SV110: a,SV11: a] :
( ( ( member_a @ SV11 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ~ ( member_a @ SV110 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY380: a] :
( ~ ( member_a @ SY380 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY381: a] :
( ~ ( member_a @ SY381 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ SV11 @ SY380 ) @ SV110 ) @ SY381 )
= ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ ( add_a_b @ r @ SV11 @ SV110 ) @ SY380 ) @ SY381 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(1026,plain,
! [SV12: a,SV150: a] :
( ( ( ~ ( member_a @ SV150 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY413: a] :
( ~ ( member_a @ SY413 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ SY413 @ SV12 ) @ SV150 )
= ( a_minus_a_b @ r @ SY413 @ ( add_a_b @ r @ SV12 @ SV150 ) ) ) ) )
= $true )
| ( ( member_a @ SV12 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1027,plain,
( ( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ~ ( member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ) )
= $true )
| ( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(1028,plain,
! [SV13: a,SV151: a] :
( ( ( ~ ( member_a @ SV151 @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( a_minus_a_b @ r @ SV13 @ SV151 ) @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( member_a @ SV13 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1029,plain,
! [SV14: a,SV152: a] :
( ( ( ~ ( member_a @ SV152 @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( add_a_b @ r @ SV14 @ SV152 ) @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( member_a @ SV14 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1030,plain,
! [SV15: a,SV153: a] :
( ( ( ~ ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY414: a] :
( ~ ( member_a @ SY414 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SV153 @ SV15 )
= ( add_a_b @ r @ SY414 @ SV15 ) )
= ( SV153 = SY414 ) ) ) )
= $true )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1031,plain,
! [SV16: a,SV154: a] :
( ( ( ~ ( member_a @ SV154 @ ( partia1066395285xt_a_b @ r ) )
| ( member_a @ ( mult_a_ring_ext_a_b @ r @ SV16 @ SV154 ) @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( member_a @ SV16 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1032,plain,
! [SV112: product_prod_a_a,SV18: product_prod_a_a] :
( ( ( ( product_fst_a_a @ SV18 )
= ( product_fst_a_a @ SV112 ) )
= $false )
| ( ( ( ( product_snd_a_a @ SV18 )
!= ( product_snd_a_a @ SV112 ) )
| ( SV18 = SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(1033,plain,
! [SV137: product_prod_a_a,SV19: a > a > $o] :
( ( ( SV19 @ ( product_snd_a_a @ SV137 ) @ ( product_fst_a_a @ SV137 ) )
= $false )
| ( ( SV19 @ ( sK12_SY249 @ SV19 ) @ ( sK11_X3 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[928]) ).
thf(1034,plain,
! [SV113: product_prod_a_a,SV20: product_prod_a_a] :
( ( ( ( product_fst_a_a @ SV20 )
!= ( product_fst_a_a @ SV113 ) )
= $true )
| ( ( ( product_snd_a_a @ SV20 )
!= ( product_snd_a_a @ SV113 ) )
= $true )
| ( ( SV20 = SV113 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(1035,plain,
! [SV21: a,SV155: a] :
( ( ( ~ ( member_a @ SV155 @ s )
| ( member_a @ ( mult_a_ring_ext_a_b @ r @ SV21 @ SV155 ) @ s ) )
= $true )
| ( ( member_a @ SV21 @ s )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1036,plain,
! [SV114: set_a,SV23: partia1833973666xt_a_b] :
( ( ( locali425460998xt_a_b @ SV23 @ SV114 )
= $false )
| ( ( ! [SY382: a] :
( ~ ( member_a @ SY382 @ SV114 )
| ! [SY383: a] :
( ~ ( member_a @ SY383 @ SV114 )
| ( member_a @ ( mult_a_ring_ext_a_b @ SV23 @ SY382 @ SY383 ) @ SV114 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(1037,plain,
! [SV156: a,SV115: partia1833973666xt_a_b] :
( ( ( a_minus_a_b @ SV115 @ SV156 )
= ( ^ [SY415: a] : ( add_a_b @ SV115 @ SV156 @ ( a_inv_a_b @ SV115 @ SY415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1038,plain,
! [SV25: set_a,SV157: set_a] :
( ( ( ~ ( additi2104487374up_a_b @ SV157 @ r )
| ( additi2104487374up_a_b @ ( set_add_a_b @ r @ SV25 @ SV157 ) @ r ) )
= $true )
| ( ( additi2104487374up_a_b @ SV25 @ r )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1039,plain,
! [SV116: a > $o,SV26: a] :
( ( ( ~ ( ( member_a @ SV26 @ ( collect_a @ SV116 ) )
| ( SV116 @ SV26 ) ) )
= $true )
| ( ( ~ ( ~ ( member_a @ SV26 @ ( collect_a @ SV116 ) )
| ~ ( SV116 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[935]) ).
thf(1040,plain,
! [SV117: a,SV28: a] :
( ( ( ( add_a_b @ r @ SV28 @ SV117 )
= ( zero_a_b @ r ) )
= $false )
| ( ( ! [SY386: a] :
( ( ( add_a_b @ r @ SV117 @ SY386 )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ SV117 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV28 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SY386 @ ( partia1066395285xt_a_b @ r ) )
| ( SV28 = SY386 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(1041,plain,
! [SV118: a,SV29: a] :
( ( ( ( add_a_b @ r @ SV29 @ SV118 )
= ( zero_a_b @ r ) )
= $false )
| ( ( ~ ( member_a @ SV29 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV118 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV118 @ SV29 )
= ( zero_a_b @ r ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(1042,plain,
! [SV30: a,SV158: a] :
( ( ( ~ ( member_a @ SV158 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SV30 @ ( a_inv_a_b @ r @ SV158 ) )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV30 @ SV158 ) ) ) )
= $true )
| ( ( member_a @ SV30 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1043,plain,
! [SV31: a,SV159: a] :
( ( ( ~ ( member_a @ SV159 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( a_inv_a_b @ r @ SV31 ) @ SV159 )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV31 @ SV159 ) ) ) )
= $true )
| ( ( member_a @ SV31 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1044,plain,
! [SV32: a,SV160: a] :
( ( ( ~ ( member_a @ SV160 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV32 @ ( add_a_b @ r @ ( a_inv_a_b @ r @ SV32 ) @ SV160 ) )
= SV160 ) )
= $true )
| ( ( member_a @ SV32 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1045,plain,
! [SV33: a,SV161: a] :
( ( ( ~ ( member_a @ SV161 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV33 ) @ ( add_a_b @ r @ SV33 @ SV161 ) )
= SV161 ) )
= $true )
| ( ( member_a @ SV33 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1046,plain,
! [SV34: a,SV162: a] :
( ( ( ~ ( member_a @ SV162 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( add_a_b @ r @ SV34 @ SV162 ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV34 ) @ ( a_inv_a_b @ r @ SV162 ) ) ) )
= $true )
| ( ( member_a @ SV34 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1047,plain,
! [SV35: a,SV163: a] :
( ( ( ~ ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY416: a] :
( ~ ( member_a @ SY416 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SY416 ) )
= SV35 )
= ( SV163
= ( add_a_b @ r @ SV35 @ SY416 ) ) ) ) )
= $true )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1048,plain,
! [SV36: a,SV164: a] :
( ( ( ~ ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY417: a] :
( ~ ( member_a @ SY417 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV36
= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SY417 ) ) )
= ( SV164
= ( add_a_b @ r @ SV36 @ SY417 ) ) ) ) )
= $true )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1049,plain,
! [SV37: a,SV165: a] :
( ( ( ~ ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY418: a] :
( ~ ( member_a @ SY418 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SY418 )
= SV37 )
= ( SY418
= ( add_a_b @ r @ SV165 @ SV37 ) ) ) ) )
= $true )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1050,plain,
! [SV38: a,SV166: a] :
( ( ( ~ ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY419: a] :
( ~ ( member_a @ SY419 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SY419 ) )
= ( SY419
= ( add_a_b @ r @ SV166 @ SV38 ) ) ) ) )
= $true )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1051,plain,
! [SV39: a,SV167: a] :
( ( ( ~ ( member_a @ SV167 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( add_a_b @ r @ SV39 @ SV167 ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV167 ) @ ( a_inv_a_b @ r @ SV39 ) ) ) )
= $true )
| ( ( member_a @ SV39 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1052,plain,
! [SV139: a,SV119: a,SV40: a] :
( ( ( ( add_a_b @ r @ SV40 @ SV119 )
!= SV139 )
= $true )
| ( ( ~ ( member_a @ SV40 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV119 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV139 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV40 ) @ SV139 )
= SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(1053,plain,
! [SV41: a,SV168: a] :
( ( ( ~ ( member_a @ SV168 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV41 @ SV168 )
!= ( zero_a_b @ r ) )
| ( SV41
= ( a_inv_a_b @ r @ SV168 ) ) )
= $true )
| ( ( member_a @ SV41 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1054,plain,
! [SV120: a,SV43: a] :
( ( ( ( add_a_b @ r @ SV43 @ SV120 )
= ( zero_a_b @ r ) )
= $false )
| ( ( ~ ( member_a @ SV120 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV43 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ SV120 )
= SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(1055,plain,
! [SV45: a,SV169: a] :
( ( ( ~ ( member_a @ SV169 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ ( add_a_b @ r @ SV45 @ SV169 ) )
= ( a_minus_a_b @ r @ ( a_inv_a_b @ r @ SV45 ) @ SV169 ) ) )
= $true )
| ( ( member_a @ SV45 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1056,plain,
! [SV52: a,SV170: a] :
( ( ( ~ ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV52
= ( add_a_b @ r @ SV170 @ SV52 ) )
= ( SV170
= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1057,plain,
! [SV53: a,SV171: a] :
( ( ( ~ ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SV171 @ SV53 )
= SV53 )
= ( SV171
= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1058,plain,
! [SV54: a,SV172: a] :
( ( ( ~ ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV54
= ( add_a_b @ r @ SV54 @ SV172 ) )
= ( SV172
= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1059,plain,
! [SV55: a,SV173: a] :
( ( ( ~ ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SV55 @ SV173 )
= SV55 )
= ( SV173
= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1060,plain,
! [SV56: a] :
( ( ( ~ ( ( ( a_inv_a_b @ r @ SV56 )
= ( zero_a_b @ r ) )
| ( SV56
= ( zero_a_b @ r ) ) )
| ~ ( ( ( a_inv_a_b @ r @ SV56 )
!= ( zero_a_b @ r ) )
| ( SV56
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[965]) ).
thf(1061,plain,
! [SV56: a] :
( ( ( ( ( a_inv_a_b @ r @ SV56 )
= ( zero_a_b @ r ) )
= ( SV56
= ( zero_a_b @ r ) ) )
= $true )
| ( ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[965]) ).
thf(1062,plain,
! [SV57: a,SV174: int] :
( ( ( ( add_pow_a_b_int @ r @ SV174 @ ( a_inv_a_b @ r @ SV57 ) )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ SV174 @ SV57 ) ) )
= $true )
| ( ( member_a @ SV57 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1063,plain,
! [SV58: partia1833973666xt_a_b,SV175: a] :
( ( ( ~ ( member_a @ SV175 @ ( partia1066395285xt_a_b @ SV58 ) )
| ( ( add_a_b @ SV58 @ SV175 @ ( zero_a_b @ SV58 ) )
= SV175 ) )
= $true )
| ( ( semiring_a_b @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1064,plain,
! [SV59: partia1833973666xt_a_b,SV176: a] :
( ( ( ~ ( member_a @ SV176 @ ( partia1066395285xt_a_b @ SV59 ) )
| ( ( add_a_b @ SV59 @ ( zero_a_b @ SV59 ) @ SV176 )
= SV176 ) )
= $true )
| ( ( semiring_a_b @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1065,plain,
! [SV60: partia1833973666xt_a_b,SV177: a] :
( ( ( ~ ( member_a @ SV177 @ ( partia1066395285xt_a_b @ SV60 ) )
| ( ( mult_a_ring_ext_a_b @ SV60 @ ( zero_a_b @ SV60 ) @ SV177 )
= ( zero_a_b @ SV60 ) ) )
= $true )
| ( ( semiring_a_b @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1066,plain,
! [SV61: partia1833973666xt_a_b,SV178: a] :
( ( ( ~ ( member_a @ SV178 @ ( partia1066395285xt_a_b @ SV61 ) )
| ( ( mult_a_ring_ext_a_b @ SV61 @ SV178 @ ( zero_a_b @ SV61 ) )
= ( zero_a_b @ SV61 ) ) )
= $true )
| ( ( semiring_a_b @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1067,plain,
! [SV121: a,SV62: partia1833973666xt_a_b] :
( ( ( semiring_a_b @ SV62 )
= $false )
| ( ( ~ ( member_a @ SV121 @ ( partia1066395285xt_a_b @ SV62 ) )
| ! [SY388: a] :
( ~ ( member_a @ SY388 @ ( partia1066395285xt_a_b @ SV62 ) )
| ! [SY389: a] :
( ~ ( member_a @ SY389 @ ( partia1066395285xt_a_b @ SV62 ) )
| ( ( mult_a_ring_ext_a_b @ SV62 @ SY389 @ ( add_a_b @ SV62 @ SV121 @ SY388 ) )
= ( add_a_b @ SV62 @ ( mult_a_ring_ext_a_b @ SV62 @ SY389 @ SV121 ) @ ( mult_a_ring_ext_a_b @ SV62 @ SY389 @ SY388 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1068,plain,
! [SV63: a,SV179: a] :
( ( ( ~ ( member_a @ SV179 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY420: int] :
( ( mult_a_ring_ext_a_b @ r @ ( add_pow_a_b_int @ r @ SY420 @ SV63 ) @ SV179 )
= ( add_pow_a_b_int @ r @ SY420 @ ( mult_a_ring_ext_a_b @ r @ SV63 @ SV179 ) ) ) )
= $true )
| ( ( member_a @ SV63 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1069,plain,
! [SV64: a,SV180: a] :
( ( ( ~ ( member_a @ SV180 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY421: int] :
( ( mult_a_ring_ext_a_b @ r @ SV64 @ ( add_pow_a_b_int @ r @ SY421 @ SV180 ) )
= ( add_pow_a_b_int @ r @ SY421 @ ( mult_a_ring_ext_a_b @ r @ SV64 @ SV180 ) ) ) )
= $true )
| ( ( member_a @ SV64 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1070,plain,
! [SV65: a,SV181: a] :
( ( ( ~ ( member_a @ SV181 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY422: int] :
( ( add_pow_a_b_int @ r @ SY422 @ ( add_a_b @ r @ SV65 @ SV181 ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY422 @ SV65 ) @ ( add_pow_a_b_int @ r @ SY422 @ SV181 ) ) ) )
= $true )
| ( ( member_a @ SV65 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1071,plain,
! [SV122: a,SV66: a] :
( ( ( ( add_a_b @ r @ SV66 @ SV122 )
= ( add_a_b @ r @ SV122 @ SV66 ) )
= $false )
| ( ( ~ ( member_a @ SV66 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV122 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY390: int] :
( ( add_pow_a_b_int @ r @ SY390 @ ( add_a_b @ r @ SV66 @ SV122 ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY390 @ SV66 ) @ ( add_pow_a_b_int @ r @ SY390 @ SV122 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[975]) ).
thf(1072,plain,
! [SV67: a,SV182: int] :
( ( ( member_a @ ( add_pow_a_b_int @ r @ SV182 @ SV67 ) @ ( partia1066395285xt_a_b @ r ) )
= $true )
| ( ( member_a @ SV67 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1073,plain,
! [SV124: set_a,SV69: partia1833973666xt_a_b] :
( ( ( locali807230110ng_a_b @ SV69 @ SV124 )
= $false )
| ( ( locali880295127ng_a_b @ SV69 @ SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1074,plain,
! [SV125: set_a,SV70: partia1833973666xt_a_b] :
( ( ( locali880295127ng_a_b @ SV70 @ SV125 )
= $false )
| ( ( locali425460998xt_a_b @ SV70 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1075,plain,
! [SV126: set_a,SV71: partia1833973666xt_a_b] :
( ( ( locali1648887798ac_a_b @ SV71 @ SV126 )
= $false )
| ( ( locali807230110ng_a_b @ SV71 @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[979]) ).
thf(1076,plain,
! [SV127: a,SV72: partia1833973666xt_a_b] :
( ( ( semiring_a_b @ SV72 )
= $false )
| ( ( ~ ( member_a @ SV127 @ ( partia1066395285xt_a_b @ SV72 ) )
| ! [SY391: a] :
( ~ ( member_a @ SY391 @ ( partia1066395285xt_a_b @ SV72 ) )
| ! [SY392: a] :
( ~ ( member_a @ SY392 @ ( partia1066395285xt_a_b @ SV72 ) )
| ( ( mult_a_ring_ext_a_b @ SV72 @ ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ SY391 ) @ SY392 )
= ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ ( mult_a_ring_ext_a_b @ SV72 @ SY391 @ SY392 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1077,plain,
! [SV73: partia1833973666xt_a_b,SV183: a] :
( ( ( ~ ( member_a @ SV183 @ ( partia1066395285xt_a_b @ SV73 ) )
| ! [SY423: a] :
( ~ ( member_a @ SY423 @ ( partia1066395285xt_a_b @ SV73 ) )
| ( member_a @ ( mult_a_ring_ext_a_b @ SV73 @ SV183 @ SY423 ) @ ( partia1066395285xt_a_b @ SV73 ) ) ) )
= $true )
| ( ( semiring_a_b @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1078,plain,
! [SV128: a,SV74: partia1833973666xt_a_b] :
( ( ( semiring_a_b @ SV74 )
= $false )
| ( ( ~ ( member_a @ SV128 @ ( partia1066395285xt_a_b @ SV74 ) )
| ! [SY393: a] :
( ~ ( member_a @ SY393 @ ( partia1066395285xt_a_b @ SV74 ) )
| ! [SY394: a] :
( ~ ( member_a @ SY394 @ ( partia1066395285xt_a_b @ SV74 ) )
| ( ( add_a_b @ SV74 @ SV128 @ ( add_a_b @ SV74 @ SY393 @ SY394 ) )
= ( add_a_b @ SV74 @ SY393 @ ( add_a_b @ SV74 @ SV128 @ SY394 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1079,plain,
! [SV75: partia1833973666xt_a_b,SV184: a] :
( ( ( ~ ( member_a @ SV184 @ ( partia1066395285xt_a_b @ SV75 ) )
| ! [SY424: a] :
( ~ ( member_a @ SY424 @ ( partia1066395285xt_a_b @ SV75 ) )
| ( ( add_a_b @ SV75 @ SV184 @ SY424 )
= ( add_a_b @ SV75 @ SY424 @ SV184 ) ) ) )
= $true )
| ( ( semiring_a_b @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1080,plain,
! [SV129: a,SV76: partia1833973666xt_a_b] :
( ( ( semiring_a_b @ SV76 )
= $false )
| ( ( ~ ( member_a @ SV129 @ ( partia1066395285xt_a_b @ SV76 ) )
| ! [SY395: a] :
( ~ ( member_a @ SY395 @ ( partia1066395285xt_a_b @ SV76 ) )
| ! [SY396: a] :
( ~ ( member_a @ SY396 @ ( partia1066395285xt_a_b @ SV76 ) )
| ( ( add_a_b @ SV76 @ ( add_a_b @ SV76 @ SV129 @ SY395 ) @ SY396 )
= ( add_a_b @ SV76 @ SV129 @ ( add_a_b @ SV76 @ SY395 @ SY396 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(1081,plain,
! [SV77: partia1833973666xt_a_b,SV185: a] :
( ( ( ~ ( member_a @ SV185 @ ( partia1066395285xt_a_b @ SV77 ) )
| ! [SY425: a] :
( ~ ( member_a @ SY425 @ ( partia1066395285xt_a_b @ SV77 ) )
| ( member_a @ ( add_a_b @ SV77 @ SV185 @ SY425 ) @ ( partia1066395285xt_a_b @ SV77 ) ) ) )
= $true )
| ( ( semiring_a_b @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1082,plain,
! [SV130: a,SV79: partia1833973666xt_a_b] :
( ( ( semiring_a_b @ SV79 )
= $false )
| ( ( ~ ( member_a @ SV130 @ ( partia1066395285xt_a_b @ SV79 ) )
| ! [SY397: a] :
( ~ ( member_a @ SY397 @ ( partia1066395285xt_a_b @ SV79 ) )
| ! [SY398: a] :
( ~ ( member_a @ SY398 @ ( partia1066395285xt_a_b @ SV79 ) )
| ( ( mult_a_ring_ext_a_b @ SV79 @ ( add_a_b @ SV79 @ SV130 @ SY397 ) @ SY398 )
= ( add_a_b @ SV79 @ ( mult_a_ring_ext_a_b @ SV79 @ SV130 @ SY398 ) @ ( mult_a_ring_ext_a_b @ SV79 @ SY397 @ SY398 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1083,plain,
! [SV80: a,SV186: int] :
( ( ( ! [SY426: int] :
( ( add_pow_a_b_int @ r @ ( minus_minus_int @ SV186 @ SY426 ) @ SV80 )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SV186 @ SV80 ) @ ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ SY426 @ SV80 ) ) ) ) )
= $true )
| ( ( member_a @ SV80 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1084,plain,
! [SV81: a,SV187: int] :
( ( ( ( add_pow_a_b_int @ r @ ( uminus_uminus_int @ SV187 ) @ SV81 )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ SV187 @ SV81 ) ) )
= $true )
| ( ( member_a @ SV81 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1085,plain,
! [SV82: a,SV188: int] :
( ( ( ! [SY427: int] :
( ( add_pow_a_b_int @ r @ ( plus_plus_int @ SV188 @ SY427 ) @ SV82 )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SV188 @ SV82 ) @ ( add_pow_a_b_int @ r @ SY427 @ SV82 ) ) ) )
= $true )
| ( ( member_a @ SV82 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1086,plain,
! [SV131: set_a,SV83: partia1833973666xt_a_b] :
( ( ( locali425460998xt_a_b @ SV83 @ SV131 )
= $false )
| ( ( ord_less_eq_set_a @ SV131 @ ( partia1066395285xt_a_b @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1087,plain,
! [SV84: set_a,SV189: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV189 @ ( partia1066395285xt_a_b @ r ) )
| ( ord_less_eq_set_a @ ( set_add_a_b @ r @ SV84 @ SV189 ) @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV84 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1088,plain,
! [SV85: set_a,SV190: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV190 @ ( partia1066395285xt_a_b @ r ) )
| ( ord_less_eq_set_a @ ( set_add_a_b @ r @ SV85 @ SV190 ) @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV85 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1089,plain,
! [SV87: set_a] :
( ( ( ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 )
| ( SV87 = bot_bot_set_a ) )
= $false )
| ( ( ~ ( ~ ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 )
| ( SV87 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1090,plain,
! [SV88: a > $o] :
( ( ( ( ( collect_a @ SV88 )
= bot_bot_set_a )
| ! [SY365: a] :
~ ( SV88 @ SY365 ) )
= $false )
| ( ( ~ ( ( ( collect_a @ SV88 )
!= bot_bot_set_a )
| ~ ! [SY365: a] :
~ ( SV88 @ SY365 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1091,plain,
! [SV89: a > $o] :
( ( ( ( bot_bot_set_a
= ( collect_a @ SV89 ) )
| ! [SY366: a] :
~ ( SV89 @ SY366 ) )
= $false )
| ( ( ~ ( ( bot_bot_set_a
!= ( collect_a @ SV89 ) )
| ~ ! [SY366: a] :
~ ( SV89 @ SY366 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1092,plain,
! [SV90: set_a] :
( ( ( ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
| ( SV90 = bot_bot_set_a ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
| ( SV90 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1093,plain,
! [SV96: set_a,SV191: a] :
( ( ( ~ ( member_a @ SV191 @ SV96 ) )
= $true )
| ( ( SV96 = bot_bot_set_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1094,plain,
! [SV132: set_a,SV98: set_a] :
( ( ( ord_less_eq_set_a @ SV98 @ SV132 )
= $false )
| ( ( ! [SY399: a] :
( ~ ( member_a @ SY399 @ SV98 )
| ( member_a @ SY399 @ SV132 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1095,plain,
! [SV133: set_a,SV99: set_a] :
( ( ( ord_less_eq_set_a @ SV99 @ SV133 )
= $false )
| ( ( ! [SY400: a] :
( ~ ( member_a @ SY400 @ SV99 )
| ( member_a @ SY400 @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1096,plain,
! [SV100: set_a,SV134: set_a] :
( ( ( ~ ( member_a @ ( sK2_X3 @ SV134 @ SV100 ) @ SV100 )
| ~ ~ ( member_a @ ( sK2_X3 @ SV134 @ SV100 ) @ SV134 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV100 @ SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1005]) ).
thf(1097,plain,
! [SV101: set_a] :
( ( ( ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 )
| ( SV101 != bot_bot_set_a ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 )
| ~ ( ( SV101 != bot_bot_set_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1098,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ord_less_eq_set_a @ SV135 @ SV192 )
= ( ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1099,plain,
! [SV103: a] :
( ( ( ( ( add_a_b @ r @ ( sK8_X3 @ SV103 ) @ SV103 )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( sK8_X3 @ SV103 ) @ ( partia1066395285xt_a_b @ r ) ) )
= $false )
| ( ( member_a @ SV103 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1100,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( SV136 = SV193 )
= ( ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1101,plain,
! [SV105: set_a] :
( ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ~ ( ~ ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 ) )
| ~ ( ~ ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 )
| ~ ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) )
| ( member_a @ ( zero_a_b @ r ) @ SV105 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1102,plain,
! [SV106: a] :
( ( ( ~ ( ~ ( member_a @ ( sK9_X3 @ SV106 ) @ ( partia1066395285xt_a_b @ r ) )
| ~ ( ( ( add_a_b @ r @ SV106 @ ( sK9_X3 @ SV106 ) )
!= ( sK9_X3 @ SV106 ) ) ) ) )
= $true )
| ( ( SV106
= ( zero_a_b @ r ) )
= $true )
| ( ( member_a @ SV106 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1103,plain,
! [SV107: a] :
( ( ( ( ( add_a_b @ r @ SV107 @ ( sK10_X3 @ SV107 ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( sK10_X3 @ SV107 ) @ ( partia1066395285xt_a_b @ r ) ) )
= $false )
| ( ( member_a @ SV107 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1104,plain,
! [SV108: a,SV1: a,SV194: a] :
( ( ( ( add_a_b @ r @ SV194 @ SV1 )
= ( add_a_b @ r @ SV194 @ SV108 ) )
= $true )
| ( ( SV1 = SV108 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1105,plain,
! [SV109: a,SV2: a,SV195: a] :
( ( ( ( a_minus_a_b @ r @ SV195 @ SV2 )
= ( a_minus_a_b @ r @ SV195 @ SV109 ) )
= $true )
| ( ( SV2 = SV109 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1106,plain,
! [SV3: a,SV142: a] :
( ( ( ~ ( member_a @ SV142 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY407: a] :
( ~ ( member_a @ SY407 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV3 @ SV142 ) @ SY407 )
= ( mult_a_ring_ext_a_b @ r @ SV3 @ ( mult_a_ring_ext_a_b @ r @ SV142 @ SY407 ) ) ) ) )
= $true )
| ( ( member_a @ SV3 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1017]) ).
thf(1107,plain,
! [SV4: a,SV143: a] :
( ( ( ~ ( member_a @ SV143 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( mult_a_ring_ext_a_b @ r @ SV4 @ SV143 )
= ( mult_a_ring_ext_a_b @ r @ SV143 @ SV4 ) )
= $true )
| ( ( member_a @ SV4 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1018]) ).
thf(1108,plain,
! [SV5: a,SV144: a] :
( ( ( ~ ( member_a @ SV144 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY408: a] :
( ~ ( member_a @ SY408 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SV5 @ ( mult_a_ring_ext_a_b @ r @ SV144 @ SY408 ) )
= ( mult_a_ring_ext_a_b @ r @ SV144 @ ( mult_a_ring_ext_a_b @ r @ SV5 @ SY408 ) ) ) ) )
= $true )
| ( ( member_a @ SV5 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1019]) ).
thf(1109,plain,
! [SV6: a,SV145: a] :
( ( ( ~ ( member_a @ SV145 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY409: a] :
( ~ ( member_a @ SY409 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( add_a_b @ r @ SV6 @ SV145 ) @ SY409 )
= ( add_a_b @ r @ SV6 @ ( add_a_b @ r @ SV145 @ SY409 ) ) ) ) )
= $true )
| ( ( member_a @ SV6 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1020]) ).
thf(1110,plain,
! [SV7: a,SV146: a] :
( ( ( ~ ( member_a @ SV146 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( add_a_b @ r @ SV7 @ SV146 )
= ( add_a_b @ r @ SV146 @ SV7 ) )
= $true )
| ( ( member_a @ SV7 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1021]) ).
thf(1111,plain,
! [SV8: a,SV147: a] :
( ( ( ~ ( member_a @ SV147 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY410: a] :
( ~ ( member_a @ SY410 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV8 @ ( add_a_b @ r @ SV147 @ SY410 ) )
= ( add_a_b @ r @ SV147 @ ( add_a_b @ r @ SV8 @ SY410 ) ) ) ) )
= $true )
| ( ( member_a @ SV8 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1022]) ).
thf(1112,plain,
! [SV9: a,SV148: a] :
( ( ( ~ ( member_a @ SV148 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY411: a] :
( ~ ( member_a @ SY411 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( add_a_b @ r @ SV9 @ SV148 ) @ SY411 )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV9 @ SY411 ) @ ( mult_a_ring_ext_a_b @ r @ SV148 @ SY411 ) ) ) ) )
= $true )
| ( ( member_a @ SV9 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1113,plain,
! [SV10: a,SV149: a] :
( ( ( ~ ( member_a @ SV149 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY412: a] :
( ~ ( member_a @ SY412 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SY412 @ ( add_a_b @ r @ SV10 @ SV149 ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SY412 @ SV10 ) @ ( mult_a_ring_ext_a_b @ r @ SY412 @ SV149 ) ) ) ) )
= $true )
| ( ( member_a @ SV10 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1114,plain,
! [SV11: a,SV110: a] :
( ( ( ~ ( member_a @ SV110 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY380: a] :
( ~ ( member_a @ SY380 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY381: a] :
( ~ ( member_a @ SY381 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ SV11 @ SY380 ) @ SV110 ) @ SY381 )
= ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ ( add_a_b @ r @ SV11 @ SV110 ) @ SY380 ) @ SY381 ) ) ) ) )
= $true )
| ( ( member_a @ SV11 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1115,plain,
! [SV12: a,SV150: a] :
( ( ( ~ ( member_a @ SV150 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY413: a] :
( ~ ( member_a @ SY413 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ SY413 @ SV12 ) @ SV150 )
= ( a_minus_a_b @ r @ SY413 @ ( add_a_b @ r @ SV12 @ SV150 ) ) ) ) )
= $true )
| ( ( member_a @ SV12 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1116,plain,
( ( ( ~ ( member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) )
= $true )
| ( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1117,plain,
! [SV13: a,SV151: a] :
( ( ( ~ ( member_a @ SV151 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( member_a @ ( a_minus_a_b @ r @ SV13 @ SV151 ) @ ( partia1066395285xt_a_b @ r ) )
= $true )
| ( ( member_a @ SV13 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1028]) ).
thf(1118,plain,
! [SV14: a,SV152: a] :
( ( ( ~ ( member_a @ SV152 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( member_a @ ( add_a_b @ r @ SV14 @ SV152 ) @ ( partia1066395285xt_a_b @ r ) )
= $true )
| ( ( member_a @ SV14 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1029]) ).
thf(1119,plain,
! [SV15: a,SV153: a] :
( ( ( ~ ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY414: a] :
( ~ ( member_a @ SY414 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SV153 @ SV15 )
= ( add_a_b @ r @ SY414 @ SV15 ) )
= ( SV153 = SY414 ) ) ) )
= $true )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1120,plain,
! [SV16: a,SV154: a] :
( ( ( ~ ( member_a @ SV154 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( member_a @ ( mult_a_ring_ext_a_b @ r @ SV16 @ SV154 ) @ ( partia1066395285xt_a_b @ r ) )
= $true )
| ( ( member_a @ SV16 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1121,plain,
! [SV112: product_prod_a_a,SV18: product_prod_a_a] :
( ( ( ( product_snd_a_a @ SV18 )
!= ( product_snd_a_a @ SV112 ) )
= $true )
| ( ( SV18 = SV112 )
= $true )
| ( ( ( product_fst_a_a @ SV18 )
= ( product_fst_a_a @ SV112 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1122,plain,
! [SV113: product_prod_a_a,SV20: product_prod_a_a] :
( ( ( ( product_fst_a_a @ SV20 )
= ( product_fst_a_a @ SV113 ) )
= $false )
| ( ( ( product_snd_a_a @ SV20 )
!= ( product_snd_a_a @ SV113 ) )
= $true )
| ( ( SV20 = SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1123,plain,
! [SV21: a,SV155: a] :
( ( ( ~ ( member_a @ SV155 @ s ) )
= $true )
| ( ( member_a @ ( mult_a_ring_ext_a_b @ r @ SV21 @ SV155 ) @ s )
= $true )
| ( ( member_a @ SV21 @ s )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1035]) ).
thf(1124,plain,
! [SV23: partia1833973666xt_a_b,SV114: set_a,SV196: a] :
( ( ( ~ ( member_a @ SV196 @ SV114 )
| ! [SY429: a] :
( ~ ( member_a @ SY429 @ SV114 )
| ( member_a @ ( mult_a_ring_ext_a_b @ SV23 @ SV196 @ SY429 ) @ SV114 ) ) )
= $true )
| ( ( locali425460998xt_a_b @ SV23 @ SV114 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1125,plain,
! [SV156: a,SV115: partia1833973666xt_a_b] :
( ( ! [SV197: a] :
( ( a_minus_a_b @ SV115 @ SV156 @ SV197 )
= ( add_a_b @ SV115 @ SV156 @ ( a_inv_a_b @ SV115 @ SV197 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1037]) ).
thf(1126,plain,
! [SV156: a,SV115: partia1833973666xt_a_b] :
( ( ( a_minus_a_b @ SV115 @ SV156 )
= ( ^ [SY415: a] : ( add_a_b @ SV115 @ SV156 @ ( a_inv_a_b @ SV115 @ SY415 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1037]) ).
thf(1127,plain,
! [SV25: set_a,SV157: set_a] :
( ( ( ~ ( additi2104487374up_a_b @ SV157 @ r ) )
= $true )
| ( ( additi2104487374up_a_b @ ( set_add_a_b @ r @ SV25 @ SV157 ) @ r )
= $true )
| ( ( additi2104487374up_a_b @ SV25 @ r )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1128,plain,
! [SV116: a > $o,SV26: a] :
( ( ( ( member_a @ SV26 @ ( collect_a @ SV116 ) )
| ( SV116 @ SV26 ) )
= $false )
| ( ( ~ ( ~ ( member_a @ SV26 @ ( collect_a @ SV116 ) )
| ~ ( SV116 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1129,plain,
! [SV28: a,SV198: a,SV117: a] :
( ( ( ( ( add_a_b @ r @ SV117 @ SV198 )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ SV117 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV28 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV198 @ ( partia1066395285xt_a_b @ r ) )
| ( SV28 = SV198 ) )
= $true )
| ( ( ( add_a_b @ r @ SV28 @ SV117 )
= ( zero_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1130,plain,
! [SV118: a,SV29: a] :
( ( ( ~ ( member_a @ SV29 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ~ ( member_a @ SV118 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV118 @ SV29 )
= ( zero_a_b @ r ) ) )
= $true )
| ( ( ( add_a_b @ r @ SV29 @ SV118 )
= ( zero_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1041]) ).
thf(1131,plain,
! [SV30: a,SV158: a] :
( ( ( ~ ( member_a @ SV158 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( mult_a_ring_ext_a_b @ r @ SV30 @ ( a_inv_a_b @ r @ SV158 ) )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV30 @ SV158 ) ) )
= $true )
| ( ( member_a @ SV30 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1042]) ).
thf(1132,plain,
! [SV31: a,SV159: a] :
( ( ( ~ ( member_a @ SV159 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( mult_a_ring_ext_a_b @ r @ ( a_inv_a_b @ r @ SV31 ) @ SV159 )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV31 @ SV159 ) ) )
= $true )
| ( ( member_a @ SV31 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1043]) ).
thf(1133,plain,
! [SV32: a,SV160: a] :
( ( ( ~ ( member_a @ SV160 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( add_a_b @ r @ SV32 @ ( add_a_b @ r @ ( a_inv_a_b @ r @ SV32 ) @ SV160 ) )
= SV160 )
= $true )
| ( ( member_a @ SV32 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1044]) ).
thf(1134,plain,
! [SV33: a,SV161: a] :
( ( ( ~ ( member_a @ SV161 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV33 ) @ ( add_a_b @ r @ SV33 @ SV161 ) )
= SV161 )
= $true )
| ( ( member_a @ SV33 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1135,plain,
! [SV34: a,SV162: a] :
( ( ( ~ ( member_a @ SV162 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( a_inv_a_b @ r @ ( add_a_b @ r @ SV34 @ SV162 ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV34 ) @ ( a_inv_a_b @ r @ SV162 ) ) )
= $true )
| ( ( member_a @ SV34 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1046]) ).
thf(1136,plain,
! [SV35: a,SV163: a] :
( ( ( ~ ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY416: a] :
( ~ ( member_a @ SY416 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SY416 ) )
= SV35 )
= ( SV163
= ( add_a_b @ r @ SV35 @ SY416 ) ) ) ) )
= $true )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1047]) ).
thf(1137,plain,
! [SV36: a,SV164: a] :
( ( ( ~ ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY417: a] :
( ~ ( member_a @ SY417 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV36
= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SY417 ) ) )
= ( SV164
= ( add_a_b @ r @ SV36 @ SY417 ) ) ) ) )
= $true )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1138,plain,
! [SV37: a,SV165: a] :
( ( ( ~ ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY418: a] :
( ~ ( member_a @ SY418 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SY418 )
= SV37 )
= ( SY418
= ( add_a_b @ r @ SV165 @ SV37 ) ) ) ) )
= $true )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1139,plain,
! [SV38: a,SV166: a] :
( ( ( ~ ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY419: a] :
( ~ ( member_a @ SY419 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SY419 ) )
= ( SY419
= ( add_a_b @ r @ SV166 @ SV38 ) ) ) ) )
= $true )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1050]) ).
thf(1140,plain,
! [SV39: a,SV167: a] :
( ( ( ~ ( member_a @ SV167 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( a_inv_a_b @ r @ ( add_a_b @ r @ SV39 @ SV167 ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV167 ) @ ( a_inv_a_b @ r @ SV39 ) ) )
= $true )
| ( ( member_a @ SV39 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1141,plain,
! [SV139: a,SV119: a,SV40: a] :
( ( ( ( add_a_b @ r @ SV40 @ SV119 )
= SV139 )
= $false )
| ( ( ~ ( member_a @ SV40 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV119 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV139 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV40 ) @ SV139 )
= SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1142,plain,
! [SV41: a,SV168: a] :
( ( ( ~ ( member_a @ SV168 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( ( add_a_b @ r @ SV41 @ SV168 )
!= ( zero_a_b @ r ) )
| ( SV41
= ( a_inv_a_b @ r @ SV168 ) ) )
= $true )
| ( ( member_a @ SV41 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1143,plain,
! [SV43: a,SV120: a] :
( ( ( ~ ( member_a @ SV120 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ~ ( member_a @ SV43 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ SV120 )
= SV43 ) )
= $true )
| ( ( ( add_a_b @ r @ SV43 @ SV120 )
= ( zero_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1054]) ).
thf(1144,plain,
! [SV45: a,SV169: a] :
( ( ( ~ ( member_a @ SV169 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( a_inv_a_b @ r @ ( add_a_b @ r @ SV45 @ SV169 ) )
= ( a_minus_a_b @ r @ ( a_inv_a_b @ r @ SV45 ) @ SV169 ) )
= $true )
| ( ( member_a @ SV45 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1145,plain,
! [SV52: a,SV170: a] :
( ( ( ~ ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( SV52
= ( add_a_b @ r @ SV170 @ SV52 ) )
= ( SV170
= ( zero_a_b @ r ) ) )
= $true )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1146,plain,
! [SV53: a,SV171: a] :
( ( ( ~ ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( ( add_a_b @ r @ SV171 @ SV53 )
= SV53 )
= ( SV171
= ( zero_a_b @ r ) ) )
= $true )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1147,plain,
! [SV54: a,SV172: a] :
( ( ( ~ ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( SV54
= ( add_a_b @ r @ SV54 @ SV172 ) )
= ( SV172
= ( zero_a_b @ r ) ) )
= $true )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1148,plain,
! [SV55: a,SV173: a] :
( ( ( ~ ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( ( add_a_b @ r @ SV55 @ SV173 )
= SV55 )
= ( SV173
= ( zero_a_b @ r ) ) )
= $true )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1149,plain,
! [SV56: a] :
( ( ( ~ ( ( ( a_inv_a_b @ r @ SV56 )
= ( zero_a_b @ r ) )
| ( SV56
= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( ~ ( ( ( a_inv_a_b @ r @ SV56 )
!= ( zero_a_b @ r ) )
| ( SV56
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1150,plain,
! [SV58: partia1833973666xt_a_b,SV175: a] :
( ( ( ~ ( member_a @ SV175 @ ( partia1066395285xt_a_b @ SV58 ) ) )
= $true )
| ( ( ( add_a_b @ SV58 @ SV175 @ ( zero_a_b @ SV58 ) )
= SV175 )
= $true )
| ( ( semiring_a_b @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1151,plain,
! [SV59: partia1833973666xt_a_b,SV176: a] :
( ( ( ~ ( member_a @ SV176 @ ( partia1066395285xt_a_b @ SV59 ) ) )
= $true )
| ( ( ( add_a_b @ SV59 @ ( zero_a_b @ SV59 ) @ SV176 )
= SV176 )
= $true )
| ( ( semiring_a_b @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1064]) ).
thf(1152,plain,
! [SV60: partia1833973666xt_a_b,SV177: a] :
( ( ( ~ ( member_a @ SV177 @ ( partia1066395285xt_a_b @ SV60 ) ) )
= $true )
| ( ( ( mult_a_ring_ext_a_b @ SV60 @ ( zero_a_b @ SV60 ) @ SV177 )
= ( zero_a_b @ SV60 ) )
= $true )
| ( ( semiring_a_b @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1153,plain,
! [SV61: partia1833973666xt_a_b,SV178: a] :
( ( ( ~ ( member_a @ SV178 @ ( partia1066395285xt_a_b @ SV61 ) ) )
= $true )
| ( ( ( mult_a_ring_ext_a_b @ SV61 @ SV178 @ ( zero_a_b @ SV61 ) )
= ( zero_a_b @ SV61 ) )
= $true )
| ( ( semiring_a_b @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1154,plain,
! [SV62: partia1833973666xt_a_b,SV121: a] :
( ( ( ~ ( member_a @ SV121 @ ( partia1066395285xt_a_b @ SV62 ) ) )
= $true )
| ( ( ! [SY388: a] :
( ~ ( member_a @ SY388 @ ( partia1066395285xt_a_b @ SV62 ) )
| ! [SY389: a] :
( ~ ( member_a @ SY389 @ ( partia1066395285xt_a_b @ SV62 ) )
| ( ( mult_a_ring_ext_a_b @ SV62 @ SY389 @ ( add_a_b @ SV62 @ SV121 @ SY388 ) )
= ( add_a_b @ SV62 @ ( mult_a_ring_ext_a_b @ SV62 @ SY389 @ SV121 ) @ ( mult_a_ring_ext_a_b @ SV62 @ SY389 @ SY388 ) ) ) ) ) )
= $true )
| ( ( semiring_a_b @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1067]) ).
thf(1155,plain,
! [SV63: a,SV179: a] :
( ( ( ~ ( member_a @ SV179 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY420: int] :
( ( mult_a_ring_ext_a_b @ r @ ( add_pow_a_b_int @ r @ SY420 @ SV63 ) @ SV179 )
= ( add_pow_a_b_int @ r @ SY420 @ ( mult_a_ring_ext_a_b @ r @ SV63 @ SV179 ) ) ) )
= $true )
| ( ( member_a @ SV63 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1156,plain,
! [SV64: a,SV180: a] :
( ( ( ~ ( member_a @ SV180 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY421: int] :
( ( mult_a_ring_ext_a_b @ r @ SV64 @ ( add_pow_a_b_int @ r @ SY421 @ SV180 ) )
= ( add_pow_a_b_int @ r @ SY421 @ ( mult_a_ring_ext_a_b @ r @ SV64 @ SV180 ) ) ) )
= $true )
| ( ( member_a @ SV64 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1157,plain,
! [SV65: a,SV181: a] :
( ( ( ~ ( member_a @ SV181 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY422: int] :
( ( add_pow_a_b_int @ r @ SY422 @ ( add_a_b @ r @ SV65 @ SV181 ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY422 @ SV65 ) @ ( add_pow_a_b_int @ r @ SY422 @ SV181 ) ) ) )
= $true )
| ( ( member_a @ SV65 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1158,plain,
! [SV122: a,SV66: a] :
( ( ( ~ ( member_a @ SV66 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ~ ( member_a @ SV122 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY390: int] :
( ( add_pow_a_b_int @ r @ SY390 @ ( add_a_b @ r @ SV66 @ SV122 ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY390 @ SV66 ) @ ( add_pow_a_b_int @ r @ SY390 @ SV122 ) ) ) )
= $true )
| ( ( ( add_a_b @ r @ SV66 @ SV122 )
= ( add_a_b @ r @ SV122 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1071]) ).
thf(1159,plain,
! [SV72: partia1833973666xt_a_b,SV127: a] :
( ( ( ~ ( member_a @ SV127 @ ( partia1066395285xt_a_b @ SV72 ) ) )
= $true )
| ( ( ! [SY391: a] :
( ~ ( member_a @ SY391 @ ( partia1066395285xt_a_b @ SV72 ) )
| ! [SY392: a] :
( ~ ( member_a @ SY392 @ ( partia1066395285xt_a_b @ SV72 ) )
| ( ( mult_a_ring_ext_a_b @ SV72 @ ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ SY391 ) @ SY392 )
= ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ ( mult_a_ring_ext_a_b @ SV72 @ SY391 @ SY392 ) ) ) ) ) )
= $true )
| ( ( semiring_a_b @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1160,plain,
! [SV73: partia1833973666xt_a_b,SV183: a] :
( ( ( ~ ( member_a @ SV183 @ ( partia1066395285xt_a_b @ SV73 ) ) )
= $true )
| ( ( ! [SY423: a] :
( ~ ( member_a @ SY423 @ ( partia1066395285xt_a_b @ SV73 ) )
| ( member_a @ ( mult_a_ring_ext_a_b @ SV73 @ SV183 @ SY423 ) @ ( partia1066395285xt_a_b @ SV73 ) ) ) )
= $true )
| ( ( semiring_a_b @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1161,plain,
! [SV74: partia1833973666xt_a_b,SV128: a] :
( ( ( ~ ( member_a @ SV128 @ ( partia1066395285xt_a_b @ SV74 ) ) )
= $true )
| ( ( ! [SY393: a] :
( ~ ( member_a @ SY393 @ ( partia1066395285xt_a_b @ SV74 ) )
| ! [SY394: a] :
( ~ ( member_a @ SY394 @ ( partia1066395285xt_a_b @ SV74 ) )
| ( ( add_a_b @ SV74 @ SV128 @ ( add_a_b @ SV74 @ SY393 @ SY394 ) )
= ( add_a_b @ SV74 @ SY393 @ ( add_a_b @ SV74 @ SV128 @ SY394 ) ) ) ) ) )
= $true )
| ( ( semiring_a_b @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1162,plain,
! [SV75: partia1833973666xt_a_b,SV184: a] :
( ( ( ~ ( member_a @ SV184 @ ( partia1066395285xt_a_b @ SV75 ) ) )
= $true )
| ( ( ! [SY424: a] :
( ~ ( member_a @ SY424 @ ( partia1066395285xt_a_b @ SV75 ) )
| ( ( add_a_b @ SV75 @ SV184 @ SY424 )
= ( add_a_b @ SV75 @ SY424 @ SV184 ) ) ) )
= $true )
| ( ( semiring_a_b @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1163,plain,
! [SV76: partia1833973666xt_a_b,SV129: a] :
( ( ( ~ ( member_a @ SV129 @ ( partia1066395285xt_a_b @ SV76 ) ) )
= $true )
| ( ( ! [SY395: a] :
( ~ ( member_a @ SY395 @ ( partia1066395285xt_a_b @ SV76 ) )
| ! [SY396: a] :
( ~ ( member_a @ SY396 @ ( partia1066395285xt_a_b @ SV76 ) )
| ( ( add_a_b @ SV76 @ ( add_a_b @ SV76 @ SV129 @ SY395 ) @ SY396 )
= ( add_a_b @ SV76 @ SV129 @ ( add_a_b @ SV76 @ SY395 @ SY396 ) ) ) ) ) )
= $true )
| ( ( semiring_a_b @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1080]) ).
thf(1164,plain,
! [SV77: partia1833973666xt_a_b,SV185: a] :
( ( ( ~ ( member_a @ SV185 @ ( partia1066395285xt_a_b @ SV77 ) ) )
= $true )
| ( ( ! [SY425: a] :
( ~ ( member_a @ SY425 @ ( partia1066395285xt_a_b @ SV77 ) )
| ( member_a @ ( add_a_b @ SV77 @ SV185 @ SY425 ) @ ( partia1066395285xt_a_b @ SV77 ) ) ) )
= $true )
| ( ( semiring_a_b @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1081]) ).
thf(1165,plain,
! [SV79: partia1833973666xt_a_b,SV130: a] :
( ( ( ~ ( member_a @ SV130 @ ( partia1066395285xt_a_b @ SV79 ) ) )
= $true )
| ( ( ! [SY397: a] :
( ~ ( member_a @ SY397 @ ( partia1066395285xt_a_b @ SV79 ) )
| ! [SY398: a] :
( ~ ( member_a @ SY398 @ ( partia1066395285xt_a_b @ SV79 ) )
| ( ( mult_a_ring_ext_a_b @ SV79 @ ( add_a_b @ SV79 @ SV130 @ SY397 ) @ SY398 )
= ( add_a_b @ SV79 @ ( mult_a_ring_ext_a_b @ SV79 @ SV130 @ SY398 ) @ ( mult_a_ring_ext_a_b @ SV79 @ SY397 @ SY398 ) ) ) ) ) )
= $true )
| ( ( semiring_a_b @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1166,plain,
! [SV80: a,SV199: int,SV186: int] :
( ( ( ( add_pow_a_b_int @ r @ ( minus_minus_int @ SV186 @ SV199 ) @ SV80 )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SV186 @ SV80 ) @ ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ SV199 @ SV80 ) ) ) )
= $true )
| ( ( member_a @ SV80 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1167,plain,
! [SV82: a,SV200: int,SV188: int] :
( ( ( ( add_pow_a_b_int @ r @ ( plus_plus_int @ SV188 @ SV200 ) @ SV82 )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SV188 @ SV82 ) @ ( add_pow_a_b_int @ r @ SV200 @ SV82 ) ) )
= $true )
| ( ( member_a @ SV82 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1168,plain,
! [SV84: set_a,SV189: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV189 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ord_less_eq_set_a @ ( set_add_a_b @ r @ SV84 @ SV189 ) @ ( partia1066395285xt_a_b @ r ) )
= $true )
| ( ( ord_less_eq_set_a @ SV84 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1169,plain,
! [SV85: set_a,SV190: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV190 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ord_less_eq_set_a @ ( set_add_a_b @ r @ SV85 @ SV190 ) @ ( partia1066395285xt_a_b @ r ) )
= $true )
| ( ( ord_less_eq_set_a @ SV85 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1170,plain,
! [SV87: set_a] :
( ( ( ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 ) )
= $false )
| ( ( ~ ( ~ ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 )
| ( SV87 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1089]) ).
thf(1171,plain,
! [SV87: set_a] :
( ( ( SV87 = bot_bot_set_a )
= $false )
| ( ( ~ ( ~ ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 )
| ( SV87 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1089]) ).
thf(1172,plain,
! [SV88: a > $o] :
( ( ( ( collect_a @ SV88 )
= bot_bot_set_a )
= $false )
| ( ( ~ ( ( ( collect_a @ SV88 )
!= bot_bot_set_a )
| ~ ! [SY365: a] :
~ ( SV88 @ SY365 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1173,plain,
! [SV88: a > $o] :
( ( ( ! [SY365: a] :
~ ( SV88 @ SY365 ) )
= $false )
| ( ( ~ ( ( ( collect_a @ SV88 )
!= bot_bot_set_a )
| ~ ! [SY365: a] :
~ ( SV88 @ SY365 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1174,plain,
! [SV89: a > $o] :
( ( ( bot_bot_set_a
= ( collect_a @ SV89 ) )
= $false )
| ( ( ~ ( ( bot_bot_set_a
!= ( collect_a @ SV89 ) )
| ~ ! [SY366: a] :
~ ( SV89 @ SY366 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1175,plain,
! [SV89: a > $o] :
( ( ( ! [SY366: a] :
~ ( SV89 @ SY366 ) )
= $false )
| ( ( ~ ( ( bot_bot_set_a
!= ( collect_a @ SV89 ) )
| ~ ! [SY366: a] :
~ ( SV89 @ SY366 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1176,plain,
! [SV90: set_a] :
( ( ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
| ( SV90 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1092]) ).
thf(1177,plain,
! [SV90: set_a] :
( ( ( SV90 = bot_bot_set_a )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
| ( SV90 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1092]) ).
thf(1178,plain,
! [SV96: set_a,SV191: a] :
( ( ( member_a @ SV191 @ SV96 )
= $false )
| ( ( SV96 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1179,plain,
! [SV132: set_a,SV98: set_a,SV201: a] :
( ( ( ~ ( member_a @ SV201 @ SV98 )
| ( member_a @ SV201 @ SV132 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV98 @ SV132 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1180,plain,
! [SV133: set_a,SV99: set_a,SV202: a] :
( ( ( ~ ( member_a @ SV202 @ SV99 )
| ( member_a @ SV202 @ SV133 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV99 @ SV133 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1181,plain,
! [SV100: set_a,SV134: set_a] :
( ( ( ~ ( member_a @ ( sK2_X3 @ SV134 @ SV100 ) @ SV100 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV100 @ SV134 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1096]) ).
thf(1182,plain,
! [SV100: set_a,SV134: set_a] :
( ( ( ~ ~ ( member_a @ ( sK2_X3 @ SV134 @ SV100 ) @ SV134 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV100 @ SV134 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1096]) ).
thf(1183,plain,
! [SV101: set_a] :
( ( ( ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 )
| ~ ( ( SV101 != bot_bot_set_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1097]) ).
thf(1184,plain,
! [SV101: set_a] :
( ( ( SV101 != bot_bot_set_a )
= $false )
| ( ( ~ ( ~ ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 )
| ~ ( ( SV101 != bot_bot_set_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1097]) ).
thf(1185,plain,
! [SV192: set_a,SV135: set_a] :
( ( ~ ( ( ord_less_eq_set_a @ SV135 @ SV192 )
| ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV135 @ SV192 )
| ~ ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1098]) ).
thf(1186,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ord_less_eq_set_a @ SV135 @ SV192 )
= ( ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1098]) ).
thf(1187,plain,
! [SV103: a] :
( ( ( ( add_a_b @ r @ ( sK8_X3 @ SV103 ) @ SV103 )
!= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV103 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1099]) ).
thf(1188,plain,
! [SV103: a] :
( ( ( ~ ( member_a @ ( sK8_X3 @ SV103 ) @ ( partia1066395285xt_a_b @ r ) ) )
= $false )
| ( ( member_a @ SV103 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1099]) ).
thf(1189,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ~ ( ( SV136 = SV193 )
| ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) )
| ~ ( ( SV136 != SV193 )
| ~ ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1100]) ).
thf(1190,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( SV136 = SV193 )
= ( ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1100]) ).
thf(1191,plain,
! [SV105: set_a] :
( ( ( ~ ( ~ ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 ) ) )
= $true )
| ( ( ~ ( ~ ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 )
| ~ ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) )
| ( member_a @ ( zero_a_b @ r ) @ SV105 ) )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1101]) ).
thf(1192,plain,
! [SV106: a] :
( ( ( ~ ( member_a @ ( sK9_X3 @ SV106 ) @ ( partia1066395285xt_a_b @ r ) )
| ~ ( ( ( add_a_b @ r @ SV106 @ ( sK9_X3 @ SV106 ) )
!= ( sK9_X3 @ SV106 ) ) ) )
= $false )
| ( ( SV106
= ( zero_a_b @ r ) )
= $true )
| ( ( member_a @ SV106 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1193,plain,
! [SV107: a] :
( ( ( ( add_a_b @ r @ SV107 @ ( sK10_X3 @ SV107 ) )
!= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV107 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1194,plain,
! [SV107: a] :
( ( ( ~ ( member_a @ ( sK10_X3 @ SV107 ) @ ( partia1066395285xt_a_b @ r ) ) )
= $false )
| ( ( member_a @ SV107 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1195,plain,
! [SV3: a,SV142: a] :
( ( ( member_a @ SV142 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY407: a] :
( ~ ( member_a @ SY407 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV3 @ SV142 ) @ SY407 )
= ( mult_a_ring_ext_a_b @ r @ SV3 @ ( mult_a_ring_ext_a_b @ r @ SV142 @ SY407 ) ) ) ) )
= $true )
| ( ( member_a @ SV3 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1196,plain,
! [SV4: a,SV143: a] :
( ( ( member_a @ SV143 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( mult_a_ring_ext_a_b @ r @ SV4 @ SV143 )
= ( mult_a_ring_ext_a_b @ r @ SV143 @ SV4 ) )
= $true )
| ( ( member_a @ SV4 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1197,plain,
! [SV5: a,SV144: a] :
( ( ( member_a @ SV144 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY408: a] :
( ~ ( member_a @ SY408 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SV5 @ ( mult_a_ring_ext_a_b @ r @ SV144 @ SY408 ) )
= ( mult_a_ring_ext_a_b @ r @ SV144 @ ( mult_a_ring_ext_a_b @ r @ SV5 @ SY408 ) ) ) ) )
= $true )
| ( ( member_a @ SV5 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1198,plain,
! [SV6: a,SV145: a] :
( ( ( member_a @ SV145 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY409: a] :
( ~ ( member_a @ SY409 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( add_a_b @ r @ SV6 @ SV145 ) @ SY409 )
= ( add_a_b @ r @ SV6 @ ( add_a_b @ r @ SV145 @ SY409 ) ) ) ) )
= $true )
| ( ( member_a @ SV6 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1199,plain,
! [SV7: a,SV146: a] :
( ( ( member_a @ SV146 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV7 @ SV146 )
= ( add_a_b @ r @ SV146 @ SV7 ) )
= $true )
| ( ( member_a @ SV7 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1200,plain,
! [SV8: a,SV147: a] :
( ( ( member_a @ SV147 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY410: a] :
( ~ ( member_a @ SY410 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV8 @ ( add_a_b @ r @ SV147 @ SY410 ) )
= ( add_a_b @ r @ SV147 @ ( add_a_b @ r @ SV8 @ SY410 ) ) ) ) )
= $true )
| ( ( member_a @ SV8 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1201,plain,
! [SV9: a,SV148: a] :
( ( ( member_a @ SV148 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY411: a] :
( ~ ( member_a @ SY411 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( add_a_b @ r @ SV9 @ SV148 ) @ SY411 )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV9 @ SY411 ) @ ( mult_a_ring_ext_a_b @ r @ SV148 @ SY411 ) ) ) ) )
= $true )
| ( ( member_a @ SV9 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1202,plain,
! [SV10: a,SV149: a] :
( ( ( member_a @ SV149 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY412: a] :
( ~ ( member_a @ SY412 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SY412 @ ( add_a_b @ r @ SV10 @ SV149 ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SY412 @ SV10 ) @ ( mult_a_ring_ext_a_b @ r @ SY412 @ SV149 ) ) ) ) )
= $true )
| ( ( member_a @ SV10 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1203,plain,
! [SV11: a,SV110: a] :
( ( ( member_a @ SV110 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY380: a] :
( ~ ( member_a @ SY380 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY381: a] :
( ~ ( member_a @ SY381 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ SV11 @ SY380 ) @ SV110 ) @ SY381 )
= ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ ( add_a_b @ r @ SV11 @ SV110 ) @ SY380 ) @ SY381 ) ) ) ) )
= $true )
| ( ( member_a @ SV11 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1204,plain,
! [SV12: a,SV150: a] :
( ( ( member_a @ SV150 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY413: a] :
( ~ ( member_a @ SY413 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ SY413 @ SV12 ) @ SV150 )
= ( a_minus_a_b @ r @ SY413 @ ( add_a_b @ r @ SV12 @ SV150 ) ) ) ) )
= $true )
| ( ( member_a @ SV12 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1205,plain,
( ( ( member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) )
= $true )
| ( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1206,plain,
! [SV13: a,SV151: a] :
( ( ( member_a @ SV151 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ ( a_minus_a_b @ r @ SV13 @ SV151 ) @ ( partia1066395285xt_a_b @ r ) )
= $true )
| ( ( member_a @ SV13 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1207,plain,
! [SV14: a,SV152: a] :
( ( ( member_a @ SV152 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ ( add_a_b @ r @ SV14 @ SV152 ) @ ( partia1066395285xt_a_b @ r ) )
= $true )
| ( ( member_a @ SV14 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1208,plain,
! [SV15: a,SV153: a] :
( ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY414: a] :
( ~ ( member_a @ SY414 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SV153 @ SV15 )
= ( add_a_b @ r @ SY414 @ SV15 ) )
= ( SV153 = SY414 ) ) ) )
= $true )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1209,plain,
! [SV16: a,SV154: a] :
( ( ( member_a @ SV154 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ ( mult_a_ring_ext_a_b @ r @ SV16 @ SV154 ) @ ( partia1066395285xt_a_b @ r ) )
= $true )
| ( ( member_a @ SV16 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1210,plain,
! [SV112: product_prod_a_a,SV18: product_prod_a_a] :
( ( ( ( product_snd_a_a @ SV18 )
= ( product_snd_a_a @ SV112 ) )
= $false )
| ( ( SV18 = SV112 )
= $true )
| ( ( ( product_fst_a_a @ SV18 )
= ( product_fst_a_a @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1211,plain,
! [SV113: product_prod_a_a,SV20: product_prod_a_a] :
( ( ( ( product_snd_a_a @ SV20 )
= ( product_snd_a_a @ SV113 ) )
= $false )
| ( ( ( product_fst_a_a @ SV20 )
= ( product_fst_a_a @ SV113 ) )
= $false )
| ( ( SV20 = SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1212,plain,
! [SV21: a,SV155: a] :
( ( ( member_a @ SV155 @ s )
= $false )
| ( ( member_a @ ( mult_a_ring_ext_a_b @ r @ SV21 @ SV155 ) @ s )
= $true )
| ( ( member_a @ SV21 @ s )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1213,plain,
! [SV23: partia1833973666xt_a_b,SV114: set_a,SV196: a] :
( ( ( ~ ( member_a @ SV196 @ SV114 ) )
= $true )
| ( ( ! [SY429: a] :
( ~ ( member_a @ SY429 @ SV114 )
| ( member_a @ ( mult_a_ring_ext_a_b @ SV23 @ SV196 @ SY429 ) @ SV114 ) ) )
= $true )
| ( ( locali425460998xt_a_b @ SV23 @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1214,plain,
! [SV203: a,SV156: a,SV115: partia1833973666xt_a_b] :
( ( ( a_minus_a_b @ SV115 @ SV156 @ SV203 )
= ( add_a_b @ SV115 @ SV156 @ ( a_inv_a_b @ SV115 @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1215,plain,
! [SV25: set_a,SV157: set_a] :
( ( ( additi2104487374up_a_b @ SV157 @ r )
= $false )
| ( ( additi2104487374up_a_b @ ( set_add_a_b @ r @ SV25 @ SV157 ) @ r )
= $true )
| ( ( additi2104487374up_a_b @ SV25 @ r )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1216,plain,
! [SV116: a > $o,SV26: a] :
( ( ( member_a @ SV26 @ ( collect_a @ SV116 ) )
= $false )
| ( ( ~ ( ~ ( member_a @ SV26 @ ( collect_a @ SV116 ) )
| ~ ( SV116 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1128]) ).
thf(1217,plain,
! [SV26: a,SV116: a > $o] :
( ( ( SV116 @ SV26 )
= $false )
| ( ( ~ ( ~ ( member_a @ SV26 @ ( collect_a @ SV116 ) )
| ~ ( SV116 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1128]) ).
thf(1218,plain,
! [SV28: a,SV198: a,SV117: a] :
( ( ( ( add_a_b @ r @ SV117 @ SV198 )
!= ( zero_a_b @ r ) )
= $true )
| ( ( ~ ( member_a @ SV117 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV28 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV198 @ ( partia1066395285xt_a_b @ r ) )
| ( SV28 = SV198 ) )
= $true )
| ( ( ( add_a_b @ r @ SV28 @ SV117 )
= ( zero_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1219,plain,
! [SV118: a,SV29: a] :
( ( ( member_a @ SV29 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ~ ( member_a @ SV118 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV118 @ SV29 )
= ( zero_a_b @ r ) ) )
= $true )
| ( ( ( add_a_b @ r @ SV29 @ SV118 )
= ( zero_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1220,plain,
! [SV30: a,SV158: a] :
( ( ( member_a @ SV158 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( mult_a_ring_ext_a_b @ r @ SV30 @ ( a_inv_a_b @ r @ SV158 ) )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV30 @ SV158 ) ) )
= $true )
| ( ( member_a @ SV30 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1221,plain,
! [SV31: a,SV159: a] :
( ( ( member_a @ SV159 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( mult_a_ring_ext_a_b @ r @ ( a_inv_a_b @ r @ SV31 ) @ SV159 )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV31 @ SV159 ) ) )
= $true )
| ( ( member_a @ SV31 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1222,plain,
! [SV32: a,SV160: a] :
( ( ( member_a @ SV160 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV32 @ ( add_a_b @ r @ ( a_inv_a_b @ r @ SV32 ) @ SV160 ) )
= SV160 )
= $true )
| ( ( member_a @ SV32 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1223,plain,
! [SV33: a,SV161: a] :
( ( ( member_a @ SV161 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV33 ) @ ( add_a_b @ r @ SV33 @ SV161 ) )
= SV161 )
= $true )
| ( ( member_a @ SV33 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1224,plain,
! [SV34: a,SV162: a] :
( ( ( member_a @ SV162 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( a_inv_a_b @ r @ ( add_a_b @ r @ SV34 @ SV162 ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV34 ) @ ( a_inv_a_b @ r @ SV162 ) ) )
= $true )
| ( ( member_a @ SV34 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1225,plain,
! [SV35: a,SV163: a] :
( ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY416: a] :
( ~ ( member_a @ SY416 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SY416 ) )
= SV35 )
= ( SV163
= ( add_a_b @ r @ SV35 @ SY416 ) ) ) ) )
= $true )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1226,plain,
! [SV36: a,SV164: a] :
( ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY417: a] :
( ~ ( member_a @ SY417 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV36
= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SY417 ) ) )
= ( SV164
= ( add_a_b @ r @ SV36 @ SY417 ) ) ) ) )
= $true )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1227,plain,
! [SV37: a,SV165: a] :
( ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY418: a] :
( ~ ( member_a @ SY418 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SY418 )
= SV37 )
= ( SY418
= ( add_a_b @ r @ SV165 @ SV37 ) ) ) ) )
= $true )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1228,plain,
! [SV38: a,SV166: a] :
( ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY419: a] :
( ~ ( member_a @ SY419 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SY419 ) )
= ( SY419
= ( add_a_b @ r @ SV166 @ SV38 ) ) ) ) )
= $true )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1229,plain,
! [SV39: a,SV167: a] :
( ( ( member_a @ SV167 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( a_inv_a_b @ r @ ( add_a_b @ r @ SV39 @ SV167 ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV167 ) @ ( a_inv_a_b @ r @ SV39 ) ) )
= $true )
| ( ( member_a @ SV39 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1230,plain,
! [SV139: a,SV119: a,SV40: a] :
( ( ( ~ ( member_a @ SV40 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ~ ( member_a @ SV119 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV139 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV40 ) @ SV139 )
= SV119 ) )
= $true )
| ( ( ( add_a_b @ r @ SV40 @ SV119 )
= SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1231,plain,
! [SV41: a,SV168: a] :
( ( ( member_a @ SV168 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( ( add_a_b @ r @ SV41 @ SV168 )
!= ( zero_a_b @ r ) )
| ( SV41
= ( a_inv_a_b @ r @ SV168 ) ) )
= $true )
| ( ( member_a @ SV41 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1232,plain,
! [SV43: a,SV120: a] :
( ( ( member_a @ SV120 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ~ ( member_a @ SV43 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_inv_a_b @ r @ SV120 )
= SV43 ) )
= $true )
| ( ( ( add_a_b @ r @ SV43 @ SV120 )
= ( zero_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1233,plain,
! [SV45: a,SV169: a] :
( ( ( member_a @ SV169 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( a_inv_a_b @ r @ ( add_a_b @ r @ SV45 @ SV169 ) )
= ( a_minus_a_b @ r @ ( a_inv_a_b @ r @ SV45 ) @ SV169 ) )
= $true )
| ( ( member_a @ SV45 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1234,plain,
! [SV52: a,SV170: a] :
( ( ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( SV52
= ( add_a_b @ r @ SV170 @ SV52 ) )
= ( SV170
= ( zero_a_b @ r ) ) )
= $true )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1235,plain,
! [SV53: a,SV171: a] :
( ( ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( ( add_a_b @ r @ SV171 @ SV53 )
= SV53 )
= ( SV171
= ( zero_a_b @ r ) ) )
= $true )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1236,plain,
! [SV54: a,SV172: a] :
( ( ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( SV54
= ( add_a_b @ r @ SV54 @ SV172 ) )
= ( SV172
= ( zero_a_b @ r ) ) )
= $true )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1237,plain,
! [SV55: a,SV173: a] :
( ( ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( ( add_a_b @ r @ SV55 @ SV173 )
= SV55 )
= ( SV173
= ( zero_a_b @ r ) ) )
= $true )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1238,plain,
! [SV56: a] :
( ( ( ( ( a_inv_a_b @ r @ SV56 )
= ( zero_a_b @ r ) )
| ( SV56
= ( zero_a_b @ r ) ) )
= $false )
| ( ( ~ ( ( ( a_inv_a_b @ r @ SV56 )
!= ( zero_a_b @ r ) )
| ( SV56
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1239,plain,
! [SV58: partia1833973666xt_a_b,SV175: a] :
( ( ( member_a @ SV175 @ ( partia1066395285xt_a_b @ SV58 ) )
= $false )
| ( ( ( add_a_b @ SV58 @ SV175 @ ( zero_a_b @ SV58 ) )
= SV175 )
= $true )
| ( ( semiring_a_b @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1240,plain,
! [SV59: partia1833973666xt_a_b,SV176: a] :
( ( ( member_a @ SV176 @ ( partia1066395285xt_a_b @ SV59 ) )
= $false )
| ( ( ( add_a_b @ SV59 @ ( zero_a_b @ SV59 ) @ SV176 )
= SV176 )
= $true )
| ( ( semiring_a_b @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1241,plain,
! [SV60: partia1833973666xt_a_b,SV177: a] :
( ( ( member_a @ SV177 @ ( partia1066395285xt_a_b @ SV60 ) )
= $false )
| ( ( ( mult_a_ring_ext_a_b @ SV60 @ ( zero_a_b @ SV60 ) @ SV177 )
= ( zero_a_b @ SV60 ) )
= $true )
| ( ( semiring_a_b @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1242,plain,
! [SV61: partia1833973666xt_a_b,SV178: a] :
( ( ( member_a @ SV178 @ ( partia1066395285xt_a_b @ SV61 ) )
= $false )
| ( ( ( mult_a_ring_ext_a_b @ SV61 @ SV178 @ ( zero_a_b @ SV61 ) )
= ( zero_a_b @ SV61 ) )
= $true )
| ( ( semiring_a_b @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1243,plain,
! [SV62: partia1833973666xt_a_b,SV121: a] :
( ( ( member_a @ SV121 @ ( partia1066395285xt_a_b @ SV62 ) )
= $false )
| ( ( ! [SY388: a] :
( ~ ( member_a @ SY388 @ ( partia1066395285xt_a_b @ SV62 ) )
| ! [SY389: a] :
( ~ ( member_a @ SY389 @ ( partia1066395285xt_a_b @ SV62 ) )
| ( ( mult_a_ring_ext_a_b @ SV62 @ SY389 @ ( add_a_b @ SV62 @ SV121 @ SY388 ) )
= ( add_a_b @ SV62 @ ( mult_a_ring_ext_a_b @ SV62 @ SY389 @ SV121 ) @ ( mult_a_ring_ext_a_b @ SV62 @ SY389 @ SY388 ) ) ) ) ) )
= $true )
| ( ( semiring_a_b @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1244,plain,
! [SV63: a,SV179: a] :
( ( ( member_a @ SV179 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY420: int] :
( ( mult_a_ring_ext_a_b @ r @ ( add_pow_a_b_int @ r @ SY420 @ SV63 ) @ SV179 )
= ( add_pow_a_b_int @ r @ SY420 @ ( mult_a_ring_ext_a_b @ r @ SV63 @ SV179 ) ) ) )
= $true )
| ( ( member_a @ SV63 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1245,plain,
! [SV64: a,SV180: a] :
( ( ( member_a @ SV180 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY421: int] :
( ( mult_a_ring_ext_a_b @ r @ SV64 @ ( add_pow_a_b_int @ r @ SY421 @ SV180 ) )
= ( add_pow_a_b_int @ r @ SY421 @ ( mult_a_ring_ext_a_b @ r @ SV64 @ SV180 ) ) ) )
= $true )
| ( ( member_a @ SV64 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1246,plain,
! [SV65: a,SV181: a] :
( ( ( member_a @ SV181 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY422: int] :
( ( add_pow_a_b_int @ r @ SY422 @ ( add_a_b @ r @ SV65 @ SV181 ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY422 @ SV65 ) @ ( add_pow_a_b_int @ r @ SY422 @ SV181 ) ) ) )
= $true )
| ( ( member_a @ SV65 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1247,plain,
! [SV122: a,SV66: a] :
( ( ( member_a @ SV66 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ~ ( member_a @ SV122 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY390: int] :
( ( add_pow_a_b_int @ r @ SY390 @ ( add_a_b @ r @ SV66 @ SV122 ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY390 @ SV66 ) @ ( add_pow_a_b_int @ r @ SY390 @ SV122 ) ) ) )
= $true )
| ( ( ( add_a_b @ r @ SV66 @ SV122 )
= ( add_a_b @ r @ SV122 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1158]) ).
thf(1248,plain,
! [SV72: partia1833973666xt_a_b,SV127: a] :
( ( ( member_a @ SV127 @ ( partia1066395285xt_a_b @ SV72 ) )
= $false )
| ( ( ! [SY391: a] :
( ~ ( member_a @ SY391 @ ( partia1066395285xt_a_b @ SV72 ) )
| ! [SY392: a] :
( ~ ( member_a @ SY392 @ ( partia1066395285xt_a_b @ SV72 ) )
| ( ( mult_a_ring_ext_a_b @ SV72 @ ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ SY391 ) @ SY392 )
= ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ ( mult_a_ring_ext_a_b @ SV72 @ SY391 @ SY392 ) ) ) ) ) )
= $true )
| ( ( semiring_a_b @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1249,plain,
! [SV73: partia1833973666xt_a_b,SV183: a] :
( ( ( member_a @ SV183 @ ( partia1066395285xt_a_b @ SV73 ) )
= $false )
| ( ( ! [SY423: a] :
( ~ ( member_a @ SY423 @ ( partia1066395285xt_a_b @ SV73 ) )
| ( member_a @ ( mult_a_ring_ext_a_b @ SV73 @ SV183 @ SY423 ) @ ( partia1066395285xt_a_b @ SV73 ) ) ) )
= $true )
| ( ( semiring_a_b @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1250,plain,
! [SV74: partia1833973666xt_a_b,SV128: a] :
( ( ( member_a @ SV128 @ ( partia1066395285xt_a_b @ SV74 ) )
= $false )
| ( ( ! [SY393: a] :
( ~ ( member_a @ SY393 @ ( partia1066395285xt_a_b @ SV74 ) )
| ! [SY394: a] :
( ~ ( member_a @ SY394 @ ( partia1066395285xt_a_b @ SV74 ) )
| ( ( add_a_b @ SV74 @ SV128 @ ( add_a_b @ SV74 @ SY393 @ SY394 ) )
= ( add_a_b @ SV74 @ SY393 @ ( add_a_b @ SV74 @ SV128 @ SY394 ) ) ) ) ) )
= $true )
| ( ( semiring_a_b @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1251,plain,
! [SV75: partia1833973666xt_a_b,SV184: a] :
( ( ( member_a @ SV184 @ ( partia1066395285xt_a_b @ SV75 ) )
= $false )
| ( ( ! [SY424: a] :
( ~ ( member_a @ SY424 @ ( partia1066395285xt_a_b @ SV75 ) )
| ( ( add_a_b @ SV75 @ SV184 @ SY424 )
= ( add_a_b @ SV75 @ SY424 @ SV184 ) ) ) )
= $true )
| ( ( semiring_a_b @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1252,plain,
! [SV76: partia1833973666xt_a_b,SV129: a] :
( ( ( member_a @ SV129 @ ( partia1066395285xt_a_b @ SV76 ) )
= $false )
| ( ( ! [SY395: a] :
( ~ ( member_a @ SY395 @ ( partia1066395285xt_a_b @ SV76 ) )
| ! [SY396: a] :
( ~ ( member_a @ SY396 @ ( partia1066395285xt_a_b @ SV76 ) )
| ( ( add_a_b @ SV76 @ ( add_a_b @ SV76 @ SV129 @ SY395 ) @ SY396 )
= ( add_a_b @ SV76 @ SV129 @ ( add_a_b @ SV76 @ SY395 @ SY396 ) ) ) ) ) )
= $true )
| ( ( semiring_a_b @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1253,plain,
! [SV77: partia1833973666xt_a_b,SV185: a] :
( ( ( member_a @ SV185 @ ( partia1066395285xt_a_b @ SV77 ) )
= $false )
| ( ( ! [SY425: a] :
( ~ ( member_a @ SY425 @ ( partia1066395285xt_a_b @ SV77 ) )
| ( member_a @ ( add_a_b @ SV77 @ SV185 @ SY425 ) @ ( partia1066395285xt_a_b @ SV77 ) ) ) )
= $true )
| ( ( semiring_a_b @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1254,plain,
! [SV79: partia1833973666xt_a_b,SV130: a] :
( ( ( member_a @ SV130 @ ( partia1066395285xt_a_b @ SV79 ) )
= $false )
| ( ( ! [SY397: a] :
( ~ ( member_a @ SY397 @ ( partia1066395285xt_a_b @ SV79 ) )
| ! [SY398: a] :
( ~ ( member_a @ SY398 @ ( partia1066395285xt_a_b @ SV79 ) )
| ( ( mult_a_ring_ext_a_b @ SV79 @ ( add_a_b @ SV79 @ SV130 @ SY397 ) @ SY398 )
= ( add_a_b @ SV79 @ ( mult_a_ring_ext_a_b @ SV79 @ SV130 @ SY398 ) @ ( mult_a_ring_ext_a_b @ SV79 @ SY397 @ SY398 ) ) ) ) ) )
= $true )
| ( ( semiring_a_b @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1255,plain,
! [SV84: set_a,SV189: set_a] :
( ( ( ord_less_eq_set_a @ SV189 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ord_less_eq_set_a @ ( set_add_a_b @ r @ SV84 @ SV189 ) @ ( partia1066395285xt_a_b @ r ) )
= $true )
| ( ( ord_less_eq_set_a @ SV84 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1256,plain,
! [SV85: set_a,SV190: set_a] :
( ( ( ord_less_eq_set_a @ SV190 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ord_less_eq_set_a @ ( set_add_a_b @ r @ SV85 @ SV190 ) @ ( partia1066395285xt_a_b @ r ) )
= $true )
| ( ( ord_less_eq_set_a @ SV85 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1257,plain,
! [SV87: set_a] :
( ( ( ~ ( member_a @ ( sK13_SY364 @ SV87 ) @ SV87 ) )
= $false )
| ( ( ~ ( ~ ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 )
| ( SV87 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1170]) ).
thf(1258,plain,
! [SV87: set_a] :
( ( ( ~ ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 )
| ( SV87 != bot_bot_set_a ) )
= $false )
| ( ( SV87 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1259,plain,
! [SV88: a > $o] :
( ( ( ( ( collect_a @ SV88 )
!= bot_bot_set_a )
| ~ ! [SY365: a] :
~ ( SV88 @ SY365 ) )
= $false )
| ( ( ( collect_a @ SV88 )
= bot_bot_set_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1260,plain,
! [SV88: a > $o] :
( ( ( ~ ( SV88 @ ( sK14_SY365 @ SV88 ) ) )
= $false )
| ( ( ~ ( ( ( collect_a @ SV88 )
!= bot_bot_set_a )
| ~ ! [SY365: a] :
~ ( SV88 @ SY365 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1173]) ).
thf(1261,plain,
! [SV89: a > $o] :
( ( ( ( bot_bot_set_a
!= ( collect_a @ SV89 ) )
| ~ ! [SY366: a] :
~ ( SV89 @ SY366 ) )
= $false )
| ( ( bot_bot_set_a
= ( collect_a @ SV89 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1262,plain,
! [SV89: a > $o] :
( ( ( ~ ( SV89 @ ( sK15_SY366 @ SV89 ) ) )
= $false )
| ( ( ~ ( ( bot_bot_set_a
!= ( collect_a @ SV89 ) )
| ~ ! [SY366: a] :
~ ( SV89 @ SY366 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1175]) ).
thf(1263,plain,
! [SV90: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
| ( SV90 != bot_bot_set_a ) )
= $false )
| ( ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1264,plain,
! [SV90: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
| ( SV90 != bot_bot_set_a ) )
= $false )
| ( ( SV90 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1265,plain,
! [SV132: set_a,SV98: set_a,SV201: a] :
( ( ( ~ ( member_a @ SV201 @ SV98 ) )
= $true )
| ( ( member_a @ SV201 @ SV132 )
= $true )
| ( ( ord_less_eq_set_a @ SV98 @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1179]) ).
thf(1266,plain,
! [SV133: set_a,SV99: set_a,SV202: a] :
( ( ( ~ ( member_a @ SV202 @ SV99 ) )
= $true )
| ( ( member_a @ SV202 @ SV133 )
= $true )
| ( ( ord_less_eq_set_a @ SV99 @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1267,plain,
! [SV100: set_a,SV134: set_a] :
( ( ( member_a @ ( sK2_X3 @ SV134 @ SV100 ) @ SV100 )
= $true )
| ( ( ord_less_eq_set_a @ SV100 @ SV134 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1181]) ).
thf(1268,plain,
! [SV100: set_a,SV134: set_a] :
( ( ( ~ ( member_a @ ( sK2_X3 @ SV134 @ SV100 ) @ SV134 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV100 @ SV134 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1182]) ).
thf(1269,plain,
! [SV101: set_a] :
( ( ( ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 )
| ~ ( ( SV101 != bot_bot_set_a ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1183]) ).
thf(1270,plain,
! [SV101: set_a] :
( ( ( SV101 = bot_bot_set_a )
= $true )
| ( ( ~ ( ~ ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 )
| ~ ( ( SV101 != bot_bot_set_a ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1184]) ).
thf(1271,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ~ ( ( ord_less_eq_set_a @ SV135 @ SV192 )
| ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV135 @ SV192 )
| ~ ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1185]) ).
thf(1272,plain,
! [SV103: a] :
( ( ( ( add_a_b @ r @ ( sK8_X3 @ SV103 ) @ SV103 )
= ( zero_a_b @ r ) )
= $true )
| ( ( member_a @ SV103 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1187]) ).
thf(1273,plain,
! [SV103: a] :
( ( ( member_a @ ( sK8_X3 @ SV103 ) @ ( partia1066395285xt_a_b @ r ) )
= $true )
| ( ( member_a @ SV103 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1188]) ).
thf(1274,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ~ ( ( SV136 = SV193 )
| ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) ) )
= $true )
| ( ( ~ ( ( SV136 != SV193 )
| ~ ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1275,plain,
! [SV105: set_a] :
( ( ( ~ ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 ) )
= $false )
| ( ( ~ ( ~ ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 )
| ~ ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) )
| ( member_a @ ( zero_a_b @ r ) @ SV105 ) )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1276,plain,
! [SV106: a] :
( ( ( ~ ( member_a @ ( sK9_X3 @ SV106 ) @ ( partia1066395285xt_a_b @ r ) ) )
= $false )
| ( ( SV106
= ( zero_a_b @ r ) )
= $true )
| ( ( member_a @ SV106 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1192]) ).
thf(1277,plain,
! [SV106: a] :
( ( ( ~ ( ( ( add_a_b @ r @ SV106 @ ( sK9_X3 @ SV106 ) )
!= ( sK9_X3 @ SV106 ) ) ) )
= $false )
| ( ( SV106
= ( zero_a_b @ r ) )
= $true )
| ( ( member_a @ SV106 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1192]) ).
thf(1278,plain,
! [SV107: a] :
( ( ( ( add_a_b @ r @ SV107 @ ( sK10_X3 @ SV107 ) )
= ( zero_a_b @ r ) )
= $true )
| ( ( member_a @ SV107 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1193]) ).
thf(1279,plain,
! [SV107: a] :
( ( ( member_a @ ( sK10_X3 @ SV107 ) @ ( partia1066395285xt_a_b @ r ) )
= $true )
| ( ( member_a @ SV107 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1194]) ).
thf(1280,plain,
! [SV142: a,SV3: a,SV204: a] :
( ( ( ~ ( member_a @ SV204 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV3 @ SV142 ) @ SV204 )
= ( mult_a_ring_ext_a_b @ r @ SV3 @ ( mult_a_ring_ext_a_b @ r @ SV142 @ SV204 ) ) ) )
= $true )
| ( ( member_a @ SV142 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV3 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1281,plain,
! [SV144: a,SV5: a,SV205: a] :
( ( ( ~ ( member_a @ SV205 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SV5 @ ( mult_a_ring_ext_a_b @ r @ SV144 @ SV205 ) )
= ( mult_a_ring_ext_a_b @ r @ SV144 @ ( mult_a_ring_ext_a_b @ r @ SV5 @ SV205 ) ) ) )
= $true )
| ( ( member_a @ SV144 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV5 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1282,plain,
! [SV145: a,SV6: a,SV206: a] :
( ( ( ~ ( member_a @ SV206 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( add_a_b @ r @ SV6 @ SV145 ) @ SV206 )
= ( add_a_b @ r @ SV6 @ ( add_a_b @ r @ SV145 @ SV206 ) ) ) )
= $true )
| ( ( member_a @ SV145 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV6 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1283,plain,
! [SV147: a,SV8: a,SV207: a] :
( ( ( ~ ( member_a @ SV207 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ SV8 @ ( add_a_b @ r @ SV147 @ SV207 ) )
= ( add_a_b @ r @ SV147 @ ( add_a_b @ r @ SV8 @ SV207 ) ) ) )
= $true )
| ( ( member_a @ SV147 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV8 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1284,plain,
! [SV148: a,SV9: a,SV208: a] :
( ( ( ~ ( member_a @ SV208 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( add_a_b @ r @ SV9 @ SV148 ) @ SV208 )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV9 @ SV208 ) @ ( mult_a_ring_ext_a_b @ r @ SV148 @ SV208 ) ) ) )
= $true )
| ( ( member_a @ SV148 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV9 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1285,plain,
! [SV149: a,SV10: a,SV209: a] :
( ( ( ~ ( member_a @ SV209 @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ SV209 @ ( add_a_b @ r @ SV10 @ SV149 ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV209 @ SV10 ) @ ( mult_a_ring_ext_a_b @ r @ SV209 @ SV149 ) ) ) )
= $true )
| ( ( member_a @ SV149 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV10 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1286,plain,
! [SV110: a,SV11: a,SV210: a] :
( ( ( ~ ( member_a @ SV210 @ ( partia1066395285xt_a_b @ r ) )
| ! [SY430: a] :
( ~ ( member_a @ SY430 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ SV11 @ SV210 ) @ SV110 ) @ SY430 )
= ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ ( add_a_b @ r @ SV11 @ SV110 ) @ SV210 ) @ SY430 ) ) ) )
= $true )
| ( ( member_a @ SV110 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV11 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1287,plain,
! [SV150: a,SV12: a,SV211: a] :
( ( ( ~ ( member_a @ SV211 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ SV211 @ SV12 ) @ SV150 )
= ( a_minus_a_b @ r @ SV211 @ ( add_a_b @ r @ SV12 @ SV150 ) ) ) )
= $true )
| ( ( member_a @ SV150 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV12 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1288,plain,
! [SV15: a,SV153: a,SV212: a] :
( ( ( ~ ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SV153 @ SV15 )
= ( add_a_b @ r @ SV212 @ SV15 ) )
= ( SV153 = SV212 ) ) )
= $true )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1289,plain,
! [SV23: partia1833973666xt_a_b,SV114: set_a,SV196: a] :
( ( ( member_a @ SV196 @ SV114 )
= $false )
| ( ( ! [SY429: a] :
( ~ ( member_a @ SY429 @ SV114 )
| ( member_a @ ( mult_a_ring_ext_a_b @ SV23 @ SV196 @ SY429 ) @ SV114 ) ) )
= $true )
| ( ( locali425460998xt_a_b @ SV23 @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1290,plain,
! [SV116: a > $o,SV26: a] :
( ( ( ~ ( member_a @ SV26 @ ( collect_a @ SV116 ) )
| ~ ( SV116 @ SV26 ) )
= $false )
| ( ( member_a @ SV26 @ ( collect_a @ SV116 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1291,plain,
! [SV116: a > $o,SV26: a] :
( ( ( ~ ( member_a @ SV26 @ ( collect_a @ SV116 ) )
| ~ ( SV116 @ SV26 ) )
= $false )
| ( ( SV116 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1292,plain,
! [SV28: a,SV198: a,SV117: a] :
( ( ( ( add_a_b @ r @ SV117 @ SV198 )
= ( zero_a_b @ r ) )
= $false )
| ( ( ~ ( member_a @ SV117 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV28 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV198 @ ( partia1066395285xt_a_b @ r ) )
| ( SV28 = SV198 ) )
= $true )
| ( ( ( add_a_b @ r @ SV28 @ SV117 )
= ( zero_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1293,plain,
! [SV29: a,SV118: a] :
( ( ( ~ ( member_a @ SV118 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( add_a_b @ r @ SV118 @ SV29 )
= ( zero_a_b @ r ) )
= $true )
| ( ( member_a @ SV29 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV29 @ SV118 )
= ( zero_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1294,plain,
! [SV35: a,SV163: a,SV213: a] :
( ( ( ~ ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
= SV35 )
= ( SV163
= ( add_a_b @ r @ SV35 @ SV213 ) ) ) )
= $true )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1295,plain,
! [SV164: a,SV36: a,SV214: a] :
( ( ( ~ ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV36
= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
= ( SV164
= ( add_a_b @ r @ SV36 @ SV214 ) ) ) )
= $true )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1296,plain,
! [SV37: a,SV165: a,SV215: a] :
( ( ( ~ ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
= SV37 )
= ( SV215
= ( add_a_b @ r @ SV165 @ SV37 ) ) ) )
= $true )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1297,plain,
! [SV166: a,SV38: a,SV216: a] :
( ( ( ~ ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) )
| ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
= ( SV216
= ( add_a_b @ r @ SV166 @ SV38 ) ) ) )
= $true )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1298,plain,
! [SV139: a,SV119: a,SV40: a] :
( ( ( member_a @ SV40 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ~ ( member_a @ SV119 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV139 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV40 ) @ SV139 )
= SV119 ) )
= $true )
| ( ( ( add_a_b @ r @ SV40 @ SV119 )
= SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1299,plain,
! [SV168: a,SV41: a] :
( ( ( ( add_a_b @ r @ SV41 @ SV168 )
!= ( zero_a_b @ r ) )
= $true )
| ( ( SV41
= ( a_inv_a_b @ r @ SV168 ) )
= $true )
| ( ( member_a @ SV168 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV41 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1231]) ).
thf(1300,plain,
! [SV120: a,SV43: a] :
( ( ( ~ ( member_a @ SV43 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( a_inv_a_b @ r @ SV120 )
= SV43 )
= $true )
| ( ( member_a @ SV120 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV43 @ SV120 )
= ( zero_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1232]) ).
thf(1301,plain,
! [SV170: a,SV52: a] :
( ( ( ~ ( ( SV52
= ( add_a_b @ r @ SV170 @ SV52 ) )
| ( SV170
= ( zero_a_b @ r ) ) )
| ~ ( ( SV52
!= ( add_a_b @ r @ SV170 @ SV52 ) )
| ( SV170
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1234]) ).
thf(1302,plain,
! [SV170: a,SV52: a] :
( ( ( ( SV52
= ( add_a_b @ r @ SV170 @ SV52 ) )
= ( SV170
= ( zero_a_b @ r ) ) )
= $true )
| ( ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1234]) ).
thf(1303,plain,
! [SV53: a,SV171: a] :
( ( ( ~ ( ( ( add_a_b @ r @ SV171 @ SV53 )
= SV53 )
| ( SV171
= ( zero_a_b @ r ) ) )
| ~ ( ( ( add_a_b @ r @ SV171 @ SV53 )
!= SV53 )
| ( SV171
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1235]) ).
thf(1304,plain,
! [SV53: a,SV171: a] :
( ( ( ( ( add_a_b @ r @ SV171 @ SV53 )
= SV53 )
= ( SV171
= ( zero_a_b @ r ) ) )
= $true )
| ( ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1235]) ).
thf(1305,plain,
! [SV172: a,SV54: a] :
( ( ( ~ ( ( SV54
= ( add_a_b @ r @ SV54 @ SV172 ) )
| ( SV172
= ( zero_a_b @ r ) ) )
| ~ ( ( SV54
!= ( add_a_b @ r @ SV54 @ SV172 ) )
| ( SV172
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1236]) ).
thf(1306,plain,
! [SV172: a,SV54: a] :
( ( ( ( SV54
= ( add_a_b @ r @ SV54 @ SV172 ) )
= ( SV172
= ( zero_a_b @ r ) ) )
= $true )
| ( ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1236]) ).
thf(1307,plain,
! [SV173: a,SV55: a] :
( ( ( ~ ( ( ( add_a_b @ r @ SV55 @ SV173 )
= SV55 )
| ( SV173
= ( zero_a_b @ r ) ) )
| ~ ( ( ( add_a_b @ r @ SV55 @ SV173 )
!= SV55 )
| ( SV173
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1237]) ).
thf(1308,plain,
! [SV173: a,SV55: a] :
( ( ( ( ( add_a_b @ r @ SV55 @ SV173 )
= SV55 )
= ( SV173
= ( zero_a_b @ r ) ) )
= $true )
| ( ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1237]) ).
thf(1309,plain,
! [SV56: a] :
( ( ( ( a_inv_a_b @ r @ SV56 )
= ( zero_a_b @ r ) )
= $false )
| ( ( ~ ( ( ( a_inv_a_b @ r @ SV56 )
!= ( zero_a_b @ r ) )
| ( SV56
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1310,plain,
! [SV56: a] :
( ( ( SV56
= ( zero_a_b @ r ) )
= $false )
| ( ( ~ ( ( ( a_inv_a_b @ r @ SV56 )
!= ( zero_a_b @ r ) )
| ( SV56
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1238]) ).
thf(1311,plain,
! [SV121: a,SV62: partia1833973666xt_a_b,SV217: a] :
( ( ( ~ ( member_a @ SV217 @ ( partia1066395285xt_a_b @ SV62 ) )
| ! [SY431: a] :
( ~ ( member_a @ SY431 @ ( partia1066395285xt_a_b @ SV62 ) )
| ( ( mult_a_ring_ext_a_b @ SV62 @ SY431 @ ( add_a_b @ SV62 @ SV121 @ SV217 ) )
= ( add_a_b @ SV62 @ ( mult_a_ring_ext_a_b @ SV62 @ SY431 @ SV121 ) @ ( mult_a_ring_ext_a_b @ SV62 @ SY431 @ SV217 ) ) ) ) )
= $true )
| ( ( member_a @ SV121 @ ( partia1066395285xt_a_b @ SV62 ) )
= $false )
| ( ( semiring_a_b @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1312,plain,
! [SV179: a,SV63: a,SV218: int] :
( ( ( ( mult_a_ring_ext_a_b @ r @ ( add_pow_a_b_int @ r @ SV218 @ SV63 ) @ SV179 )
= ( add_pow_a_b_int @ r @ SV218 @ ( mult_a_ring_ext_a_b @ r @ SV63 @ SV179 ) ) )
= $true )
| ( ( member_a @ SV179 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV63 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1313,plain,
! [SV180: a,SV219: int,SV64: a] :
( ( ( ( mult_a_ring_ext_a_b @ r @ SV64 @ ( add_pow_a_b_int @ r @ SV219 @ SV180 ) )
= ( add_pow_a_b_int @ r @ SV219 @ ( mult_a_ring_ext_a_b @ r @ SV64 @ SV180 ) ) )
= $true )
| ( ( member_a @ SV180 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV64 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1314,plain,
! [SV181: a,SV65: a,SV220: int] :
( ( ( ( add_pow_a_b_int @ r @ SV220 @ ( add_a_b @ r @ SV65 @ SV181 ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SV220 @ SV65 ) @ ( add_pow_a_b_int @ r @ SV220 @ SV181 ) ) )
= $true )
| ( ( member_a @ SV181 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV65 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1315,plain,
! [SV66: a,SV122: a] :
( ( ( ~ ( member_a @ SV122 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY390: int] :
( ( add_pow_a_b_int @ r @ SY390 @ ( add_a_b @ r @ SV66 @ SV122 ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY390 @ SV66 ) @ ( add_pow_a_b_int @ r @ SY390 @ SV122 ) ) ) )
= $true )
| ( ( member_a @ SV66 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV66 @ SV122 )
= ( add_a_b @ r @ SV122 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1247]) ).
thf(1316,plain,
! [SV127: a,SV72: partia1833973666xt_a_b,SV221: a] :
( ( ( ~ ( member_a @ SV221 @ ( partia1066395285xt_a_b @ SV72 ) )
| ! [SY432: a] :
( ~ ( member_a @ SY432 @ ( partia1066395285xt_a_b @ SV72 ) )
| ( ( mult_a_ring_ext_a_b @ SV72 @ ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ SV221 ) @ SY432 )
= ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ ( mult_a_ring_ext_a_b @ SV72 @ SV221 @ SY432 ) ) ) ) )
= $true )
| ( ( member_a @ SV127 @ ( partia1066395285xt_a_b @ SV72 ) )
= $false )
| ( ( semiring_a_b @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1317,plain,
! [SV183: a,SV73: partia1833973666xt_a_b,SV222: a] :
( ( ( ~ ( member_a @ SV222 @ ( partia1066395285xt_a_b @ SV73 ) )
| ( member_a @ ( mult_a_ring_ext_a_b @ SV73 @ SV183 @ SV222 ) @ ( partia1066395285xt_a_b @ SV73 ) ) )
= $true )
| ( ( member_a @ SV183 @ ( partia1066395285xt_a_b @ SV73 ) )
= $false )
| ( ( semiring_a_b @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1318,plain,
! [SV128: a,SV74: partia1833973666xt_a_b,SV223: a] :
( ( ( ~ ( member_a @ SV223 @ ( partia1066395285xt_a_b @ SV74 ) )
| ! [SY433: a] :
( ~ ( member_a @ SY433 @ ( partia1066395285xt_a_b @ SV74 ) )
| ( ( add_a_b @ SV74 @ SV128 @ ( add_a_b @ SV74 @ SV223 @ SY433 ) )
= ( add_a_b @ SV74 @ SV223 @ ( add_a_b @ SV74 @ SV128 @ SY433 ) ) ) ) )
= $true )
| ( ( member_a @ SV128 @ ( partia1066395285xt_a_b @ SV74 ) )
= $false )
| ( ( semiring_a_b @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1319,plain,
! [SV184: a,SV75: partia1833973666xt_a_b,SV224: a] :
( ( ( ~ ( member_a @ SV224 @ ( partia1066395285xt_a_b @ SV75 ) )
| ( ( add_a_b @ SV75 @ SV184 @ SV224 )
= ( add_a_b @ SV75 @ SV224 @ SV184 ) ) )
= $true )
| ( ( member_a @ SV184 @ ( partia1066395285xt_a_b @ SV75 ) )
= $false )
| ( ( semiring_a_b @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1320,plain,
! [SV129: a,SV76: partia1833973666xt_a_b,SV225: a] :
( ( ( ~ ( member_a @ SV225 @ ( partia1066395285xt_a_b @ SV76 ) )
| ! [SY434: a] :
( ~ ( member_a @ SY434 @ ( partia1066395285xt_a_b @ SV76 ) )
| ( ( add_a_b @ SV76 @ ( add_a_b @ SV76 @ SV129 @ SV225 ) @ SY434 )
= ( add_a_b @ SV76 @ SV129 @ ( add_a_b @ SV76 @ SV225 @ SY434 ) ) ) ) )
= $true )
| ( ( member_a @ SV129 @ ( partia1066395285xt_a_b @ SV76 ) )
= $false )
| ( ( semiring_a_b @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1321,plain,
! [SV185: a,SV77: partia1833973666xt_a_b,SV226: a] :
( ( ( ~ ( member_a @ SV226 @ ( partia1066395285xt_a_b @ SV77 ) )
| ( member_a @ ( add_a_b @ SV77 @ SV185 @ SV226 ) @ ( partia1066395285xt_a_b @ SV77 ) ) )
= $true )
| ( ( member_a @ SV185 @ ( partia1066395285xt_a_b @ SV77 ) )
= $false )
| ( ( semiring_a_b @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1322,plain,
! [SV130: a,SV79: partia1833973666xt_a_b,SV227: a] :
( ( ( ~ ( member_a @ SV227 @ ( partia1066395285xt_a_b @ SV79 ) )
| ! [SY435: a] :
( ~ ( member_a @ SY435 @ ( partia1066395285xt_a_b @ SV79 ) )
| ( ( mult_a_ring_ext_a_b @ SV79 @ ( add_a_b @ SV79 @ SV130 @ SV227 ) @ SY435 )
= ( add_a_b @ SV79 @ ( mult_a_ring_ext_a_b @ SV79 @ SV130 @ SY435 ) @ ( mult_a_ring_ext_a_b @ SV79 @ SV227 @ SY435 ) ) ) ) )
= $true )
| ( ( member_a @ SV130 @ ( partia1066395285xt_a_b @ SV79 ) )
= $false )
| ( ( semiring_a_b @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1323,plain,
! [SV87: set_a] :
( ( ( member_a @ ( sK13_SY364 @ SV87 ) @ SV87 )
= $true )
| ( ( ~ ( ~ ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 )
| ( SV87 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1257]) ).
thf(1324,plain,
! [SV87: set_a] :
( ( ( ~ ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 ) )
= $false )
| ( ( SV87 = bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1258]) ).
thf(1325,plain,
! [SV87: set_a] :
( ( ( SV87 != bot_bot_set_a )
= $false )
| ( ( SV87 = bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1258]) ).
thf(1326,plain,
! [SV88: a > $o] :
( ( ( ( collect_a @ SV88 )
!= bot_bot_set_a )
= $false )
| ( ( ( collect_a @ SV88 )
= bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1327,plain,
! [SV88: a > $o] :
( ( ( ~ ! [SY365: a] :
~ ( SV88 @ SY365 ) )
= $false )
| ( ( ( collect_a @ SV88 )
= bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1328,plain,
! [SV88: a > $o] :
( ( ( SV88 @ ( sK14_SY365 @ SV88 ) )
= $true )
| ( ( ~ ( ( ( collect_a @ SV88 )
!= bot_bot_set_a )
| ~ ! [SY365: a] :
~ ( SV88 @ SY365 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1260]) ).
thf(1329,plain,
! [SV89: a > $o] :
( ( ( bot_bot_set_a
!= ( collect_a @ SV89 ) )
= $false )
| ( ( bot_bot_set_a
= ( collect_a @ SV89 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1261]) ).
thf(1330,plain,
! [SV89: a > $o] :
( ( ( ~ ! [SY366: a] :
~ ( SV89 @ SY366 ) )
= $false )
| ( ( bot_bot_set_a
= ( collect_a @ SV89 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1261]) ).
thf(1331,plain,
! [SV89: a > $o] :
( ( ( SV89 @ ( sK15_SY366 @ SV89 ) )
= $true )
| ( ( ~ ( ( bot_bot_set_a
!= ( collect_a @ SV89 ) )
| ~ ! [SY366: a] :
~ ( SV89 @ SY366 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1262]) ).
thf(1332,plain,
! [SV90: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a ) )
= $false )
| ( ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1263]) ).
thf(1333,plain,
! [SV90: set_a] :
( ( ( SV90 != bot_bot_set_a )
= $false )
| ( ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1263]) ).
thf(1334,plain,
! [SV90: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a ) )
= $false )
| ( ( SV90 = bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1264]) ).
thf(1335,plain,
! [SV90: set_a] :
( ( ( SV90 != bot_bot_set_a )
= $false )
| ( ( SV90 = bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1264]) ).
thf(1336,plain,
! [SV132: set_a,SV98: set_a,SV201: a] :
( ( ( member_a @ SV201 @ SV98 )
= $false )
| ( ( member_a @ SV201 @ SV132 )
= $true )
| ( ( ord_less_eq_set_a @ SV98 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1337,plain,
! [SV133: set_a,SV99: set_a,SV202: a] :
( ( ( member_a @ SV202 @ SV99 )
= $false )
| ( ( member_a @ SV202 @ SV133 )
= $true )
| ( ( ord_less_eq_set_a @ SV99 @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1338,plain,
! [SV100: set_a,SV134: set_a] :
( ( ( member_a @ ( sK2_X3 @ SV134 @ SV100 ) @ SV134 )
= $false )
| ( ( ord_less_eq_set_a @ SV100 @ SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1339,plain,
! [SV101: set_a,SV228: a] :
( ( ( ~ ( member_a @ SV228 @ SV101 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 )
| ~ ( ( SV101 != bot_bot_set_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1340,plain,
! [SV101: set_a] :
( ( ( ~ ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 )
| ~ ( ( SV101 != bot_bot_set_a ) ) )
= $false )
| ( ( SV101 = bot_bot_set_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1341,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ( ord_less_eq_set_a @ SV135 @ SV192 )
| ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV135 @ SV192 )
| ~ ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1342,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ( SV136 = SV193 )
| ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) )
= $false )
| ( ( ~ ( ( SV136 != SV193 )
| ~ ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1343,plain,
! [SV105: set_a] :
( ( ( ~ ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 ) )
= $false )
| ( ( ~ ( ~ ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 )
| ~ ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) )
| ( member_a @ ( zero_a_b @ r ) @ SV105 ) )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1275]) ).
thf(1344,plain,
! [SV105: set_a] :
( ( ( ~ ~ ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 ) )
= $false )
| ( ( ~ ( ~ ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 )
| ~ ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) )
| ( member_a @ ( zero_a_b @ r ) @ SV105 ) )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1275]) ).
thf(1345,plain,
! [SV106: a] :
( ( ( member_a @ ( sK9_X3 @ SV106 ) @ ( partia1066395285xt_a_b @ r ) )
= $true )
| ( ( SV106
= ( zero_a_b @ r ) )
= $true )
| ( ( member_a @ SV106 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1276]) ).
thf(1346,plain,
! [SV106: a] :
( ( ( ( add_a_b @ r @ SV106 @ ( sK9_X3 @ SV106 ) )
!= ( sK9_X3 @ SV106 ) )
= $true )
| ( ( SV106
= ( zero_a_b @ r ) )
= $true )
| ( ( member_a @ SV106 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1277]) ).
thf(1347,plain,
! [SV142: a,SV3: a,SV204: a] :
( ( ( ~ ( member_a @ SV204 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV3 @ SV142 ) @ SV204 )
= ( mult_a_ring_ext_a_b @ r @ SV3 @ ( mult_a_ring_ext_a_b @ r @ SV142 @ SV204 ) ) )
= $true )
| ( ( member_a @ SV142 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV3 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1280]) ).
thf(1348,plain,
! [SV144: a,SV5: a,SV205: a] :
( ( ( ~ ( member_a @ SV205 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( mult_a_ring_ext_a_b @ r @ SV5 @ ( mult_a_ring_ext_a_b @ r @ SV144 @ SV205 ) )
= ( mult_a_ring_ext_a_b @ r @ SV144 @ ( mult_a_ring_ext_a_b @ r @ SV5 @ SV205 ) ) )
= $true )
| ( ( member_a @ SV144 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV5 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1281]) ).
thf(1349,plain,
! [SV145: a,SV6: a,SV206: a] :
( ( ( ~ ( member_a @ SV206 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( add_a_b @ r @ ( add_a_b @ r @ SV6 @ SV145 ) @ SV206 )
= ( add_a_b @ r @ SV6 @ ( add_a_b @ r @ SV145 @ SV206 ) ) )
= $true )
| ( ( member_a @ SV145 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV6 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1282]) ).
thf(1350,plain,
! [SV147: a,SV8: a,SV207: a] :
( ( ( ~ ( member_a @ SV207 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( add_a_b @ r @ SV8 @ ( add_a_b @ r @ SV147 @ SV207 ) )
= ( add_a_b @ r @ SV147 @ ( add_a_b @ r @ SV8 @ SV207 ) ) )
= $true )
| ( ( member_a @ SV147 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV8 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1283]) ).
thf(1351,plain,
! [SV148: a,SV9: a,SV208: a] :
( ( ( ~ ( member_a @ SV208 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( mult_a_ring_ext_a_b @ r @ ( add_a_b @ r @ SV9 @ SV148 ) @ SV208 )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV9 @ SV208 ) @ ( mult_a_ring_ext_a_b @ r @ SV148 @ SV208 ) ) )
= $true )
| ( ( member_a @ SV148 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV9 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1284]) ).
thf(1352,plain,
! [SV149: a,SV10: a,SV209: a] :
( ( ( ~ ( member_a @ SV209 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( mult_a_ring_ext_a_b @ r @ SV209 @ ( add_a_b @ r @ SV10 @ SV149 ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV209 @ SV10 ) @ ( mult_a_ring_ext_a_b @ r @ SV209 @ SV149 ) ) )
= $true )
| ( ( member_a @ SV149 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV10 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1285]) ).
thf(1353,plain,
! [SV110: a,SV11: a,SV210: a] :
( ( ( ~ ( member_a @ SV210 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ! [SY430: a] :
( ~ ( member_a @ SY430 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ SV11 @ SV210 ) @ SV110 ) @ SY430 )
= ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ ( add_a_b @ r @ SV11 @ SV110 ) @ SV210 ) @ SY430 ) ) ) )
= $true )
| ( ( member_a @ SV110 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV11 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1286]) ).
thf(1354,plain,
! [SV150: a,SV12: a,SV211: a] :
( ( ( ~ ( member_a @ SV211 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ SV211 @ SV12 ) @ SV150 )
= ( a_minus_a_b @ r @ SV211 @ ( add_a_b @ r @ SV12 @ SV150 ) ) )
= $true )
| ( ( member_a @ SV150 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV12 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1287]) ).
thf(1355,plain,
! [SV15: a,SV153: a,SV212: a] :
( ( ( ~ ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( ( add_a_b @ r @ SV153 @ SV15 )
= ( add_a_b @ r @ SV212 @ SV15 ) )
= ( SV153 = SV212 ) )
= $true )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1288]) ).
thf(1356,plain,
! [SV196: a,SV23: partia1833973666xt_a_b,SV114: set_a,SV229: a] :
( ( ( ~ ( member_a @ SV229 @ SV114 )
| ( member_a @ ( mult_a_ring_ext_a_b @ SV23 @ SV196 @ SV229 ) @ SV114 ) )
= $true )
| ( ( member_a @ SV196 @ SV114 )
= $false )
| ( ( locali425460998xt_a_b @ SV23 @ SV114 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1357,plain,
! [SV116: a > $o,SV26: a] :
( ( ( ~ ( member_a @ SV26 @ ( collect_a @ SV116 ) ) )
= $false )
| ( ( member_a @ SV26 @ ( collect_a @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1358,plain,
! [SV26: a,SV116: a > $o] :
( ( ( ~ ( SV116 @ SV26 ) )
= $false )
| ( ( member_a @ SV26 @ ( collect_a @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1359,plain,
! [SV116: a > $o,SV26: a] :
( ( ( ~ ( member_a @ SV26 @ ( collect_a @ SV116 ) ) )
= $false )
| ( ( SV116 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1360,plain,
! [SV26: a,SV116: a > $o] :
( ( ( ~ ( SV116 @ SV26 ) )
= $false )
| ( ( SV116 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1361,plain,
! [SV198: a,SV28: a,SV117: a] :
( ( ( ~ ( member_a @ SV117 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ~ ( member_a @ SV28 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV198 @ ( partia1066395285xt_a_b @ r ) )
| ( SV28 = SV198 ) )
= $true )
| ( ( ( add_a_b @ r @ SV117 @ SV198 )
= ( zero_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV28 @ SV117 )
= ( zero_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1292]) ).
thf(1362,plain,
! [SV29: a,SV118: a] :
( ( ( member_a @ SV118 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV118 @ SV29 )
= ( zero_a_b @ r ) )
= $true )
| ( ( member_a @ SV29 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV29 @ SV118 )
= ( zero_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1363,plain,
! [SV35: a,SV163: a,SV213: a] :
( ( ( ~ ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
= SV35 )
= ( SV163
= ( add_a_b @ r @ SV35 @ SV213 ) ) )
= $true )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1294]) ).
thf(1364,plain,
! [SV164: a,SV36: a,SV214: a] :
( ( ( ~ ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( SV36
= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
= ( SV164
= ( add_a_b @ r @ SV36 @ SV214 ) ) )
= $true )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1295]) ).
thf(1365,plain,
! [SV37: a,SV165: a,SV215: a] :
( ( ( ~ ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
= SV37 )
= ( SV215
= ( add_a_b @ r @ SV165 @ SV37 ) ) )
= $true )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1366,plain,
! [SV166: a,SV38: a,SV216: a] :
( ( ( ~ ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
= ( SV216
= ( add_a_b @ r @ SV166 @ SV38 ) ) )
= $true )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1297]) ).
thf(1367,plain,
! [SV40: a,SV139: a,SV119: a] :
( ( ( ~ ( member_a @ SV119 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ~ ( member_a @ SV139 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV40 ) @ SV139 )
= SV119 ) )
= $true )
| ( ( member_a @ SV40 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV40 @ SV119 )
= SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1298]) ).
thf(1368,plain,
! [SV168: a,SV41: a] :
( ( ( ( add_a_b @ r @ SV41 @ SV168 )
= ( zero_a_b @ r ) )
= $false )
| ( ( SV41
= ( a_inv_a_b @ r @ SV168 ) )
= $true )
| ( ( member_a @ SV168 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV41 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1369,plain,
! [SV120: a,SV43: a] :
( ( ( member_a @ SV43 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( a_inv_a_b @ r @ SV120 )
= SV43 )
= $true )
| ( ( member_a @ SV120 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV43 @ SV120 )
= ( zero_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1370,plain,
! [SV170: a,SV52: a] :
( ( ( ~ ( ( SV52
= ( add_a_b @ r @ SV170 @ SV52 ) )
| ( SV170
= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( ~ ( ( SV52
!= ( add_a_b @ r @ SV170 @ SV52 ) )
| ( SV170
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1301]) ).
thf(1371,plain,
! [SV53: a,SV171: a] :
( ( ( ~ ( ( ( add_a_b @ r @ SV171 @ SV53 )
= SV53 )
| ( SV171
= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( ~ ( ( ( add_a_b @ r @ SV171 @ SV53 )
!= SV53 )
| ( SV171
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1303]) ).
thf(1372,plain,
! [SV172: a,SV54: a] :
( ( ( ~ ( ( SV54
= ( add_a_b @ r @ SV54 @ SV172 ) )
| ( SV172
= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( ~ ( ( SV54
!= ( add_a_b @ r @ SV54 @ SV172 ) )
| ( SV172
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1305]) ).
thf(1373,plain,
! [SV173: a,SV55: a] :
( ( ( ~ ( ( ( add_a_b @ r @ SV55 @ SV173 )
= SV55 )
| ( SV173
= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( ~ ( ( ( add_a_b @ r @ SV55 @ SV173 )
!= SV55 )
| ( SV173
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1307]) ).
thf(1374,plain,
! [SV56: a] :
( ( ( ( ( a_inv_a_b @ r @ SV56 )
!= ( zero_a_b @ r ) )
| ( SV56
!= ( zero_a_b @ r ) ) )
= $false )
| ( ( ( a_inv_a_b @ r @ SV56 )
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1375,plain,
! [SV56: a] :
( ( ( ( ( a_inv_a_b @ r @ SV56 )
!= ( zero_a_b @ r ) )
| ( SV56
!= ( zero_a_b @ r ) ) )
= $false )
| ( ( SV56
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1376,plain,
! [SV121: a,SV62: partia1833973666xt_a_b,SV217: a] :
( ( ( ~ ( member_a @ SV217 @ ( partia1066395285xt_a_b @ SV62 ) ) )
= $true )
| ( ( ! [SY431: a] :
( ~ ( member_a @ SY431 @ ( partia1066395285xt_a_b @ SV62 ) )
| ( ( mult_a_ring_ext_a_b @ SV62 @ SY431 @ ( add_a_b @ SV62 @ SV121 @ SV217 ) )
= ( add_a_b @ SV62 @ ( mult_a_ring_ext_a_b @ SV62 @ SY431 @ SV121 ) @ ( mult_a_ring_ext_a_b @ SV62 @ SY431 @ SV217 ) ) ) ) )
= $true )
| ( ( member_a @ SV121 @ ( partia1066395285xt_a_b @ SV62 ) )
= $false )
| ( ( semiring_a_b @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1377,plain,
! [SV66: a,SV122: a] :
( ( ( member_a @ SV122 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY390: int] :
( ( add_pow_a_b_int @ r @ SY390 @ ( add_a_b @ r @ SV66 @ SV122 ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SY390 @ SV66 ) @ ( add_pow_a_b_int @ r @ SY390 @ SV122 ) ) ) )
= $true )
| ( ( member_a @ SV66 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV66 @ SV122 )
= ( add_a_b @ r @ SV122 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1315]) ).
thf(1378,plain,
! [SV127: a,SV72: partia1833973666xt_a_b,SV221: a] :
( ( ( ~ ( member_a @ SV221 @ ( partia1066395285xt_a_b @ SV72 ) ) )
= $true )
| ( ( ! [SY432: a] :
( ~ ( member_a @ SY432 @ ( partia1066395285xt_a_b @ SV72 ) )
| ( ( mult_a_ring_ext_a_b @ SV72 @ ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ SV221 ) @ SY432 )
= ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ ( mult_a_ring_ext_a_b @ SV72 @ SV221 @ SY432 ) ) ) ) )
= $true )
| ( ( member_a @ SV127 @ ( partia1066395285xt_a_b @ SV72 ) )
= $false )
| ( ( semiring_a_b @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1379,plain,
! [SV183: a,SV73: partia1833973666xt_a_b,SV222: a] :
( ( ( ~ ( member_a @ SV222 @ ( partia1066395285xt_a_b @ SV73 ) ) )
= $true )
| ( ( member_a @ ( mult_a_ring_ext_a_b @ SV73 @ SV183 @ SV222 ) @ ( partia1066395285xt_a_b @ SV73 ) )
= $true )
| ( ( member_a @ SV183 @ ( partia1066395285xt_a_b @ SV73 ) )
= $false )
| ( ( semiring_a_b @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1317]) ).
thf(1380,plain,
! [SV128: a,SV74: partia1833973666xt_a_b,SV223: a] :
( ( ( ~ ( member_a @ SV223 @ ( partia1066395285xt_a_b @ SV74 ) ) )
= $true )
| ( ( ! [SY433: a] :
( ~ ( member_a @ SY433 @ ( partia1066395285xt_a_b @ SV74 ) )
| ( ( add_a_b @ SV74 @ SV128 @ ( add_a_b @ SV74 @ SV223 @ SY433 ) )
= ( add_a_b @ SV74 @ SV223 @ ( add_a_b @ SV74 @ SV128 @ SY433 ) ) ) ) )
= $true )
| ( ( member_a @ SV128 @ ( partia1066395285xt_a_b @ SV74 ) )
= $false )
| ( ( semiring_a_b @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1318]) ).
thf(1381,plain,
! [SV184: a,SV75: partia1833973666xt_a_b,SV224: a] :
( ( ( ~ ( member_a @ SV224 @ ( partia1066395285xt_a_b @ SV75 ) ) )
= $true )
| ( ( ( add_a_b @ SV75 @ SV184 @ SV224 )
= ( add_a_b @ SV75 @ SV224 @ SV184 ) )
= $true )
| ( ( member_a @ SV184 @ ( partia1066395285xt_a_b @ SV75 ) )
= $false )
| ( ( semiring_a_b @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1319]) ).
thf(1382,plain,
! [SV129: a,SV76: partia1833973666xt_a_b,SV225: a] :
( ( ( ~ ( member_a @ SV225 @ ( partia1066395285xt_a_b @ SV76 ) ) )
= $true )
| ( ( ! [SY434: a] :
( ~ ( member_a @ SY434 @ ( partia1066395285xt_a_b @ SV76 ) )
| ( ( add_a_b @ SV76 @ ( add_a_b @ SV76 @ SV129 @ SV225 ) @ SY434 )
= ( add_a_b @ SV76 @ SV129 @ ( add_a_b @ SV76 @ SV225 @ SY434 ) ) ) ) )
= $true )
| ( ( member_a @ SV129 @ ( partia1066395285xt_a_b @ SV76 ) )
= $false )
| ( ( semiring_a_b @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1320]) ).
thf(1383,plain,
! [SV185: a,SV77: partia1833973666xt_a_b,SV226: a] :
( ( ( ~ ( member_a @ SV226 @ ( partia1066395285xt_a_b @ SV77 ) ) )
= $true )
| ( ( member_a @ ( add_a_b @ SV77 @ SV185 @ SV226 ) @ ( partia1066395285xt_a_b @ SV77 ) )
= $true )
| ( ( member_a @ SV185 @ ( partia1066395285xt_a_b @ SV77 ) )
= $false )
| ( ( semiring_a_b @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1321]) ).
thf(1384,plain,
! [SV130: a,SV79: partia1833973666xt_a_b,SV227: a] :
( ( ( ~ ( member_a @ SV227 @ ( partia1066395285xt_a_b @ SV79 ) ) )
= $true )
| ( ( ! [SY435: a] :
( ~ ( member_a @ SY435 @ ( partia1066395285xt_a_b @ SV79 ) )
| ( ( mult_a_ring_ext_a_b @ SV79 @ ( add_a_b @ SV79 @ SV130 @ SV227 ) @ SY435 )
= ( add_a_b @ SV79 @ ( mult_a_ring_ext_a_b @ SV79 @ SV130 @ SY435 ) @ ( mult_a_ring_ext_a_b @ SV79 @ SV227 @ SY435 ) ) ) ) )
= $true )
| ( ( member_a @ SV130 @ ( partia1066395285xt_a_b @ SV79 ) )
= $false )
| ( ( semiring_a_b @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1385,plain,
! [SV87: set_a] :
( ( ( ~ ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 )
| ( SV87 != bot_bot_set_a ) )
= $false )
| ( ( member_a @ ( sK13_SY364 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1386,plain,
! [SV87: set_a] :
( ( ( ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 ) )
= $true )
| ( ( SV87 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1324]) ).
thf(1387,plain,
! [SV87: set_a] :
( ( ( SV87 = bot_bot_set_a )
= $true )
| ( ( SV87 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1325]) ).
thf(1388,plain,
! [SV88: a > $o] :
( ( ( ( collect_a @ SV88 )
= bot_bot_set_a )
= $true )
| ( ( ( collect_a @ SV88 )
= bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1326]) ).
thf(1389,plain,
! [SV88: a > $o] :
( ( ( ! [SY365: a] :
~ ( SV88 @ SY365 ) )
= $true )
| ( ( ( collect_a @ SV88 )
= bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1327]) ).
thf(1390,plain,
! [SV88: a > $o] :
( ( ( ( ( collect_a @ SV88 )
!= bot_bot_set_a )
| ~ ! [SY365: a] :
~ ( SV88 @ SY365 ) )
= $false )
| ( ( SV88 @ ( sK14_SY365 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1391,plain,
! [SV89: a > $o] :
( ( ( bot_bot_set_a
= ( collect_a @ SV89 ) )
= $true )
| ( ( bot_bot_set_a
= ( collect_a @ SV89 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1329]) ).
thf(1392,plain,
! [SV89: a > $o] :
( ( ( ! [SY366: a] :
~ ( SV89 @ SY366 ) )
= $true )
| ( ( bot_bot_set_a
= ( collect_a @ SV89 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1330]) ).
thf(1393,plain,
! [SV89: a > $o] :
( ( ( ( bot_bot_set_a
!= ( collect_a @ SV89 ) )
| ~ ! [SY366: a] :
~ ( SV89 @ SY366 ) )
= $false )
| ( ( SV89 @ ( sK15_SY366 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1394,plain,
! [SV90: set_a] :
( ( ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1332]) ).
thf(1395,plain,
! [SV90: set_a] :
( ( ( SV90 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1333]) ).
thf(1396,plain,
! [SV90: set_a] :
( ( ( ord_less_eq_set_a @ SV90 @ bot_bot_set_a )
= $true )
| ( ( SV90 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1397,plain,
! [SV90: set_a] :
( ( ( SV90 = bot_bot_set_a )
= $true )
| ( ( SV90 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1335]) ).
thf(1398,plain,
! [SV101: set_a,SV228: a] :
( ( ( member_a @ SV228 @ SV101 )
= $false )
| ( ( ~ ( ~ ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 )
| ~ ( ( SV101 != bot_bot_set_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1399,plain,
! [SV101: set_a] :
( ( ( ~ ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 ) )
= $false )
| ( ( SV101 = bot_bot_set_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1340]) ).
thf(1400,plain,
! [SV101: set_a] :
( ( ( ~ ( ( SV101 != bot_bot_set_a ) ) )
= $false )
| ( ( SV101 = bot_bot_set_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1340]) ).
thf(1401,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ord_less_eq_set_a @ SV135 @ SV192 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV135 @ SV192 )
| ~ ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1341]) ).
thf(1402,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV135 @ SV192 )
| ~ ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1341]) ).
thf(1403,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( SV136 = SV193 )
= $false )
| ( ( ~ ( ( SV136 != SV193 )
| ~ ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1342]) ).
thf(1404,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) )
= $false )
| ( ( ~ ( ( SV136 != SV193 )
| ~ ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1342]) ).
thf(1405,plain,
! [SV105: set_a] :
( ( ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
= $true )
| ( ( ~ ( ~ ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 )
| ~ ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) )
| ( member_a @ ( zero_a_b @ r ) @ SV105 ) )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1343]) ).
thf(1406,plain,
! [SV105: set_a] :
( ( ( ~ ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 ) )
= $true )
| ( ( ~ ( ~ ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 )
| ~ ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) )
| ( member_a @ ( zero_a_b @ r ) @ SV105 ) )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1344]) ).
thf(1407,plain,
! [SV106: a] :
( ( ( ( add_a_b @ r @ SV106 @ ( sK9_X3 @ SV106 ) )
= ( sK9_X3 @ SV106 ) )
= $false )
| ( ( SV106
= ( zero_a_b @ r ) )
= $true )
| ( ( member_a @ SV106 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1346]) ).
thf(1408,plain,
! [SV142: a,SV3: a,SV204: a] :
( ( ( member_a @ SV204 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV3 @ SV142 ) @ SV204 )
= ( mult_a_ring_ext_a_b @ r @ SV3 @ ( mult_a_ring_ext_a_b @ r @ SV142 @ SV204 ) ) )
= $true )
| ( ( member_a @ SV142 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV3 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1347]) ).
thf(1409,plain,
! [SV144: a,SV5: a,SV205: a] :
( ( ( member_a @ SV205 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( mult_a_ring_ext_a_b @ r @ SV5 @ ( mult_a_ring_ext_a_b @ r @ SV144 @ SV205 ) )
= ( mult_a_ring_ext_a_b @ r @ SV144 @ ( mult_a_ring_ext_a_b @ r @ SV5 @ SV205 ) ) )
= $true )
| ( ( member_a @ SV144 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV5 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1348]) ).
thf(1410,plain,
! [SV145: a,SV6: a,SV206: a] :
( ( ( member_a @ SV206 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ ( add_a_b @ r @ SV6 @ SV145 ) @ SV206 )
= ( add_a_b @ r @ SV6 @ ( add_a_b @ r @ SV145 @ SV206 ) ) )
= $true )
| ( ( member_a @ SV145 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV6 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1349]) ).
thf(1411,plain,
! [SV147: a,SV8: a,SV207: a] :
( ( ( member_a @ SV207 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV8 @ ( add_a_b @ r @ SV147 @ SV207 ) )
= ( add_a_b @ r @ SV147 @ ( add_a_b @ r @ SV8 @ SV207 ) ) )
= $true )
| ( ( member_a @ SV147 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV8 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1412,plain,
! [SV148: a,SV9: a,SV208: a] :
( ( ( member_a @ SV208 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( mult_a_ring_ext_a_b @ r @ ( add_a_b @ r @ SV9 @ SV148 ) @ SV208 )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV9 @ SV208 ) @ ( mult_a_ring_ext_a_b @ r @ SV148 @ SV208 ) ) )
= $true )
| ( ( member_a @ SV148 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV9 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1413,plain,
! [SV149: a,SV10: a,SV209: a] :
( ( ( member_a @ SV209 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( mult_a_ring_ext_a_b @ r @ SV209 @ ( add_a_b @ r @ SV10 @ SV149 ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ SV209 @ SV10 ) @ ( mult_a_ring_ext_a_b @ r @ SV209 @ SV149 ) ) )
= $true )
| ( ( member_a @ SV149 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV10 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1352]) ).
thf(1414,plain,
! [SV110: a,SV11: a,SV210: a] :
( ( ( member_a @ SV210 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ! [SY430: a] :
( ~ ( member_a @ SY430 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ SV11 @ SV210 ) @ SV110 ) @ SY430 )
= ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ ( add_a_b @ r @ SV11 @ SV110 ) @ SV210 ) @ SY430 ) ) ) )
= $true )
| ( ( member_a @ SV110 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV11 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1415,plain,
! [SV150: a,SV12: a,SV211: a] :
( ( ( member_a @ SV211 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ SV211 @ SV12 ) @ SV150 )
= ( a_minus_a_b @ r @ SV211 @ ( add_a_b @ r @ SV12 @ SV150 ) ) )
= $true )
| ( ( member_a @ SV150 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV12 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1416,plain,
! [SV15: a,SV153: a,SV212: a] :
( ( ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( ( add_a_b @ r @ SV153 @ SV15 )
= ( add_a_b @ r @ SV212 @ SV15 ) )
= ( SV153 = SV212 ) )
= $true )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1417,plain,
! [SV196: a,SV23: partia1833973666xt_a_b,SV114: set_a,SV229: a] :
( ( ( ~ ( member_a @ SV229 @ SV114 ) )
= $true )
| ( ( member_a @ ( mult_a_ring_ext_a_b @ SV23 @ SV196 @ SV229 ) @ SV114 )
= $true )
| ( ( member_a @ SV196 @ SV114 )
= $false )
| ( ( locali425460998xt_a_b @ SV23 @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1418,plain,
! [SV116: a > $o,SV26: a] :
( ( ( member_a @ SV26 @ ( collect_a @ SV116 ) )
= $true )
| ( ( member_a @ SV26 @ ( collect_a @ SV116 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1357]) ).
thf(1419,plain,
! [SV26: a,SV116: a > $o] :
( ( ( SV116 @ SV26 )
= $true )
| ( ( member_a @ SV26 @ ( collect_a @ SV116 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1358]) ).
thf(1420,plain,
! [SV116: a > $o,SV26: a] :
( ( ( member_a @ SV26 @ ( collect_a @ SV116 ) )
= $true )
| ( ( SV116 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1359]) ).
thf(1421,plain,
! [SV26: a,SV116: a > $o] :
( ( ( SV116 @ SV26 )
= $true )
| ( ( SV116 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1360]) ).
thf(1422,plain,
! [SV198: a,SV28: a,SV117: a] :
( ( ( member_a @ SV117 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ~ ( member_a @ SV28 @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ SV198 @ ( partia1066395285xt_a_b @ r ) )
| ( SV28 = SV198 ) )
= $true )
| ( ( ( add_a_b @ r @ SV117 @ SV198 )
= ( zero_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV28 @ SV117 )
= ( zero_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1423,plain,
! [SV35: a,SV163: a,SV213: a] :
( ( ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
= SV35 )
= ( SV163
= ( add_a_b @ r @ SV35 @ SV213 ) ) )
= $true )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1424,plain,
! [SV164: a,SV36: a,SV214: a] :
( ( ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( SV36
= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
= ( SV164
= ( add_a_b @ r @ SV36 @ SV214 ) ) )
= $true )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1425,plain,
! [SV37: a,SV165: a,SV215: a] :
( ( ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
= SV37 )
= ( SV215
= ( add_a_b @ r @ SV165 @ SV37 ) ) )
= $true )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1426,plain,
! [SV166: a,SV38: a,SV216: a] :
( ( ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
= ( SV216
= ( add_a_b @ r @ SV166 @ SV38 ) ) )
= $true )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1366]) ).
thf(1427,plain,
! [SV40: a,SV139: a,SV119: a] :
( ( ( member_a @ SV119 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ~ ( member_a @ SV139 @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV40 ) @ SV139 )
= SV119 ) )
= $true )
| ( ( member_a @ SV40 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV40 @ SV119 )
= SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1367]) ).
thf(1428,plain,
! [SV170: a,SV52: a] :
( ( ( ( SV52
= ( add_a_b @ r @ SV170 @ SV52 ) )
| ( SV170
= ( zero_a_b @ r ) ) )
= $false )
| ( ( ~ ( ( SV52
!= ( add_a_b @ r @ SV170 @ SV52 ) )
| ( SV170
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1370]) ).
thf(1429,plain,
! [SV53: a,SV171: a] :
( ( ( ( ( add_a_b @ r @ SV171 @ SV53 )
= SV53 )
| ( SV171
= ( zero_a_b @ r ) ) )
= $false )
| ( ( ~ ( ( ( add_a_b @ r @ SV171 @ SV53 )
!= SV53 )
| ( SV171
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1430,plain,
! [SV172: a,SV54: a] :
( ( ( ( SV54
= ( add_a_b @ r @ SV54 @ SV172 ) )
| ( SV172
= ( zero_a_b @ r ) ) )
= $false )
| ( ( ~ ( ( SV54
!= ( add_a_b @ r @ SV54 @ SV172 ) )
| ( SV172
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1431,plain,
! [SV173: a,SV55: a] :
( ( ( ( ( add_a_b @ r @ SV55 @ SV173 )
= SV55 )
| ( SV173
= ( zero_a_b @ r ) ) )
= $false )
| ( ( ~ ( ( ( add_a_b @ r @ SV55 @ SV173 )
!= SV55 )
| ( SV173
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1432,plain,
! [SV56: a] :
( ( ( ( a_inv_a_b @ r @ SV56 )
!= ( zero_a_b @ r ) )
= $false )
| ( ( ( a_inv_a_b @ r @ SV56 )
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1374]) ).
thf(1433,plain,
! [SV56: a] :
( ( ( SV56
!= ( zero_a_b @ r ) )
= $false )
| ( ( ( a_inv_a_b @ r @ SV56 )
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1374]) ).
thf(1434,plain,
! [SV56: a] :
( ( ( ( a_inv_a_b @ r @ SV56 )
!= ( zero_a_b @ r ) )
= $false )
| ( ( SV56
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1375]) ).
thf(1435,plain,
! [SV56: a] :
( ( ( SV56
!= ( zero_a_b @ r ) )
= $false )
| ( ( SV56
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1375]) ).
thf(1436,plain,
! [SV121: a,SV62: partia1833973666xt_a_b,SV217: a] :
( ( ( member_a @ SV217 @ ( partia1066395285xt_a_b @ SV62 ) )
= $false )
| ( ( ! [SY431: a] :
( ~ ( member_a @ SY431 @ ( partia1066395285xt_a_b @ SV62 ) )
| ( ( mult_a_ring_ext_a_b @ SV62 @ SY431 @ ( add_a_b @ SV62 @ SV121 @ SV217 ) )
= ( add_a_b @ SV62 @ ( mult_a_ring_ext_a_b @ SV62 @ SY431 @ SV121 ) @ ( mult_a_ring_ext_a_b @ SV62 @ SY431 @ SV217 ) ) ) ) )
= $true )
| ( ( member_a @ SV121 @ ( partia1066395285xt_a_b @ SV62 ) )
= $false )
| ( ( semiring_a_b @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1437,plain,
! [SV122: a,SV66: a,SV230: int] :
( ( ( ( add_pow_a_b_int @ r @ SV230 @ ( add_a_b @ r @ SV66 @ SV122 ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ SV230 @ SV66 ) @ ( add_pow_a_b_int @ r @ SV230 @ SV122 ) ) )
= $true )
| ( ( member_a @ SV122 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV66 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV66 @ SV122 )
= ( add_a_b @ r @ SV122 @ SV66 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1438,plain,
! [SV127: a,SV72: partia1833973666xt_a_b,SV221: a] :
( ( ( member_a @ SV221 @ ( partia1066395285xt_a_b @ SV72 ) )
= $false )
| ( ( ! [SY432: a] :
( ~ ( member_a @ SY432 @ ( partia1066395285xt_a_b @ SV72 ) )
| ( ( mult_a_ring_ext_a_b @ SV72 @ ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ SV221 ) @ SY432 )
= ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ ( mult_a_ring_ext_a_b @ SV72 @ SV221 @ SY432 ) ) ) ) )
= $true )
| ( ( member_a @ SV127 @ ( partia1066395285xt_a_b @ SV72 ) )
= $false )
| ( ( semiring_a_b @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1439,plain,
! [SV183: a,SV73: partia1833973666xt_a_b,SV222: a] :
( ( ( member_a @ SV222 @ ( partia1066395285xt_a_b @ SV73 ) )
= $false )
| ( ( member_a @ ( mult_a_ring_ext_a_b @ SV73 @ SV183 @ SV222 ) @ ( partia1066395285xt_a_b @ SV73 ) )
= $true )
| ( ( member_a @ SV183 @ ( partia1066395285xt_a_b @ SV73 ) )
= $false )
| ( ( semiring_a_b @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1440,plain,
! [SV128: a,SV74: partia1833973666xt_a_b,SV223: a] :
( ( ( member_a @ SV223 @ ( partia1066395285xt_a_b @ SV74 ) )
= $false )
| ( ( ! [SY433: a] :
( ~ ( member_a @ SY433 @ ( partia1066395285xt_a_b @ SV74 ) )
| ( ( add_a_b @ SV74 @ SV128 @ ( add_a_b @ SV74 @ SV223 @ SY433 ) )
= ( add_a_b @ SV74 @ SV223 @ ( add_a_b @ SV74 @ SV128 @ SY433 ) ) ) ) )
= $true )
| ( ( member_a @ SV128 @ ( partia1066395285xt_a_b @ SV74 ) )
= $false )
| ( ( semiring_a_b @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1441,plain,
! [SV184: a,SV75: partia1833973666xt_a_b,SV224: a] :
( ( ( member_a @ SV224 @ ( partia1066395285xt_a_b @ SV75 ) )
= $false )
| ( ( ( add_a_b @ SV75 @ SV184 @ SV224 )
= ( add_a_b @ SV75 @ SV224 @ SV184 ) )
= $true )
| ( ( member_a @ SV184 @ ( partia1066395285xt_a_b @ SV75 ) )
= $false )
| ( ( semiring_a_b @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1442,plain,
! [SV129: a,SV76: partia1833973666xt_a_b,SV225: a] :
( ( ( member_a @ SV225 @ ( partia1066395285xt_a_b @ SV76 ) )
= $false )
| ( ( ! [SY434: a] :
( ~ ( member_a @ SY434 @ ( partia1066395285xt_a_b @ SV76 ) )
| ( ( add_a_b @ SV76 @ ( add_a_b @ SV76 @ SV129 @ SV225 ) @ SY434 )
= ( add_a_b @ SV76 @ SV129 @ ( add_a_b @ SV76 @ SV225 @ SY434 ) ) ) ) )
= $true )
| ( ( member_a @ SV129 @ ( partia1066395285xt_a_b @ SV76 ) )
= $false )
| ( ( semiring_a_b @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1382]) ).
thf(1443,plain,
! [SV185: a,SV77: partia1833973666xt_a_b,SV226: a] :
( ( ( member_a @ SV226 @ ( partia1066395285xt_a_b @ SV77 ) )
= $false )
| ( ( member_a @ ( add_a_b @ SV77 @ SV185 @ SV226 ) @ ( partia1066395285xt_a_b @ SV77 ) )
= $true )
| ( ( member_a @ SV185 @ ( partia1066395285xt_a_b @ SV77 ) )
= $false )
| ( ( semiring_a_b @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1444,plain,
! [SV130: a,SV79: partia1833973666xt_a_b,SV227: a] :
( ( ( member_a @ SV227 @ ( partia1066395285xt_a_b @ SV79 ) )
= $false )
| ( ( ! [SY435: a] :
( ~ ( member_a @ SY435 @ ( partia1066395285xt_a_b @ SV79 ) )
| ( ( mult_a_ring_ext_a_b @ SV79 @ ( add_a_b @ SV79 @ SV130 @ SV227 ) @ SY435 )
= ( add_a_b @ SV79 @ ( mult_a_ring_ext_a_b @ SV79 @ SV130 @ SY435 ) @ ( mult_a_ring_ext_a_b @ SV79 @ SV227 @ SY435 ) ) ) ) )
= $true )
| ( ( member_a @ SV130 @ ( partia1066395285xt_a_b @ SV79 ) )
= $false )
| ( ( semiring_a_b @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1445,plain,
! [SV87: set_a] :
( ( ( ~ ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 ) )
= $false )
| ( ( member_a @ ( sK13_SY364 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1385]) ).
thf(1446,plain,
! [SV87: set_a] :
( ( ( SV87 != bot_bot_set_a )
= $false )
| ( ( member_a @ ( sK13_SY364 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1385]) ).
thf(1447,plain,
! [SV87: set_a,SV231: a] :
( ( ( ~ ( member_a @ SV231 @ SV87 ) )
= $true )
| ( ( SV87 = bot_bot_set_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1448,plain,
! [SV232: a,SV88: a > $o] :
( ( ( ~ ( SV88 @ SV232 ) )
= $true )
| ( ( ( collect_a @ SV88 )
= bot_bot_set_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1449,plain,
! [SV88: a > $o] :
( ( ( ( collect_a @ SV88 )
!= bot_bot_set_a )
= $false )
| ( ( SV88 @ ( sK14_SY365 @ SV88 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1390]) ).
thf(1450,plain,
! [SV88: a > $o] :
( ( ( ~ ! [SY365: a] :
~ ( SV88 @ SY365 ) )
= $false )
| ( ( SV88 @ ( sK14_SY365 @ SV88 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1390]) ).
thf(1451,plain,
! [SV233: a,SV89: a > $o] :
( ( ( ~ ( SV89 @ SV233 ) )
= $true )
| ( ( bot_bot_set_a
= ( collect_a @ SV89 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1452,plain,
! [SV89: a > $o] :
( ( ( bot_bot_set_a
!= ( collect_a @ SV89 ) )
= $false )
| ( ( SV89 @ ( sK15_SY366 @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1393]) ).
thf(1453,plain,
! [SV89: a > $o] :
( ( ( ~ ! [SY366: a] :
~ ( SV89 @ SY366 ) )
= $false )
| ( ( SV89 @ ( sK15_SY366 @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1393]) ).
thf(1454,plain,
! [SV228: a,SV101: set_a] :
( ( ( ~ ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 )
| ~ ( ( SV101 != bot_bot_set_a ) ) )
= $false )
| ( ( member_a @ SV228 @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1455,plain,
! [SV101: set_a] :
( ( ( ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 ) )
= $true )
| ( ( SV101 = bot_bot_set_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1399]) ).
thf(1456,plain,
! [SV101: set_a] :
( ( ( SV101 != bot_bot_set_a )
= $true )
| ( ( SV101 = bot_bot_set_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1400]) ).
thf(1457,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV135 @ SV192 )
| ~ ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV135 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1401]) ).
thf(1458,plain,
! [SV135: set_a,SV192: set_a] :
( ( ( ~ ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV135 )
| ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV192 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV135 @ SV192 )
| ~ ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1402]) ).
thf(1459,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ( SV136 != SV193 )
| ~ ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) )
= $false )
| ( ( SV136 = SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1460,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) )
= $true )
| ( ( ~ ( ( SV136 != SV193 )
| ~ ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1404]) ).
thf(1461,plain,
! [SV105: set_a] :
( ( ( ~ ( ~ ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 )
| ~ ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) ) )
= $true )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1462,plain,
! [SV105: set_a] :
( ( ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 )
= $false )
| ( ( ~ ( ~ ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 )
| ~ ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) )
| ( member_a @ ( zero_a_b @ r ) @ SV105 ) )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1406]) ).
thf(1463,plain,
! [SV110: a,SV210: a,SV11: a,SV234: a] :
( ( ( ~ ( member_a @ SV234 @ ( partia1066395285xt_a_b @ r ) )
| ( ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ SV11 @ SV210 ) @ SV110 ) @ SV234 )
= ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ ( add_a_b @ r @ SV11 @ SV110 ) @ SV210 ) @ SV234 ) ) )
= $true )
| ( ( member_a @ SV210 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV110 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV11 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1464,plain,
! [SV212: a,SV15: a,SV153: a] :
( ( ( ~ ( ( ( add_a_b @ r @ SV153 @ SV15 )
= ( add_a_b @ r @ SV212 @ SV15 ) )
| ( SV153 = SV212 ) )
| ~ ( ( ( add_a_b @ r @ SV153 @ SV15 )
!= ( add_a_b @ r @ SV212 @ SV15 ) )
| ( SV153 != SV212 ) ) )
= $true )
| ( ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1416]) ).
thf(1465,plain,
! [SV212: a,SV15: a,SV153: a] :
( ( ( ( ( add_a_b @ r @ SV153 @ SV15 )
= ( add_a_b @ r @ SV212 @ SV15 ) )
= ( SV153 = SV212 ) )
= $true )
| ( ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1416]) ).
thf(1466,plain,
! [SV196: a,SV23: partia1833973666xt_a_b,SV114: set_a,SV229: a] :
( ( ( member_a @ SV229 @ SV114 )
= $false )
| ( ( member_a @ ( mult_a_ring_ext_a_b @ SV23 @ SV196 @ SV229 ) @ SV114 )
= $true )
| ( ( member_a @ SV196 @ SV114 )
= $false )
| ( ( locali425460998xt_a_b @ SV23 @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1417]) ).
thf(1467,plain,
! [SV117: a,SV198: a,SV28: a] :
( ( ( ~ ( member_a @ SV28 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ~ ( member_a @ SV198 @ ( partia1066395285xt_a_b @ r ) )
| ( SV28 = SV198 ) )
= $true )
| ( ( member_a @ SV117 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV117 @ SV198 )
= ( zero_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV28 @ SV117 )
= ( zero_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1422]) ).
thf(1468,plain,
! [SV35: a,SV213: a,SV163: a] :
( ( ( ~ ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
= SV35 )
| ( SV163
= ( add_a_b @ r @ SV35 @ SV213 ) ) )
| ~ ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
!= SV35 )
| ( SV163
!= ( add_a_b @ r @ SV35 @ SV213 ) ) ) )
= $true )
| ( ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1423]) ).
thf(1469,plain,
! [SV35: a,SV213: a,SV163: a] :
( ( ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
= SV35 )
= ( SV163
= ( add_a_b @ r @ SV35 @ SV213 ) ) )
= $true )
| ( ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1423]) ).
thf(1470,plain,
! [SV214: a,SV164: a,SV36: a] :
( ( ( ~ ( ( SV36
= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
| ( SV164
= ( add_a_b @ r @ SV36 @ SV214 ) ) )
| ~ ( ( SV36
!= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
| ( SV164
!= ( add_a_b @ r @ SV36 @ SV214 ) ) ) )
= $true )
| ( ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1424]) ).
thf(1471,plain,
! [SV214: a,SV164: a,SV36: a] :
( ( ( ( SV36
= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
= ( SV164
= ( add_a_b @ r @ SV36 @ SV214 ) ) )
= $true )
| ( ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1424]) ).
thf(1472,plain,
! [SV37: a,SV215: a,SV165: a] :
( ( ( ~ ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
= SV37 )
| ( SV215
= ( add_a_b @ r @ SV165 @ SV37 ) ) )
| ~ ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
!= SV37 )
| ( SV215
!= ( add_a_b @ r @ SV165 @ SV37 ) ) ) )
= $true )
| ( ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1425]) ).
thf(1473,plain,
! [SV37: a,SV215: a,SV165: a] :
( ( ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
= SV37 )
= ( SV215
= ( add_a_b @ r @ SV165 @ SV37 ) ) )
= $true )
| ( ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1425]) ).
thf(1474,plain,
! [SV216: a,SV166: a,SV38: a] :
( ( ( ~ ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
| ( SV216
= ( add_a_b @ r @ SV166 @ SV38 ) ) )
| ~ ( ( SV38
!= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
| ( SV216
!= ( add_a_b @ r @ SV166 @ SV38 ) ) ) )
= $true )
| ( ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1426]) ).
thf(1475,plain,
! [SV216: a,SV166: a,SV38: a] :
( ( ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
= ( SV216
= ( add_a_b @ r @ SV166 @ SV38 ) ) )
= $true )
| ( ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1426]) ).
thf(1476,plain,
! [SV119: a,SV40: a,SV139: a] :
( ( ( ~ ( member_a @ SV139 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV40 ) @ SV139 )
= SV119 )
= $true )
| ( ( member_a @ SV119 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV40 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV40 @ SV119 )
= SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1477,plain,
! [SV170: a,SV52: a] :
( ( ( SV52
= ( add_a_b @ r @ SV170 @ SV52 ) )
= $false )
| ( ( ~ ( ( SV52
!= ( add_a_b @ r @ SV170 @ SV52 ) )
| ( SV170
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1478,plain,
! [SV52: a,SV170: a] :
( ( ( SV170
= ( zero_a_b @ r ) )
= $false )
| ( ( ~ ( ( SV52
!= ( add_a_b @ r @ SV170 @ SV52 ) )
| ( SV170
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1479,plain,
! [SV53: a,SV171: a] :
( ( ( ( add_a_b @ r @ SV171 @ SV53 )
= SV53 )
= $false )
| ( ( ~ ( ( ( add_a_b @ r @ SV171 @ SV53 )
!= SV53 )
| ( SV171
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1480,plain,
! [SV53: a,SV171: a] :
( ( ( SV171
= ( zero_a_b @ r ) )
= $false )
| ( ( ~ ( ( ( add_a_b @ r @ SV171 @ SV53 )
!= SV53 )
| ( SV171
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1481,plain,
! [SV172: a,SV54: a] :
( ( ( SV54
= ( add_a_b @ r @ SV54 @ SV172 ) )
= $false )
| ( ( ~ ( ( SV54
!= ( add_a_b @ r @ SV54 @ SV172 ) )
| ( SV172
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1430]) ).
thf(1482,plain,
! [SV54: a,SV172: a] :
( ( ( SV172
= ( zero_a_b @ r ) )
= $false )
| ( ( ~ ( ( SV54
!= ( add_a_b @ r @ SV54 @ SV172 ) )
| ( SV172
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1430]) ).
thf(1483,plain,
! [SV173: a,SV55: a] :
( ( ( ( add_a_b @ r @ SV55 @ SV173 )
= SV55 )
= $false )
| ( ( ~ ( ( ( add_a_b @ r @ SV55 @ SV173 )
!= SV55 )
| ( SV173
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1431]) ).
thf(1484,plain,
! [SV55: a,SV173: a] :
( ( ( SV173
= ( zero_a_b @ r ) )
= $false )
| ( ( ~ ( ( ( add_a_b @ r @ SV55 @ SV173 )
!= SV55 )
| ( SV173
!= ( zero_a_b @ r ) ) ) )
= $true )
| ( ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1431]) ).
thf(1485,plain,
! [SV56: a] :
( ( ( ( a_inv_a_b @ r @ SV56 )
= ( zero_a_b @ r ) )
= $true )
| ( ( ( a_inv_a_b @ r @ SV56 )
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1432]) ).
thf(1486,plain,
! [SV56: a] :
( ( ( SV56
= ( zero_a_b @ r ) )
= $true )
| ( ( ( a_inv_a_b @ r @ SV56 )
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1433]) ).
thf(1487,plain,
! [SV56: a] :
( ( ( ( a_inv_a_b @ r @ SV56 )
= ( zero_a_b @ r ) )
= $true )
| ( ( SV56
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1434]) ).
thf(1488,plain,
! [SV56: a] :
( ( ( SV56
= ( zero_a_b @ r ) )
= $true )
| ( ( SV56
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV56 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1435]) ).
thf(1489,plain,
! [SV217: a,SV121: a,SV62: partia1833973666xt_a_b,SV235: a] :
( ( ( ~ ( member_a @ SV235 @ ( partia1066395285xt_a_b @ SV62 ) )
| ( ( mult_a_ring_ext_a_b @ SV62 @ SV235 @ ( add_a_b @ SV62 @ SV121 @ SV217 ) )
= ( add_a_b @ SV62 @ ( mult_a_ring_ext_a_b @ SV62 @ SV235 @ SV121 ) @ ( mult_a_ring_ext_a_b @ SV62 @ SV235 @ SV217 ) ) ) )
= $true )
| ( ( member_a @ SV217 @ ( partia1066395285xt_a_b @ SV62 ) )
= $false )
| ( ( member_a @ SV121 @ ( partia1066395285xt_a_b @ SV62 ) )
= $false )
| ( ( semiring_a_b @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(1490,plain,
! [SV221: a,SV127: a,SV72: partia1833973666xt_a_b,SV236: a] :
( ( ( ~ ( member_a @ SV236 @ ( partia1066395285xt_a_b @ SV72 ) )
| ( ( mult_a_ring_ext_a_b @ SV72 @ ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ SV221 ) @ SV236 )
= ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ ( mult_a_ring_ext_a_b @ SV72 @ SV221 @ SV236 ) ) ) )
= $true )
| ( ( member_a @ SV221 @ ( partia1066395285xt_a_b @ SV72 ) )
= $false )
| ( ( member_a @ SV127 @ ( partia1066395285xt_a_b @ SV72 ) )
= $false )
| ( ( semiring_a_b @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1491,plain,
! [SV223: a,SV128: a,SV74: partia1833973666xt_a_b,SV237: a] :
( ( ( ~ ( member_a @ SV237 @ ( partia1066395285xt_a_b @ SV74 ) )
| ( ( add_a_b @ SV74 @ SV128 @ ( add_a_b @ SV74 @ SV223 @ SV237 ) )
= ( add_a_b @ SV74 @ SV223 @ ( add_a_b @ SV74 @ SV128 @ SV237 ) ) ) )
= $true )
| ( ( member_a @ SV223 @ ( partia1066395285xt_a_b @ SV74 ) )
= $false )
| ( ( member_a @ SV128 @ ( partia1066395285xt_a_b @ SV74 ) )
= $false )
| ( ( semiring_a_b @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1492,plain,
! [SV225: a,SV129: a,SV76: partia1833973666xt_a_b,SV238: a] :
( ( ( ~ ( member_a @ SV238 @ ( partia1066395285xt_a_b @ SV76 ) )
| ( ( add_a_b @ SV76 @ ( add_a_b @ SV76 @ SV129 @ SV225 ) @ SV238 )
= ( add_a_b @ SV76 @ SV129 @ ( add_a_b @ SV76 @ SV225 @ SV238 ) ) ) )
= $true )
| ( ( member_a @ SV225 @ ( partia1066395285xt_a_b @ SV76 ) )
= $false )
| ( ( member_a @ SV129 @ ( partia1066395285xt_a_b @ SV76 ) )
= $false )
| ( ( semiring_a_b @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1493,plain,
! [SV227: a,SV130: a,SV79: partia1833973666xt_a_b,SV239: a] :
( ( ( ~ ( member_a @ SV239 @ ( partia1066395285xt_a_b @ SV79 ) )
| ( ( mult_a_ring_ext_a_b @ SV79 @ ( add_a_b @ SV79 @ SV130 @ SV227 ) @ SV239 )
= ( add_a_b @ SV79 @ ( mult_a_ring_ext_a_b @ SV79 @ SV130 @ SV239 ) @ ( mult_a_ring_ext_a_b @ SV79 @ SV227 @ SV239 ) ) ) )
= $true )
| ( ( member_a @ SV227 @ ( partia1066395285xt_a_b @ SV79 ) )
= $false )
| ( ( member_a @ SV130 @ ( partia1066395285xt_a_b @ SV79 ) )
= $false )
| ( ( semiring_a_b @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1494,plain,
! [SV87: set_a] :
( ( ( ! [SY364: a] :
~ ( member_a @ SY364 @ SV87 ) )
= $true )
| ( ( member_a @ ( sK13_SY364 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1445]) ).
thf(1495,plain,
! [SV87: set_a] :
( ( ( SV87 = bot_bot_set_a )
= $true )
| ( ( member_a @ ( sK13_SY364 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1446]) ).
thf(1496,plain,
! [SV87: set_a,SV231: a] :
( ( ( member_a @ SV231 @ SV87 )
= $false )
| ( ( SV87 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1447]) ).
thf(1497,plain,
! [SV232: a,SV88: a > $o] :
( ( ( SV88 @ SV232 )
= $false )
| ( ( ( collect_a @ SV88 )
= bot_bot_set_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1498,plain,
! [SV88: a > $o] :
( ( ( ( collect_a @ SV88 )
= bot_bot_set_a )
= $true )
| ( ( SV88 @ ( sK14_SY365 @ SV88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1449]) ).
thf(1499,plain,
! [SV88: a > $o] :
( ( ( ! [SY365: a] :
~ ( SV88 @ SY365 ) )
= $true )
| ( ( SV88 @ ( sK14_SY365 @ SV88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1450]) ).
thf(1500,plain,
! [SV233: a,SV89: a > $o] :
( ( ( SV89 @ SV233 )
= $false )
| ( ( bot_bot_set_a
= ( collect_a @ SV89 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1501,plain,
! [SV89: a > $o] :
( ( ( bot_bot_set_a
= ( collect_a @ SV89 ) )
= $true )
| ( ( SV89 @ ( sK15_SY366 @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1452]) ).
thf(1502,plain,
! [SV89: a > $o] :
( ( ( ! [SY366: a] :
~ ( SV89 @ SY366 ) )
= $true )
| ( ( SV89 @ ( sK15_SY366 @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1453]) ).
thf(1503,plain,
! [SV228: a,SV101: set_a] :
( ( ( ~ ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 ) )
= $false )
| ( ( member_a @ SV228 @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1504,plain,
! [SV228: a,SV101: set_a] :
( ( ( ~ ( ( SV101 != bot_bot_set_a ) ) )
= $false )
| ( ( member_a @ SV228 @ SV101 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1505,plain,
! [SV101: set_a] :
( ( ( ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 ) )
= $false )
| ( ( SV101 = bot_bot_set_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1506,plain,
! [SV101: set_a] :
( ( ( SV101 = bot_bot_set_a )
= $false )
| ( ( SV101 = bot_bot_set_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1456]) ).
thf(1507,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV135 @ SV192 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV135 @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1457]) ).
thf(1508,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ~ ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV135 @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1457]) ).
thf(1509,plain,
! [SV135: set_a,SV192: set_a] :
( ( ( ~ ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV135 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV135 @ SV192 )
| ~ ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1510,plain,
! [SV135: set_a,SV192: set_a] :
( ( ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV192 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV135 @ SV192 )
| ~ ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1511,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( SV136 != SV193 )
= $false )
| ( ( SV136 = SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1459]) ).
thf(1512,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ~ ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) )
= $false )
| ( ( SV136 = SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1459]) ).
thf(1513,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
= $true )
| ( ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) )
= $true )
| ( ( ~ ( ( SV136 != SV193 )
| ~ ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1460]) ).
thf(1514,plain,
! [SV105: set_a] :
( ( ( ~ ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 )
| ~ ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) )
= $false )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1515,plain,
! [SV105: set_a] :
( ( ( ~ ( ~ ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 )
| ~ ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) ) )
= $true )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 )
= $false )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1516,plain,
! [SV110: a,SV210: a,SV11: a,SV234: a] :
( ( ( ~ ( member_a @ SV234 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ SV11 @ SV210 ) @ SV110 ) @ SV234 )
= ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ ( add_a_b @ r @ SV11 @ SV110 ) @ SV210 ) @ SV234 ) )
= $true )
| ( ( member_a @ SV210 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV110 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV11 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1463]) ).
thf(1517,plain,
! [SV212: a,SV15: a,SV153: a] :
( ( ( ~ ( ( ( add_a_b @ r @ SV153 @ SV15 )
= ( add_a_b @ r @ SV212 @ SV15 ) )
| ( SV153 = SV212 ) ) )
= $true )
| ( ( ~ ( ( ( add_a_b @ r @ SV153 @ SV15 )
!= ( add_a_b @ r @ SV212 @ SV15 ) )
| ( SV153 != SV212 ) ) )
= $true )
| ( ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1518,plain,
! [SV117: a,SV198: a,SV28: a] :
( ( ( member_a @ SV28 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ~ ( member_a @ SV198 @ ( partia1066395285xt_a_b @ r ) )
| ( SV28 = SV198 ) )
= $true )
| ( ( member_a @ SV117 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV117 @ SV198 )
= ( zero_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV28 @ SV117 )
= ( zero_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1519,plain,
! [SV35: a,SV213: a,SV163: a] :
( ( ( ~ ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
= SV35 )
| ( SV163
= ( add_a_b @ r @ SV35 @ SV213 ) ) ) )
= $true )
| ( ( ~ ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
!= SV35 )
| ( SV163
!= ( add_a_b @ r @ SV35 @ SV213 ) ) ) )
= $true )
| ( ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1468]) ).
thf(1520,plain,
! [SV214: a,SV164: a,SV36: a] :
( ( ( ~ ( ( SV36
= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
| ( SV164
= ( add_a_b @ r @ SV36 @ SV214 ) ) ) )
= $true )
| ( ( ~ ( ( SV36
!= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
| ( SV164
!= ( add_a_b @ r @ SV36 @ SV214 ) ) ) )
= $true )
| ( ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1470]) ).
thf(1521,plain,
! [SV37: a,SV215: a,SV165: a] :
( ( ( ~ ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
= SV37 )
| ( SV215
= ( add_a_b @ r @ SV165 @ SV37 ) ) ) )
= $true )
| ( ( ~ ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
!= SV37 )
| ( SV215
!= ( add_a_b @ r @ SV165 @ SV37 ) ) ) )
= $true )
| ( ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1472]) ).
thf(1522,plain,
! [SV216: a,SV166: a,SV38: a] :
( ( ( ~ ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
| ( SV216
= ( add_a_b @ r @ SV166 @ SV38 ) ) ) )
= $true )
| ( ( ~ ( ( SV38
!= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
| ( SV216
!= ( add_a_b @ r @ SV166 @ SV38 ) ) ) )
= $true )
| ( ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1474]) ).
thf(1523,plain,
! [SV119: a,SV40: a,SV139: a] :
( ( ( member_a @ SV139 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV40 ) @ SV139 )
= SV119 )
= $true )
| ( ( member_a @ SV119 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV40 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV40 @ SV119 )
= SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1524,plain,
! [SV170: a,SV52: a] :
( ( ( ( SV52
!= ( add_a_b @ r @ SV170 @ SV52 ) )
| ( SV170
!= ( zero_a_b @ r ) ) )
= $false )
| ( ( SV52
= ( add_a_b @ r @ SV170 @ SV52 ) )
= $false )
| ( ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1477]) ).
thf(1525,plain,
! [SV170: a,SV52: a] :
( ( ( ( SV52
!= ( add_a_b @ r @ SV170 @ SV52 ) )
| ( SV170
!= ( zero_a_b @ r ) ) )
= $false )
| ( ( SV170
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1478]) ).
thf(1526,plain,
! [SV53: a,SV171: a] :
( ( ( ( ( add_a_b @ r @ SV171 @ SV53 )
!= SV53 )
| ( SV171
!= ( zero_a_b @ r ) ) )
= $false )
| ( ( ( add_a_b @ r @ SV171 @ SV53 )
= SV53 )
= $false )
| ( ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1527,plain,
! [SV53: a,SV171: a] :
( ( ( ( ( add_a_b @ r @ SV171 @ SV53 )
!= SV53 )
| ( SV171
!= ( zero_a_b @ r ) ) )
= $false )
| ( ( SV171
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1528,plain,
! [SV172: a,SV54: a] :
( ( ( ( SV54
!= ( add_a_b @ r @ SV54 @ SV172 ) )
| ( SV172
!= ( zero_a_b @ r ) ) )
= $false )
| ( ( SV54
= ( add_a_b @ r @ SV54 @ SV172 ) )
= $false )
| ( ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1529,plain,
! [SV172: a,SV54: a] :
( ( ( ( SV54
!= ( add_a_b @ r @ SV54 @ SV172 ) )
| ( SV172
!= ( zero_a_b @ r ) ) )
= $false )
| ( ( SV172
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1530,plain,
! [SV173: a,SV55: a] :
( ( ( ( ( add_a_b @ r @ SV55 @ SV173 )
!= SV55 )
| ( SV173
!= ( zero_a_b @ r ) ) )
= $false )
| ( ( ( add_a_b @ r @ SV55 @ SV173 )
= SV55 )
= $false )
| ( ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1531,plain,
! [SV173: a,SV55: a] :
( ( ( ( ( add_a_b @ r @ SV55 @ SV173 )
!= SV55 )
| ( SV173
!= ( zero_a_b @ r ) ) )
= $false )
| ( ( SV173
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1484]) ).
thf(1532,plain,
! [SV217: a,SV121: a,SV62: partia1833973666xt_a_b,SV235: a] :
( ( ( ~ ( member_a @ SV235 @ ( partia1066395285xt_a_b @ SV62 ) ) )
= $true )
| ( ( ( mult_a_ring_ext_a_b @ SV62 @ SV235 @ ( add_a_b @ SV62 @ SV121 @ SV217 ) )
= ( add_a_b @ SV62 @ ( mult_a_ring_ext_a_b @ SV62 @ SV235 @ SV121 ) @ ( mult_a_ring_ext_a_b @ SV62 @ SV235 @ SV217 ) ) )
= $true )
| ( ( member_a @ SV217 @ ( partia1066395285xt_a_b @ SV62 ) )
= $false )
| ( ( member_a @ SV121 @ ( partia1066395285xt_a_b @ SV62 ) )
= $false )
| ( ( semiring_a_b @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1489]) ).
thf(1533,plain,
! [SV221: a,SV127: a,SV72: partia1833973666xt_a_b,SV236: a] :
( ( ( ~ ( member_a @ SV236 @ ( partia1066395285xt_a_b @ SV72 ) ) )
= $true )
| ( ( ( mult_a_ring_ext_a_b @ SV72 @ ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ SV221 ) @ SV236 )
= ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ ( mult_a_ring_ext_a_b @ SV72 @ SV221 @ SV236 ) ) )
= $true )
| ( ( member_a @ SV221 @ ( partia1066395285xt_a_b @ SV72 ) )
= $false )
| ( ( member_a @ SV127 @ ( partia1066395285xt_a_b @ SV72 ) )
= $false )
| ( ( semiring_a_b @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1490]) ).
thf(1534,plain,
! [SV223: a,SV128: a,SV74: partia1833973666xt_a_b,SV237: a] :
( ( ( ~ ( member_a @ SV237 @ ( partia1066395285xt_a_b @ SV74 ) ) )
= $true )
| ( ( ( add_a_b @ SV74 @ SV128 @ ( add_a_b @ SV74 @ SV223 @ SV237 ) )
= ( add_a_b @ SV74 @ SV223 @ ( add_a_b @ SV74 @ SV128 @ SV237 ) ) )
= $true )
| ( ( member_a @ SV223 @ ( partia1066395285xt_a_b @ SV74 ) )
= $false )
| ( ( member_a @ SV128 @ ( partia1066395285xt_a_b @ SV74 ) )
= $false )
| ( ( semiring_a_b @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1491]) ).
thf(1535,plain,
! [SV225: a,SV129: a,SV76: partia1833973666xt_a_b,SV238: a] :
( ( ( ~ ( member_a @ SV238 @ ( partia1066395285xt_a_b @ SV76 ) ) )
= $true )
| ( ( ( add_a_b @ SV76 @ ( add_a_b @ SV76 @ SV129 @ SV225 ) @ SV238 )
= ( add_a_b @ SV76 @ SV129 @ ( add_a_b @ SV76 @ SV225 @ SV238 ) ) )
= $true )
| ( ( member_a @ SV225 @ ( partia1066395285xt_a_b @ SV76 ) )
= $false )
| ( ( member_a @ SV129 @ ( partia1066395285xt_a_b @ SV76 ) )
= $false )
| ( ( semiring_a_b @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1492]) ).
thf(1536,plain,
! [SV227: a,SV130: a,SV79: partia1833973666xt_a_b,SV239: a] :
( ( ( ~ ( member_a @ SV239 @ ( partia1066395285xt_a_b @ SV79 ) ) )
= $true )
| ( ( ( mult_a_ring_ext_a_b @ SV79 @ ( add_a_b @ SV79 @ SV130 @ SV227 ) @ SV239 )
= ( add_a_b @ SV79 @ ( mult_a_ring_ext_a_b @ SV79 @ SV130 @ SV239 ) @ ( mult_a_ring_ext_a_b @ SV79 @ SV227 @ SV239 ) ) )
= $true )
| ( ( member_a @ SV227 @ ( partia1066395285xt_a_b @ SV79 ) )
= $false )
| ( ( member_a @ SV130 @ ( partia1066395285xt_a_b @ SV79 ) )
= $false )
| ( ( semiring_a_b @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1493]) ).
thf(1537,plain,
! [SV87: set_a,SV240: a] :
( ( ( ~ ( member_a @ SV240 @ SV87 ) )
= $true )
| ( ( member_a @ ( sK13_SY364 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1538,plain,
! [SV241: a,SV88: a > $o] :
( ( ( ~ ( SV88 @ SV241 ) )
= $true )
| ( ( SV88 @ ( sK14_SY365 @ SV88 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1539,plain,
! [SV242: a,SV89: a > $o] :
( ( ( ~ ( SV89 @ SV242 ) )
= $true )
| ( ( SV89 @ ( sK15_SY366 @ SV89 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1540,plain,
! [SV228: a,SV101: set_a] :
( ( ( ~ ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 ) )
= $true )
| ( ( member_a @ SV228 @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1503]) ).
thf(1541,plain,
! [SV228: a,SV101: set_a] :
( ( ( SV101 != bot_bot_set_a )
= $true )
| ( ( member_a @ SV228 @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1504]) ).
thf(1542,plain,
! [SV101: set_a] :
( ( ( ~ ( member_a @ ( sK17_SY373 @ SV101 ) @ SV101 ) )
= $false )
| ( ( SV101 = bot_bot_set_a )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1505]) ).
thf(1543,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ord_less_eq_set_a @ SV135 @ SV192 )
= $true )
| ( ( ord_less_eq_set_a @ SV135 @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1507]) ).
thf(1544,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV135 @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1508]) ).
thf(1545,plain,
! [SV135: set_a,SV192: set_a] :
( ( ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV135 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV135 @ SV192 )
| ~ ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1509]) ).
thf(1546,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV135 @ SV192 )
| ~ ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) )
= $false )
| ( ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1547,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( SV136 = SV193 )
= $true )
| ( ( SV136 = SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1511]) ).
thf(1548,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) )
= $true )
| ( ( SV136 = SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1512]) ).
thf(1549,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ( product_fst_a_a @ SV136 )
= ( product_fst_a_a @ SV193 ) )
= $false )
| ( ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) )
= $true )
| ( ( ~ ( ( SV136 != SV193 )
| ~ ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1513]) ).
thf(1550,plain,
! [SV105: set_a] :
( ( ( ~ ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 ) )
= $false )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1514]) ).
thf(1551,plain,
! [SV105: set_a] :
( ( ( ~ ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) )
= $false )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1514]) ).
thf(1552,plain,
! [SV105: set_a] :
( ( ( ~ ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 )
| ~ ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) )
= $false )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 )
= $false )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1553,plain,
! [SV110: a,SV210: a,SV11: a,SV234: a] :
( ( ( member_a @ SV234 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ SV11 @ SV210 ) @ SV110 ) @ SV234 )
= ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ ( add_a_b @ r @ SV11 @ SV110 ) @ SV210 ) @ SV234 ) )
= $true )
| ( ( member_a @ SV210 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV110 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV11 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1554,plain,
! [SV212: a,SV15: a,SV153: a] :
( ( ( ( ( add_a_b @ r @ SV153 @ SV15 )
= ( add_a_b @ r @ SV212 @ SV15 ) )
| ( SV153 = SV212 ) )
= $false )
| ( ( ~ ( ( ( add_a_b @ r @ SV153 @ SV15 )
!= ( add_a_b @ r @ SV212 @ SV15 ) )
| ( SV153 != SV212 ) ) )
= $true )
| ( ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1555,plain,
! [SV117: a,SV28: a,SV198: a] :
( ( ( ~ ( member_a @ SV198 @ ( partia1066395285xt_a_b @ r ) ) )
= $true )
| ( ( SV28 = SV198 )
= $true )
| ( ( member_a @ SV28 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV117 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV117 @ SV198 )
= ( zero_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV28 @ SV117 )
= ( zero_a_b @ r ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1518]) ).
thf(1556,plain,
! [SV35: a,SV213: a,SV163: a] :
( ( ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
= SV35 )
| ( SV163
= ( add_a_b @ r @ SV35 @ SV213 ) ) )
= $false )
| ( ( ~ ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
!= SV35 )
| ( SV163
!= ( add_a_b @ r @ SV35 @ SV213 ) ) ) )
= $true )
| ( ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1557,plain,
! [SV214: a,SV164: a,SV36: a] :
( ( ( ( SV36
= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
| ( SV164
= ( add_a_b @ r @ SV36 @ SV214 ) ) )
= $false )
| ( ( ~ ( ( SV36
!= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
| ( SV164
!= ( add_a_b @ r @ SV36 @ SV214 ) ) ) )
= $true )
| ( ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1520]) ).
thf(1558,plain,
! [SV37: a,SV215: a,SV165: a] :
( ( ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
= SV37 )
| ( SV215
= ( add_a_b @ r @ SV165 @ SV37 ) ) )
= $false )
| ( ( ~ ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
!= SV37 )
| ( SV215
!= ( add_a_b @ r @ SV165 @ SV37 ) ) ) )
= $true )
| ( ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1521]) ).
thf(1559,plain,
! [SV216: a,SV166: a,SV38: a] :
( ( ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
| ( SV216
= ( add_a_b @ r @ SV166 @ SV38 ) ) )
= $false )
| ( ( ~ ( ( SV38
!= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
| ( SV216
!= ( add_a_b @ r @ SV166 @ SV38 ) ) ) )
= $true )
| ( ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1522]) ).
thf(1560,plain,
! [SV170: a,SV52: a] :
( ( ( SV52
!= ( add_a_b @ r @ SV170 @ SV52 ) )
= $false )
| ( ( SV52
= ( add_a_b @ r @ SV170 @ SV52 ) )
= $false )
| ( ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1524]) ).
thf(1561,plain,
! [SV52: a,SV170: a] :
( ( ( SV170
!= ( zero_a_b @ r ) )
= $false )
| ( ( SV52
= ( add_a_b @ r @ SV170 @ SV52 ) )
= $false )
| ( ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1524]) ).
thf(1562,plain,
! [SV170: a,SV52: a] :
( ( ( SV52
!= ( add_a_b @ r @ SV170 @ SV52 ) )
= $false )
| ( ( SV170
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1525]) ).
thf(1563,plain,
! [SV52: a,SV170: a] :
( ( ( SV170
!= ( zero_a_b @ r ) )
= $false )
| ( ( SV170
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1525]) ).
thf(1564,plain,
! [SV53: a,SV171: a] :
( ( ( ( add_a_b @ r @ SV171 @ SV53 )
!= SV53 )
= $false )
| ( ( ( add_a_b @ r @ SV171 @ SV53 )
= SV53 )
= $false )
| ( ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1526]) ).
thf(1565,plain,
! [SV53: a,SV171: a] :
( ( ( SV171
!= ( zero_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV171 @ SV53 )
= SV53 )
= $false )
| ( ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1526]) ).
thf(1566,plain,
! [SV53: a,SV171: a] :
( ( ( ( add_a_b @ r @ SV171 @ SV53 )
!= SV53 )
= $false )
| ( ( SV171
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1527]) ).
thf(1567,plain,
! [SV53: a,SV171: a] :
( ( ( SV171
!= ( zero_a_b @ r ) )
= $false )
| ( ( SV171
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1527]) ).
thf(1568,plain,
! [SV172: a,SV54: a] :
( ( ( SV54
!= ( add_a_b @ r @ SV54 @ SV172 ) )
= $false )
| ( ( SV54
= ( add_a_b @ r @ SV54 @ SV172 ) )
= $false )
| ( ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1528]) ).
thf(1569,plain,
! [SV54: a,SV172: a] :
( ( ( SV172
!= ( zero_a_b @ r ) )
= $false )
| ( ( SV54
= ( add_a_b @ r @ SV54 @ SV172 ) )
= $false )
| ( ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1528]) ).
thf(1570,plain,
! [SV172: a,SV54: a] :
( ( ( SV54
!= ( add_a_b @ r @ SV54 @ SV172 ) )
= $false )
| ( ( SV172
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1571,plain,
! [SV54: a,SV172: a] :
( ( ( SV172
!= ( zero_a_b @ r ) )
= $false )
| ( ( SV172
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1572,plain,
! [SV173: a,SV55: a] :
( ( ( ( add_a_b @ r @ SV55 @ SV173 )
!= SV55 )
= $false )
| ( ( ( add_a_b @ r @ SV55 @ SV173 )
= SV55 )
= $false )
| ( ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1530]) ).
thf(1573,plain,
! [SV55: a,SV173: a] :
( ( ( SV173
!= ( zero_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV55 @ SV173 )
= SV55 )
= $false )
| ( ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1530]) ).
thf(1574,plain,
! [SV173: a,SV55: a] :
( ( ( ( add_a_b @ r @ SV55 @ SV173 )
!= SV55 )
= $false )
| ( ( SV173
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1531]) ).
thf(1575,plain,
! [SV55: a,SV173: a] :
( ( ( SV173
!= ( zero_a_b @ r ) )
= $false )
| ( ( SV173
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1531]) ).
thf(1576,plain,
! [SV217: a,SV121: a,SV62: partia1833973666xt_a_b,SV235: a] :
( ( ( member_a @ SV235 @ ( partia1066395285xt_a_b @ SV62 ) )
= $false )
| ( ( ( mult_a_ring_ext_a_b @ SV62 @ SV235 @ ( add_a_b @ SV62 @ SV121 @ SV217 ) )
= ( add_a_b @ SV62 @ ( mult_a_ring_ext_a_b @ SV62 @ SV235 @ SV121 ) @ ( mult_a_ring_ext_a_b @ SV62 @ SV235 @ SV217 ) ) )
= $true )
| ( ( member_a @ SV217 @ ( partia1066395285xt_a_b @ SV62 ) )
= $false )
| ( ( member_a @ SV121 @ ( partia1066395285xt_a_b @ SV62 ) )
= $false )
| ( ( semiring_a_b @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1532]) ).
thf(1577,plain,
! [SV221: a,SV127: a,SV72: partia1833973666xt_a_b,SV236: a] :
( ( ( member_a @ SV236 @ ( partia1066395285xt_a_b @ SV72 ) )
= $false )
| ( ( ( mult_a_ring_ext_a_b @ SV72 @ ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ SV221 ) @ SV236 )
= ( mult_a_ring_ext_a_b @ SV72 @ SV127 @ ( mult_a_ring_ext_a_b @ SV72 @ SV221 @ SV236 ) ) )
= $true )
| ( ( member_a @ SV221 @ ( partia1066395285xt_a_b @ SV72 ) )
= $false )
| ( ( member_a @ SV127 @ ( partia1066395285xt_a_b @ SV72 ) )
= $false )
| ( ( semiring_a_b @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1578,plain,
! [SV223: a,SV128: a,SV74: partia1833973666xt_a_b,SV237: a] :
( ( ( member_a @ SV237 @ ( partia1066395285xt_a_b @ SV74 ) )
= $false )
| ( ( ( add_a_b @ SV74 @ SV128 @ ( add_a_b @ SV74 @ SV223 @ SV237 ) )
= ( add_a_b @ SV74 @ SV223 @ ( add_a_b @ SV74 @ SV128 @ SV237 ) ) )
= $true )
| ( ( member_a @ SV223 @ ( partia1066395285xt_a_b @ SV74 ) )
= $false )
| ( ( member_a @ SV128 @ ( partia1066395285xt_a_b @ SV74 ) )
= $false )
| ( ( semiring_a_b @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1534]) ).
thf(1579,plain,
! [SV225: a,SV129: a,SV76: partia1833973666xt_a_b,SV238: a] :
( ( ( member_a @ SV238 @ ( partia1066395285xt_a_b @ SV76 ) )
= $false )
| ( ( ( add_a_b @ SV76 @ ( add_a_b @ SV76 @ SV129 @ SV225 ) @ SV238 )
= ( add_a_b @ SV76 @ SV129 @ ( add_a_b @ SV76 @ SV225 @ SV238 ) ) )
= $true )
| ( ( member_a @ SV225 @ ( partia1066395285xt_a_b @ SV76 ) )
= $false )
| ( ( member_a @ SV129 @ ( partia1066395285xt_a_b @ SV76 ) )
= $false )
| ( ( semiring_a_b @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1535]) ).
thf(1580,plain,
! [SV227: a,SV130: a,SV79: partia1833973666xt_a_b,SV239: a] :
( ( ( member_a @ SV239 @ ( partia1066395285xt_a_b @ SV79 ) )
= $false )
| ( ( ( mult_a_ring_ext_a_b @ SV79 @ ( add_a_b @ SV79 @ SV130 @ SV227 ) @ SV239 )
= ( add_a_b @ SV79 @ ( mult_a_ring_ext_a_b @ SV79 @ SV130 @ SV239 ) @ ( mult_a_ring_ext_a_b @ SV79 @ SV227 @ SV239 ) ) )
= $true )
| ( ( member_a @ SV227 @ ( partia1066395285xt_a_b @ SV79 ) )
= $false )
| ( ( member_a @ SV130 @ ( partia1066395285xt_a_b @ SV79 ) )
= $false )
| ( ( semiring_a_b @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1581,plain,
! [SV87: set_a,SV240: a] :
( ( ( member_a @ SV240 @ SV87 )
= $false )
| ( ( member_a @ ( sK13_SY364 @ SV87 ) @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1582,plain,
! [SV241: a,SV88: a > $o] :
( ( ( SV88 @ SV241 )
= $false )
| ( ( SV88 @ ( sK14_SY365 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1583,plain,
! [SV242: a,SV89: a > $o] :
( ( ( SV89 @ SV242 )
= $false )
| ( ( SV89 @ ( sK15_SY366 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1584,plain,
! [SV228: a,SV101: set_a] :
( ( ( ! [SY373: a] :
~ ( member_a @ SY373 @ SV101 ) )
= $false )
| ( ( member_a @ SV228 @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1585,plain,
! [SV228: a,SV101: set_a] :
( ( ( SV101 = bot_bot_set_a )
= $false )
| ( ( member_a @ SV228 @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1541]) ).
thf(1586,plain,
! [SV101: set_a] :
( ( ( member_a @ ( sK17_SY373 @ SV101 ) @ SV101 )
= $true )
| ( ( SV101 = bot_bot_set_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1542]) ).
thf(1587,plain,
! [SV192: set_a,SV135: set_a,SV243: a] :
( ( ( ~ ( member_a @ SV243 @ SV135 )
| ( member_a @ SV243 @ SV192 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV135 @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1588,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV135 @ SV192 )
| ~ ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) )
= $false )
| ( ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1545]) ).
thf(1589,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV135 @ SV192 ) )
= $false )
| ( ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1546]) ).
thf(1590,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ~ ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) )
= $false )
| ( ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1546]) ).
thf(1591,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) )
= $false )
| ( ( SV136 = SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1592,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ( product_snd_a_a @ SV136 )
= ( product_snd_a_a @ SV193 ) )
= $false )
| ( ( ( product_fst_a_a @ SV136 )
= ( product_fst_a_a @ SV193 ) )
= $false )
| ( ( ~ ( ( SV136 != SV193 )
| ~ ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1593,plain,
! [SV105: set_a] :
( ( ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 )
= $true )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1550]) ).
thf(1594,plain,
! [SV105: set_a] :
( ( ( ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) )
= $true )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1551]) ).
thf(1595,plain,
! [SV105: set_a] :
( ( ( ~ ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 ) )
= $false )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 )
= $false )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1596,plain,
! [SV105: set_a] :
( ( ( ~ ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) )
= $false )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 )
= $false )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1597,plain,
! [SV212: a,SV15: a,SV153: a] :
( ( ( ( add_a_b @ r @ SV153 @ SV15 )
= ( add_a_b @ r @ SV212 @ SV15 ) )
= $false )
| ( ( ~ ( ( ( add_a_b @ r @ SV153 @ SV15 )
!= ( add_a_b @ r @ SV212 @ SV15 ) )
| ( SV153 != SV212 ) ) )
= $true )
| ( ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1554]) ).
thf(1598,plain,
! [SV15: a,SV212: a,SV153: a] :
( ( ( SV153 = SV212 )
= $false )
| ( ( ~ ( ( ( add_a_b @ r @ SV153 @ SV15 )
!= ( add_a_b @ r @ SV212 @ SV15 ) )
| ( SV153 != SV212 ) ) )
= $true )
| ( ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1554]) ).
thf(1599,plain,
! [SV117: a,SV28: a,SV198: a] :
( ( ( member_a @ SV198 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( SV28 = SV198 )
= $true )
| ( ( member_a @ SV28 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV117 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV117 @ SV198 )
= ( zero_a_b @ r ) )
= $false )
| ( ( ( add_a_b @ r @ SV28 @ SV117 )
= ( zero_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1600,plain,
! [SV35: a,SV213: a,SV163: a] :
( ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
= SV35 )
= $false )
| ( ( ~ ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
!= SV35 )
| ( SV163
!= ( add_a_b @ r @ SV35 @ SV213 ) ) ) )
= $true )
| ( ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1601,plain,
! [SV213: a,SV35: a,SV163: a] :
( ( ( SV163
= ( add_a_b @ r @ SV35 @ SV213 ) )
= $false )
| ( ( ~ ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
!= SV35 )
| ( SV163
!= ( add_a_b @ r @ SV35 @ SV213 ) ) ) )
= $true )
| ( ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1602,plain,
! [SV214: a,SV164: a,SV36: a] :
( ( ( SV36
= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
= $false )
| ( ( ~ ( ( SV36
!= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
| ( SV164
!= ( add_a_b @ r @ SV36 @ SV214 ) ) ) )
= $true )
| ( ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1603,plain,
! [SV214: a,SV36: a,SV164: a] :
( ( ( SV164
= ( add_a_b @ r @ SV36 @ SV214 ) )
= $false )
| ( ( ~ ( ( SV36
!= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
| ( SV164
!= ( add_a_b @ r @ SV36 @ SV214 ) ) ) )
= $true )
| ( ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1604,plain,
! [SV37: a,SV215: a,SV165: a] :
( ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
= SV37 )
= $false )
| ( ( ~ ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
!= SV37 )
| ( SV215
!= ( add_a_b @ r @ SV165 @ SV37 ) ) ) )
= $true )
| ( ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1605,plain,
! [SV37: a,SV165: a,SV215: a] :
( ( ( SV215
= ( add_a_b @ r @ SV165 @ SV37 ) )
= $false )
| ( ( ~ ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
!= SV37 )
| ( SV215
!= ( add_a_b @ r @ SV165 @ SV37 ) ) ) )
= $true )
| ( ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1606,plain,
! [SV216: a,SV166: a,SV38: a] :
( ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
= $false )
| ( ( ~ ( ( SV38
!= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
| ( SV216
!= ( add_a_b @ r @ SV166 @ SV38 ) ) ) )
= $true )
| ( ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1559]) ).
thf(1607,plain,
! [SV38: a,SV166: a,SV216: a] :
( ( ( SV216
= ( add_a_b @ r @ SV166 @ SV38 ) )
= $false )
| ( ( ~ ( ( SV38
!= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
| ( SV216
!= ( add_a_b @ r @ SV166 @ SV38 ) ) ) )
= $true )
| ( ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1559]) ).
thf(1608,plain,
! [SV170: a,SV52: a] :
( ( ( SV52
= ( add_a_b @ r @ SV170 @ SV52 ) )
= $true )
| ( ( SV52
= ( add_a_b @ r @ SV170 @ SV52 ) )
= $false )
| ( ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1560]) ).
thf(1609,plain,
! [SV52: a,SV170: a] :
( ( ( SV170
= ( zero_a_b @ r ) )
= $true )
| ( ( SV52
= ( add_a_b @ r @ SV170 @ SV52 ) )
= $false )
| ( ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1561]) ).
thf(1610,plain,
! [SV170: a,SV52: a] :
( ( ( SV52
= ( add_a_b @ r @ SV170 @ SV52 ) )
= $true )
| ( ( SV170
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1562]) ).
thf(1611,plain,
! [SV52: a,SV170: a] :
( ( ( SV170
= ( zero_a_b @ r ) )
= $true )
| ( ( SV170
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV170 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV52 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1563]) ).
thf(1612,plain,
! [SV53: a,SV171: a] :
( ( ( ( add_a_b @ r @ SV171 @ SV53 )
= SV53 )
= $true )
| ( ( ( add_a_b @ r @ SV171 @ SV53 )
= SV53 )
= $false )
| ( ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1564]) ).
thf(1613,plain,
! [SV53: a,SV171: a] :
( ( ( SV171
= ( zero_a_b @ r ) )
= $true )
| ( ( ( add_a_b @ r @ SV171 @ SV53 )
= SV53 )
= $false )
| ( ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1565]) ).
thf(1614,plain,
! [SV53: a,SV171: a] :
( ( ( ( add_a_b @ r @ SV171 @ SV53 )
= SV53 )
= $true )
| ( ( SV171
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1566]) ).
thf(1615,plain,
! [SV53: a,SV171: a] :
( ( ( SV171
= ( zero_a_b @ r ) )
= $true )
| ( ( SV171
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV171 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV53 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1567]) ).
thf(1616,plain,
! [SV172: a,SV54: a] :
( ( ( SV54
= ( add_a_b @ r @ SV54 @ SV172 ) )
= $true )
| ( ( SV54
= ( add_a_b @ r @ SV54 @ SV172 ) )
= $false )
| ( ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1568]) ).
thf(1617,plain,
! [SV54: a,SV172: a] :
( ( ( SV172
= ( zero_a_b @ r ) )
= $true )
| ( ( SV54
= ( add_a_b @ r @ SV54 @ SV172 ) )
= $false )
| ( ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1569]) ).
thf(1618,plain,
! [SV172: a,SV54: a] :
( ( ( SV54
= ( add_a_b @ r @ SV54 @ SV172 ) )
= $true )
| ( ( SV172
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1570]) ).
thf(1619,plain,
! [SV54: a,SV172: a] :
( ( ( SV172
= ( zero_a_b @ r ) )
= $true )
| ( ( SV172
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV172 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV54 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1571]) ).
thf(1620,plain,
! [SV173: a,SV55: a] :
( ( ( ( add_a_b @ r @ SV55 @ SV173 )
= SV55 )
= $true )
| ( ( ( add_a_b @ r @ SV55 @ SV173 )
= SV55 )
= $false )
| ( ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1572]) ).
thf(1621,plain,
! [SV55: a,SV173: a] :
( ( ( SV173
= ( zero_a_b @ r ) )
= $true )
| ( ( ( add_a_b @ r @ SV55 @ SV173 )
= SV55 )
= $false )
| ( ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1573]) ).
thf(1622,plain,
! [SV173: a,SV55: a] :
( ( ( ( add_a_b @ r @ SV55 @ SV173 )
= SV55 )
= $true )
| ( ( SV173
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1574]) ).
thf(1623,plain,
! [SV55: a,SV173: a] :
( ( ( SV173
= ( zero_a_b @ r ) )
= $true )
| ( ( SV173
= ( zero_a_b @ r ) )
= $false )
| ( ( member_a @ SV173 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV55 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1575]) ).
thf(1624,plain,
! [SV101: set_a,SV228: a] :
( ( ( ~ ( member_a @ ( sK18_SY373 @ SV228 @ SV101 ) @ SV101 ) )
= $false )
| ( ( member_a @ SV228 @ SV101 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1584]) ).
thf(1625,plain,
! [SV192: set_a,SV135: set_a,SV243: a] :
( ( ( ~ ( member_a @ SV243 @ SV135 ) )
= $true )
| ( ( member_a @ SV243 @ SV192 )
= $true )
| ( ( ord_less_eq_set_a @ SV135 @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1587]) ).
thf(1626,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV135 @ SV192 ) )
= $false )
| ( ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1627,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ~ ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) )
= $false )
| ( ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1628,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ord_less_eq_set_a @ SV135 @ SV192 )
= $true )
| ( ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1589]) ).
thf(1629,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) )
= $true )
| ( ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1590]) ).
thf(1630,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
= $false )
| ( ( SV136 = SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1591]) ).
thf(1631,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) )
= $false )
| ( ( SV136 = SV193 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1591]) ).
thf(1632,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ( SV136 != SV193 )
| ~ ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) )
= $false )
| ( ( ( product_fst_a_a @ SV136 )
= ( product_fst_a_a @ SV193 ) )
= $false )
| ( ( ( product_snd_a_a @ SV136 )
= ( product_snd_a_a @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1633,plain,
! [SV105: set_a] :
( ( ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) )
= $false )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1634,plain,
! [SV105: set_a] :
( ( ( member_a @ ( sK3_X3 @ SV105 ) @ SV105 )
= $true )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 )
= $false )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1595]) ).
thf(1635,plain,
! [SV105: set_a] :
( ( ( ~ ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) ) )
= $true )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 )
= $false )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1596]) ).
thf(1636,plain,
! [SV212: a,SV15: a,SV153: a] :
( ( ( ( ( add_a_b @ r @ SV153 @ SV15 )
!= ( add_a_b @ r @ SV212 @ SV15 ) )
| ( SV153 != SV212 ) )
= $false )
| ( ( ( add_a_b @ r @ SV153 @ SV15 )
= ( add_a_b @ r @ SV212 @ SV15 ) )
= $false )
| ( ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1637,plain,
! [SV212: a,SV15: a,SV153: a] :
( ( ( ( ( add_a_b @ r @ SV153 @ SV15 )
!= ( add_a_b @ r @ SV212 @ SV15 ) )
| ( SV153 != SV212 ) )
= $false )
| ( ( SV153 = SV212 )
= $false )
| ( ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1638,plain,
! [SV35: a,SV213: a,SV163: a] :
( ( ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
!= SV35 )
| ( SV163
!= ( add_a_b @ r @ SV35 @ SV213 ) ) )
= $false )
| ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
= SV35 )
= $false )
| ( ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1639,plain,
! [SV35: a,SV213: a,SV163: a] :
( ( ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
!= SV35 )
| ( SV163
!= ( add_a_b @ r @ SV35 @ SV213 ) ) )
= $false )
| ( ( SV163
= ( add_a_b @ r @ SV35 @ SV213 ) )
= $false )
| ( ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1640,plain,
! [SV214: a,SV164: a,SV36: a] :
( ( ( ( SV36
!= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
| ( SV164
!= ( add_a_b @ r @ SV36 @ SV214 ) ) )
= $false )
| ( ( SV36
= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
= $false )
| ( ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1641,plain,
! [SV214: a,SV164: a,SV36: a] :
( ( ( ( SV36
!= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
| ( SV164
!= ( add_a_b @ r @ SV36 @ SV214 ) ) )
= $false )
| ( ( SV164
= ( add_a_b @ r @ SV36 @ SV214 ) )
= $false )
| ( ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1642,plain,
! [SV37: a,SV215: a,SV165: a] :
( ( ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
!= SV37 )
| ( SV215
!= ( add_a_b @ r @ SV165 @ SV37 ) ) )
= $false )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
= SV37 )
= $false )
| ( ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1604]) ).
thf(1643,plain,
! [SV37: a,SV215: a,SV165: a] :
( ( ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
!= SV37 )
| ( SV215
!= ( add_a_b @ r @ SV165 @ SV37 ) ) )
= $false )
| ( ( SV215
= ( add_a_b @ r @ SV165 @ SV37 ) )
= $false )
| ( ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1605]) ).
thf(1644,plain,
! [SV216: a,SV166: a,SV38: a] :
( ( ( ( SV38
!= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
| ( SV216
!= ( add_a_b @ r @ SV166 @ SV38 ) ) )
= $false )
| ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
= $false )
| ( ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1606]) ).
thf(1645,plain,
! [SV216: a,SV166: a,SV38: a] :
( ( ( ( SV38
!= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
| ( SV216
!= ( add_a_b @ r @ SV166 @ SV38 ) ) )
= $false )
| ( ( SV216
= ( add_a_b @ r @ SV166 @ SV38 ) )
= $false )
| ( ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1646,plain,
! [SV101: set_a,SV228: a] :
( ( ( member_a @ ( sK18_SY373 @ SV228 @ SV101 ) @ SV101 )
= $true )
| ( ( member_a @ SV228 @ SV101 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1624]) ).
thf(1647,plain,
! [SV192: set_a,SV135: set_a,SV243: a] :
( ( ( member_a @ SV243 @ SV135 )
= $false )
| ( ( member_a @ SV243 @ SV192 )
= $true )
| ( ( ord_less_eq_set_a @ SV135 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1648,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ord_less_eq_set_a @ SV135 @ SV192 )
= $true )
| ( ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV135 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1626]) ).
thf(1649,plain,
! [SV192: set_a,SV135: set_a] :
( ( ( ! [SY428: a] :
( ~ ( member_a @ SY428 @ SV135 )
| ( member_a @ SY428 @ SV192 ) ) )
= $true )
| ( ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV135 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1627]) ).
thf(1650,plain,
! [SV192: set_a,SV135: set_a,SV244: a] :
( ( ( ~ ( member_a @ SV244 @ SV135 )
| ( member_a @ SV244 @ SV192 ) )
= $true )
| ( ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(1651,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ( product_fst_a_a @ SV136 )
= ( product_fst_a_a @ SV193 ) )
= $true )
| ( ( SV136 = SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1630]) ).
thf(1652,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ( product_snd_a_a @ SV136 )
= ( product_snd_a_a @ SV193 ) )
= $true )
| ( ( SV136 = SV193 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1631]) ).
thf(1653,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( SV136 != SV193 )
= $false )
| ( ( ( product_fst_a_a @ SV136 )
= ( product_fst_a_a @ SV193 ) )
= $false )
| ( ( ( product_snd_a_a @ SV136 )
= ( product_snd_a_a @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1632]) ).
thf(1654,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ~ ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) )
= $false )
| ( ( ( product_fst_a_a @ SV136 )
= ( product_fst_a_a @ SV193 ) )
= $false )
| ( ( ( product_snd_a_a @ SV136 )
= ( product_snd_a_a @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1632]) ).
thf(1655,plain,
! [SV105: set_a] :
( ( ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 ) )
= $false )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1633]) ).
thf(1656,plain,
! [SV105: set_a] :
( ( ( ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) )
= $false )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1633]) ).
thf(1657,plain,
! [SV105: set_a] :
( ( ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
| ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) )
= $false )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 )
= $false )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1635]) ).
thf(1658,plain,
! [SV212: a,SV15: a,SV153: a] :
( ( ( ( add_a_b @ r @ SV153 @ SV15 )
!= ( add_a_b @ r @ SV212 @ SV15 ) )
= $false )
| ( ( ( add_a_b @ r @ SV153 @ SV15 )
= ( add_a_b @ r @ SV212 @ SV15 ) )
= $false )
| ( ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1636]) ).
thf(1659,plain,
! [SV15: a,SV212: a,SV153: a] :
( ( ( SV153 != SV212 )
= $false )
| ( ( ( add_a_b @ r @ SV153 @ SV15 )
= ( add_a_b @ r @ SV212 @ SV15 ) )
= $false )
| ( ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1636]) ).
thf(1660,plain,
! [SV212: a,SV15: a,SV153: a] :
( ( ( ( add_a_b @ r @ SV153 @ SV15 )
!= ( add_a_b @ r @ SV212 @ SV15 ) )
= $false )
| ( ( SV153 = SV212 )
= $false )
| ( ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1637]) ).
thf(1661,plain,
! [SV15: a,SV212: a,SV153: a] :
( ( ( SV153 != SV212 )
= $false )
| ( ( SV153 = SV212 )
= $false )
| ( ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1637]) ).
thf(1662,plain,
! [SV35: a,SV213: a,SV163: a] :
( ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
!= SV35 )
= $false )
| ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
= SV35 )
= $false )
| ( ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1638]) ).
thf(1663,plain,
! [SV213: a,SV35: a,SV163: a] :
( ( ( SV163
!= ( add_a_b @ r @ SV35 @ SV213 ) )
= $false )
| ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
= SV35 )
= $false )
| ( ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1638]) ).
thf(1664,plain,
! [SV35: a,SV213: a,SV163: a] :
( ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
!= SV35 )
= $false )
| ( ( SV163
= ( add_a_b @ r @ SV35 @ SV213 ) )
= $false )
| ( ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1639]) ).
thf(1665,plain,
! [SV213: a,SV35: a,SV163: a] :
( ( ( SV163
!= ( add_a_b @ r @ SV35 @ SV213 ) )
= $false )
| ( ( SV163
= ( add_a_b @ r @ SV35 @ SV213 ) )
= $false )
| ( ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1639]) ).
thf(1666,plain,
! [SV214: a,SV164: a,SV36: a] :
( ( ( SV36
!= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
= $false )
| ( ( SV36
= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
= $false )
| ( ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1667,plain,
! [SV214: a,SV36: a,SV164: a] :
( ( ( SV164
!= ( add_a_b @ r @ SV36 @ SV214 ) )
= $false )
| ( ( SV36
= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
= $false )
| ( ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1668,plain,
! [SV214: a,SV164: a,SV36: a] :
( ( ( SV36
!= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
= $false )
| ( ( SV164
= ( add_a_b @ r @ SV36 @ SV214 ) )
= $false )
| ( ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1641]) ).
thf(1669,plain,
! [SV214: a,SV36: a,SV164: a] :
( ( ( SV164
!= ( add_a_b @ r @ SV36 @ SV214 ) )
= $false )
| ( ( SV164
= ( add_a_b @ r @ SV36 @ SV214 ) )
= $false )
| ( ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1641]) ).
thf(1670,plain,
! [SV37: a,SV215: a,SV165: a] :
( ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
!= SV37 )
= $false )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
= SV37 )
= $false )
| ( ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1642]) ).
thf(1671,plain,
! [SV37: a,SV165: a,SV215: a] :
( ( ( SV215
!= ( add_a_b @ r @ SV165 @ SV37 ) )
= $false )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
= SV37 )
= $false )
| ( ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1642]) ).
thf(1672,plain,
! [SV37: a,SV215: a,SV165: a] :
( ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
!= SV37 )
= $false )
| ( ( SV215
= ( add_a_b @ r @ SV165 @ SV37 ) )
= $false )
| ( ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1643]) ).
thf(1673,plain,
! [SV37: a,SV165: a,SV215: a] :
( ( ( SV215
!= ( add_a_b @ r @ SV165 @ SV37 ) )
= $false )
| ( ( SV215
= ( add_a_b @ r @ SV165 @ SV37 ) )
= $false )
| ( ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1643]) ).
thf(1674,plain,
! [SV216: a,SV166: a,SV38: a] :
( ( ( SV38
!= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
= $false )
| ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
= $false )
| ( ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1644]) ).
thf(1675,plain,
! [SV38: a,SV166: a,SV216: a] :
( ( ( SV216
!= ( add_a_b @ r @ SV166 @ SV38 ) )
= $false )
| ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
= $false )
| ( ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1644]) ).
thf(1676,plain,
! [SV216: a,SV166: a,SV38: a] :
( ( ( SV38
!= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
= $false )
| ( ( SV216
= ( add_a_b @ r @ SV166 @ SV38 ) )
= $false )
| ( ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1645]) ).
thf(1677,plain,
! [SV38: a,SV166: a,SV216: a] :
( ( ( SV216
!= ( add_a_b @ r @ SV166 @ SV38 ) )
= $false )
| ( ( SV216
= ( add_a_b @ r @ SV166 @ SV38 ) )
= $false )
| ( ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1645]) ).
thf(1678,plain,
! [SV192: set_a,SV135: set_a,SV245: a] :
( ( ( ~ ( member_a @ SV245 @ SV135 )
| ( member_a @ SV245 @ SV192 ) )
= $true )
| ( ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV135 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(1679,plain,
! [SV192: set_a,SV135: set_a,SV244: a] :
( ( ( ~ ( member_a @ SV244 @ SV135 ) )
= $true )
| ( ( member_a @ SV244 @ SV192 )
= $true )
| ( ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1650]) ).
thf(1680,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( SV136 = SV193 )
= $true )
| ( ( ( product_fst_a_a @ SV136 )
= ( product_fst_a_a @ SV193 ) )
= $false )
| ( ( ( product_snd_a_a @ SV136 )
= ( product_snd_a_a @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1653]) ).
thf(1681,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ~ ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) ) )
= $true )
| ( ( ( product_fst_a_a @ SV136 )
= ( product_fst_a_a @ SV193 ) )
= $false )
| ( ( ( product_snd_a_a @ SV136 )
= ( product_snd_a_a @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1654]) ).
thf(1682,plain,
! [SV105: set_a] :
( ( ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
= $true )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1655]) ).
thf(1683,plain,
! [SV105: set_a] :
( ( ( ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) )
= $true )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1656]) ).
thf(1684,plain,
! [SV105: set_a] :
( ( ( ~ ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 ) )
= $false )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 )
= $false )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1657]) ).
thf(1685,plain,
! [SV105: set_a] :
( ( ( ~ ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) )
= $false )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 )
= $false )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1657]) ).
thf(1686,plain,
! [SV212: a,SV15: a,SV153: a] :
( ( ( ( add_a_b @ r @ SV153 @ SV15 )
= ( add_a_b @ r @ SV212 @ SV15 ) )
= $true )
| ( ( ( add_a_b @ r @ SV153 @ SV15 )
= ( add_a_b @ r @ SV212 @ SV15 ) )
= $false )
| ( ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1658]) ).
thf(1687,plain,
! [SV15: a,SV212: a,SV153: a] :
( ( ( SV153 = SV212 )
= $true )
| ( ( ( add_a_b @ r @ SV153 @ SV15 )
= ( add_a_b @ r @ SV212 @ SV15 ) )
= $false )
| ( ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1659]) ).
thf(1688,plain,
! [SV212: a,SV15: a,SV153: a] :
( ( ( ( add_a_b @ r @ SV153 @ SV15 )
= ( add_a_b @ r @ SV212 @ SV15 ) )
= $true )
| ( ( SV153 = SV212 )
= $false )
| ( ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1660]) ).
thf(1689,plain,
! [SV15: a,SV212: a,SV153: a] :
( ( ( SV153 = SV212 )
= $true )
| ( ( SV153 = SV212 )
= $false )
| ( ( member_a @ SV212 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV153 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV15 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1661]) ).
thf(1690,plain,
! [SV35: a,SV213: a,SV163: a] :
( ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
= SV35 )
= $true )
| ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
= SV35 )
= $false )
| ( ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1662]) ).
thf(1691,plain,
! [SV213: a,SV35: a,SV163: a] :
( ( ( SV163
= ( add_a_b @ r @ SV35 @ SV213 ) )
= $true )
| ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
= SV35 )
= $false )
| ( ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1663]) ).
thf(1692,plain,
! [SV35: a,SV213: a,SV163: a] :
( ( ( ( add_a_b @ r @ SV163 @ ( a_inv_a_b @ r @ SV213 ) )
= SV35 )
= $true )
| ( ( SV163
= ( add_a_b @ r @ SV35 @ SV213 ) )
= $false )
| ( ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1664]) ).
thf(1693,plain,
! [SV213: a,SV35: a,SV163: a] :
( ( ( SV163
= ( add_a_b @ r @ SV35 @ SV213 ) )
= $true )
| ( ( SV163
= ( add_a_b @ r @ SV35 @ SV213 ) )
= $false )
| ( ( member_a @ SV213 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV163 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV35 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1665]) ).
thf(1694,plain,
! [SV214: a,SV164: a,SV36: a] :
( ( ( SV36
= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
= $true )
| ( ( SV36
= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
= $false )
| ( ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1666]) ).
thf(1695,plain,
! [SV214: a,SV36: a,SV164: a] :
( ( ( SV164
= ( add_a_b @ r @ SV36 @ SV214 ) )
= $true )
| ( ( SV36
= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
= $false )
| ( ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1667]) ).
thf(1696,plain,
! [SV214: a,SV164: a,SV36: a] :
( ( ( SV36
= ( add_a_b @ r @ SV164 @ ( a_inv_a_b @ r @ SV214 ) ) )
= $true )
| ( ( SV164
= ( add_a_b @ r @ SV36 @ SV214 ) )
= $false )
| ( ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1668]) ).
thf(1697,plain,
! [SV214: a,SV36: a,SV164: a] :
( ( ( SV164
= ( add_a_b @ r @ SV36 @ SV214 ) )
= $true )
| ( ( SV164
= ( add_a_b @ r @ SV36 @ SV214 ) )
= $false )
| ( ( member_a @ SV214 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV164 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV36 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1669]) ).
thf(1698,plain,
! [SV37: a,SV215: a,SV165: a] :
( ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
= SV37 )
= $true )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
= SV37 )
= $false )
| ( ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1670]) ).
thf(1699,plain,
! [SV37: a,SV165: a,SV215: a] :
( ( ( SV215
= ( add_a_b @ r @ SV165 @ SV37 ) )
= $true )
| ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
= SV37 )
= $false )
| ( ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1671]) ).
thf(1700,plain,
! [SV37: a,SV215: a,SV165: a] :
( ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ SV165 ) @ SV215 )
= SV37 )
= $true )
| ( ( SV215
= ( add_a_b @ r @ SV165 @ SV37 ) )
= $false )
| ( ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1672]) ).
thf(1701,plain,
! [SV37: a,SV165: a,SV215: a] :
( ( ( SV215
= ( add_a_b @ r @ SV165 @ SV37 ) )
= $true )
| ( ( SV215
= ( add_a_b @ r @ SV165 @ SV37 ) )
= $false )
| ( ( member_a @ SV215 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV165 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV37 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1673]) ).
thf(1702,plain,
! [SV216: a,SV166: a,SV38: a] :
( ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
= $true )
| ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
= $false )
| ( ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1703,plain,
! [SV38: a,SV166: a,SV216: a] :
( ( ( SV216
= ( add_a_b @ r @ SV166 @ SV38 ) )
= $true )
| ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
= $false )
| ( ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1675]) ).
thf(1704,plain,
! [SV216: a,SV166: a,SV38: a] :
( ( ( SV38
= ( add_a_b @ r @ ( a_inv_a_b @ r @ SV166 ) @ SV216 ) )
= $true )
| ( ( SV216
= ( add_a_b @ r @ SV166 @ SV38 ) )
= $false )
| ( ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1676]) ).
thf(1705,plain,
! [SV38: a,SV166: a,SV216: a] :
( ( ( SV216
= ( add_a_b @ r @ SV166 @ SV38 ) )
= $true )
| ( ( SV216
= ( add_a_b @ r @ SV166 @ SV38 ) )
= $false )
| ( ( member_a @ SV216 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV166 @ ( partia1066395285xt_a_b @ r ) )
= $false )
| ( ( member_a @ SV38 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1677]) ).
thf(1706,plain,
! [SV192: set_a,SV135: set_a,SV245: a] :
( ( ( ~ ( member_a @ SV245 @ SV135 ) )
= $true )
| ( ( member_a @ SV245 @ SV192 )
= $true )
| ( ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1678]) ).
thf(1707,plain,
! [SV192: set_a,SV135: set_a,SV244: a] :
( ( ( member_a @ SV244 @ SV135 )
= $false )
| ( ( member_a @ SV244 @ SV192 )
= $true )
| ( ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1708,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
| ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) ) )
= $false )
| ( ( ( product_fst_a_a @ SV136 )
= ( product_fst_a_a @ SV193 ) )
= $false )
| ( ( ( product_snd_a_a @ SV136 )
= ( product_snd_a_a @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1681]) ).
thf(1709,plain,
! [SV105: set_a] :
( ( ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 )
= $false )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( sK5_X3 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1683]) ).
thf(1710,plain,
! [SV105: set_a] :
( ( ( member_a @ ( sK4_SY248 @ SV105 ) @ SV105 )
= $true )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 )
= $false )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1684]) ).
thf(1711,plain,
! [SV105: set_a] :
( ( ( ~ ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 ) )
= $true )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 )
= $false )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1685]) ).
thf(1712,plain,
! [SV192: set_a,SV135: set_a,SV245: a] :
( ( ( member_a @ SV245 @ SV135 )
= $false )
| ( ( member_a @ SV245 @ SV192 )
= $true )
| ( ( member_a @ ( sK16_SY428 @ SV192 @ SV135 ) @ SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1706]) ).
thf(1713,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ( product_fst_a_a @ SV136 )
!= ( product_fst_a_a @ SV193 ) )
= $false )
| ( ( ( product_fst_a_a @ SV136 )
= ( product_fst_a_a @ SV193 ) )
= $false )
| ( ( ( product_snd_a_a @ SV136 )
= ( product_snd_a_a @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1708]) ).
thf(1714,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ( product_snd_a_a @ SV136 )
!= ( product_snd_a_a @ SV193 ) )
= $false )
| ( ( ( product_fst_a_a @ SV136 )
= ( product_fst_a_a @ SV193 ) )
= $false )
| ( ( ( product_snd_a_a @ SV136 )
= ( product_snd_a_a @ SV193 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1708]) ).
thf(1715,plain,
! [SV105: set_a] :
( ( ( member_a @ ( add_a_b @ r @ ( sK3_X3 @ SV105 ) @ ( sK4_SY248 @ SV105 ) ) @ SV105 )
= $false )
| ( ( member_a @ ( zero_a_b @ r ) @ SV105 )
= $true )
| ( ( member_a @ ( a_inv_a_b @ r @ ( sK5_X3 @ SV105 ) ) @ SV105 )
= $false )
| ( ( SV105 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV105 @ ( partia1066395285xt_a_b @ r ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(1716,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ( product_fst_a_a @ SV136 )
= ( product_fst_a_a @ SV193 ) )
= $true )
| ( ( ( product_fst_a_a @ SV136 )
= ( product_fst_a_a @ SV193 ) )
= $false )
| ( ( ( product_snd_a_a @ SV136 )
= ( product_snd_a_a @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1713]) ).
thf(1717,plain,
! [SV193: product_prod_a_a,SV136: product_prod_a_a] :
( ( ( ( product_snd_a_a @ SV136 )
= ( product_snd_a_a @ SV193 ) )
= $true )
| ( ( ( product_fst_a_a @ SV136 )
= ( product_fst_a_a @ SV193 ) )
= $false )
| ( ( ( product_snd_a_a @ SV136 )
= ( product_snd_a_a @ SV193 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1714]) ).
thf(1718,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[508,1717,1716,1715,1712,1710,1709,1707,1705,1704,1703,1702,1701,1700,1699,1698,1697,1696,1695,1694,1693,1692,1691,1690,1689,1688,1687,1686,1682,1680,1652,1651,1648,1647,1646,1634,1628,1623,1622,1621,1620,1619,1618,1617,1616,1615,1614,1613,1612,1611,1610,1609,1608,1599,1593,1586,1585,1583,1582,1581,1580,1579,1578,1577,1576,1553,1547,1543,1523,1506,1501,1500,1498,1497,1496,1495,1488,1487,1486,1485,1475,1473,1471,1469,1466,1465,1443,1441,1439,1437,1421,1420,1419,1418,1415,1413,1412,1411,1410,1409,1408,1407,1397,1396,1395,1394,1391,1388,1387,1369,1368,1362,1345,1338,1337,1336,1314,1313,1312,1308,1306,1304,1302,1279,1278,1273,1272,1267,1256,1255,1242,1241,1240,1239,1233,1229,1224,1223,1222,1221,1220,1215,1214,1212,1211,1210,1209,1207,1206,1205,1199,1196,1190,1186,1178,1167,1166,1126,1105,1104,1086,1084,1075,1074,1073,1072,1062,1061,1033,1011,1008,1004,1003,1002,1001,986,960,959,958,957,956,955,953,951,936,933,903,894,892,891,889,887,885,883,865,816,795,792,786,780,779,778,777,713,710,709,706,651,613,582,580,579,577,576,571,570,569,568,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,534,533,532,531,530,528,527,526,521,520,519,518,509]) ).
thf(1719,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1718]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP108^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n019.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 11:17:31 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.69/2.88 .
% 15.69/2.88
% 15.69/2.88 No.of.Axioms: 244
% 15.69/2.88
% 15.69/2.88 Length.of.Defs: 0
% 15.69/2.88
% 15.69/2.88 Contains.Choice.Funs: false
% 15.69/2.88 ........................................................
% 15.69/2.88
% 15.69/2.88 ********************************
% 15.69/2.88 * All subproblems solved! *
% 15.69/2.88 ********************************
% 15.69/2.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:165,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:1718,loop_count:0,foatp_calls:1,translation:fof_full)
% 15.69/2.88
% 15.69/2.88 %**** Beginning of derivation protocol ****
% 15.69/2.88 % SZS output start CNFRefutation
% See solution above
% 2.86/2.90
% 2.86/2.90 %**** End of derivation protocol ****
% 2.86/2.90 %**** no. of clauses in derivation: 1640 ****
% 2.86/2.90 %**** clause counter: 1718 ****
% 2.86/2.90
% 2.86/2.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:165,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:1718,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------