%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP148^1 : 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 : n026.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 10:24:19 AM UTC 2026
% Result : Theorem 8.27s 1.64s
% Output : CNFRefutation 8.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 67
% Syntax : Number of formulae : 747 ( 458 unt; 0 typ; 0 def)
% Number of atoms : 3535 (2095 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 7692 ( 479 ~; 598 |; 3 &;6495 @)
% ( 0 <=>; 117 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 12 ( 11 usr)
% Number of type conns : 2192 (2192 >; 0 *; 0 +; 0 <<)
% Number of symbols : 118 ( 115 usr; 12 con; 0-6 aty)
% Number of variables : 2647 ( 47 ^;2600 !; 0 ?;2647 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_complex,type,
complex: $tType ).
thf(tp_real,type,
real: $tType ).
thf(tp_set_a,type,
set_a: $tType ).
thf(tp_set_a_a,type,
set_a_a: $tType ).
thf(tp_set_a_complex,type,
set_a_complex: $tType ).
thf(tp_set_complex,type,
set_complex: $tType ).
thf(tp_set_complex_a,type,
set_complex_a: $tType ).
thf(tp_set_real,type,
set_real: $tType ).
thf(tp_set_real_a,type,
set_real_a: $tType ).
thf(tp_set_real_real,type,
set_real_real: $tType ).
thf(tp_bij_be122140626omplex,type,
bij_be122140626omplex: ( real > complex ) > set_real > set_complex > $o ).
thf(tp_bij_be209634132omplex,type,
bij_be209634132omplex: ( complex > complex ) > set_complex > set_complex > $o ).
thf(tp_bij_betw_a_a,type,
bij_betw_a_a: ( a > a ) > set_a > set_a > $o ).
thf(tp_bij_betw_a_complex,type,
bij_betw_a_complex: ( a > complex ) > set_a > set_complex > $o ).
thf(tp_bij_betw_complex_a,type,
bij_betw_complex_a: ( complex > a ) > set_complex > set_a > $o ).
thf(tp_bij_betw_real_a,type,
bij_betw_real_a: ( real > a ) > set_real > set_a > $o ).
thf(tp_bij_betw_real_real,type,
bij_betw_real_real: ( real > real ) > set_real > set_real > $o ).
thf(tp_c,type,
c: real > a ).
thf(tp_collect_a,type,
collect_a: ( a > $o ) > set_a ).
thf(tp_collect_complex,type,
collect_complex: ( complex > $o ) > set_complex ).
thf(tp_comp_a1063143865omplex,type,
comp_a1063143865omplex: ( a > complex ) > ( complex > a ) > complex > complex ).
thf(tp_comp_a_a_a,type,
comp_a_a_a: ( a > a ) > ( a > a ) > a > a ).
thf(tp_comp_a_a_complex,type,
comp_a_a_complex: ( a > a ) > ( complex > a ) > complex > a ).
thf(tp_comp_a_a_real,type,
comp_a_a_real: ( a > a ) > ( real > a ) > real > a ).
thf(tp_comp_a_complex_a,type,
comp_a_complex_a: ( a > complex ) > ( a > a ) > a > complex ).
thf(tp_comp_a_complex_real,type,
comp_a_complex_real: ( a > complex ) > ( real > a ) > real > complex ).
thf(tp_comp_a_real_a,type,
comp_a_real_a: ( a > real ) > ( a > a ) > a > real ).
thf(tp_comp_a_real_complex,type,
comp_a_real_complex: ( a > real ) > ( complex > a ) > complex > real ).
thf(tp_comp_a_real_real,type,
comp_a_real_real: ( a > real ) > ( real > a ) > real > real ).
thf(tp_comp_c124850173plex_a,type,
comp_c124850173plex_a: ( complex > complex ) > ( a > complex ) > a > complex ).
thf(tp_comp_c130555887omplex,type,
comp_c130555887omplex: ( complex > complex ) > ( complex > complex ) > complex > complex ).
thf(tp_comp_c274302683omplex,type,
comp_c274302683omplex: ( complex > a ) > ( complex > complex ) > complex > a ).
thf(tp_comp_c595887981x_real,type,
comp_c595887981x_real: ( complex > complex ) > ( real > complex ) > real > complex ).
thf(tp_comp_c819638635l_real,type,
comp_c819638635l_real: ( complex > real ) > ( real > complex ) > real > real ).
thf(tp_comp_complex_a_a,type,
comp_complex_a_a: ( complex > a ) > ( a > complex ) > a > a ).
thf(tp_comp_complex_a_real,type,
comp_complex_a_real: ( complex > a ) > ( real > complex ) > real > a ).
thf(tp_comp_complex_real_a,type,
comp_complex_real_a: ( complex > real ) > ( a > complex ) > a > real ).
thf(tp_comp_r422820971omplex,type,
comp_r422820971omplex: ( real > real ) > ( complex > real ) > complex > real ).
thf(tp_comp_r667767405omplex,type,
comp_r667767405omplex: ( real > complex ) > ( complex > real ) > complex > complex ).
thf(tp_comp_r701421291x_real,type,
comp_r701421291x_real: ( real > complex ) > ( real > real ) > real > complex ).
thf(tp_comp_real_a_a,type,
comp_real_a_a: ( real > a ) > ( a > real ) > a > a ).
thf(tp_comp_real_a_complex,type,
comp_real_a_complex: ( real > a ) > ( complex > real ) > complex > a ).
thf(tp_comp_real_a_real,type,
comp_real_a_real: ( real > a ) > ( real > real ) > real > a ).
thf(tp_comp_real_complex_a,type,
comp_real_complex_a: ( real > complex ) > ( a > real ) > a > complex ).
thf(tp_comp_real_real_a,type,
comp_real_real_a: ( real > real ) > ( a > real ) > a > real ).
thf(tp_comp_real_real_real,type,
comp_real_real_real: ( real > real ) > ( real > real ) > real > real ).
thf(tp_id_a,type,
id_a: a > a ).
thf(tp_id_a_a,type,
id_a_a: ( a > a ) > a > a ).
thf(tp_id_complex,type,
id_complex: complex > complex ).
thf(tp_id_complex_a,type,
id_complex_a: ( complex > a ) > complex > a ).
thf(tp_id_real,type,
id_real: real > real ).
thf(tp_id_real_a,type,
id_real_a: ( real > a ) > real > a ).
thf(tp_inj_on1576005937plex_a,type,
inj_on1576005937plex_a: ( ( complex > a ) > complex > a ) > set_complex_a > $o ).
thf(tp_inj_on319905617omplex,type,
inj_on319905617omplex: ( ( real > a ) > real > complex ) > set_real_a > $o ).
thf(tp_inj_on893405649omplex,type,
inj_on893405649omplex: ( ( complex > a ) > complex > complex ) > set_complex_a > $o ).
thf(tp_inj_on94911183omplex,type,
inj_on94911183omplex: ( complex > complex ) > set_complex > $o ).
thf(tp_inj_on958237983real_a,type,
inj_on958237983real_a: ( ( real > real ) > real > a ) > set_real_real > $o ).
thf(tp_inj_on_a_a,type,
inj_on_a_a: ( a > a ) > set_a > $o ).
thf(tp_inj_on_a_a_a_a,type,
inj_on_a_a_a_a: ( ( a > a ) > a > a ) > set_a_a > $o ).
thf(tp_inj_on_a_a_a_complex,type,
inj_on_a_a_a_complex: ( ( a > a ) > a > complex ) > set_a_a > $o ).
thf(tp_inj_on_a_complex,type,
inj_on_a_complex: ( a > complex ) > set_a > $o ).
thf(tp_inj_on_a_complex_a_a,type,
inj_on_a_complex_a_a: ( ( a > complex ) > a > a ) > set_a_complex > $o ).
thf(tp_inj_on_complex_a,type,
inj_on_complex_a: ( complex > a ) > set_complex > $o ).
thf(tp_inj_on_real_a,type,
inj_on_real_a: ( real > a ) > set_real > $o ).
thf(tp_inj_on_real_a_real_a,type,
inj_on_real_a_real_a: ( ( real > a ) > real > a ) > set_real_a > $o ).
thf(tp_inj_on_real_complex,type,
inj_on_real_complex: ( real > complex ) > set_real > $o ).
thf(tp_inj_on_real_real,type,
inj_on_real_real: ( real > real ) > set_real > $o ).
thf(tp_member_a,type,
member_a: a > set_a > $o ).
thf(tp_member_complex,type,
member_complex: complex > set_complex > $o ).
thf(tp_path_arc_a,type,
path_arc_a: ( real > a ) > $o ).
thf(tp_path_arc_complex,type,
path_arc_complex: ( real > complex ) > $o ).
thf(tp_path_arc_real,type,
path_arc_real: ( real > real ) > $o ).
thf(tp_path_p769714271omplex,type,
path_p769714271omplex: ( real > complex ) > complex ).
thf(tp_path_p797330068omplex,type,
path_p797330068omplex: ( real > complex ) > complex ).
thf(tp_path_path_a,type,
path_path_a: ( real > a ) > $o ).
thf(tp_path_path_complex,type,
path_path_complex: ( real > complex ) > $o ).
thf(tp_path_path_real,type,
path_path_real: ( real > real ) > $o ).
thf(tp_path_pathfinish_a,type,
path_pathfinish_a: ( real > a ) > a ).
thf(tp_path_pathfinish_real,type,
path_pathfinish_real: ( real > real ) > real ).
thf(tp_path_pathstart_a,type,
path_pathstart_a: ( real > a ) > a ).
thf(tp_path_pathstart_real,type,
path_pathstart_real: ( real > real ) > real ).
thf(tp_path_rectpath,type,
path_rectpath: complex > complex > real > complex ).
thf(tp_path_s1005760220h_real,type,
path_s1005760220h_real: ( real > real ) > $o ).
thf(tp_path_s36253918omplex,type,
path_s36253918omplex: ( real > complex ) > $o ).
thf(tp_path_simple_path_a,type,
path_simple_path_a: ( real > a ) > $o ).
thf(tp_poinca1910941596x_of_a,type,
poinca1910941596x_of_a: a > complex ).
thf(tp_poinca837721858l_of_a,type,
poinca837721858l_of_a: complex > a ).
thf(tp_real_V1327653935plex_a,type,
real_V1327653935plex_a: ( complex > a ) > $o ).
thf(tp_real_V1354572473l_real,type,
real_V1354572473l_real: ( real > real ) > $o ).
thf(tp_real_V1477106445omplex,type,
real_V1477106445omplex: ( a > complex ) > $o ).
thf(tp_real_V1948715323omplex,type,
real_V1948715323omplex: ( real > complex ) > $o ).
thf(tp_real_V202220639ar_a_a,type,
real_V202220639ar_a_a: ( a > a ) > $o ).
thf(tp_real_V301987619plex_a,type,
real_V301987619plex_a: ( complex > a ) > $o ).
thf(tp_real_V451440129omplex,type,
real_V451440129omplex: ( a > complex ) > $o ).
thf(tp_real_V670066493omplex,type,
real_V670066493omplex: ( complex > complex ) > $o ).
thf(tp_real_V762982918plex_a,type,
real_V762982918plex_a: ( complex > a ) > $o ).
thf(tp_real_V779700657real_a,type,
real_V779700657real_a: ( real > a ) > $o ).
thf(tp_real_V912435428omplex,type,
real_V912435428omplex: ( a > complex ) > $o ).
thf(tp_sK10_SV238,type,
sK10_SV238: real > ( real > complex ) > ( real > a ) > ( a > complex ) > real ).
thf(tp_sK11_SV239,type,
sK11_SV239: ( real > real ) > ( real > complex ) > ( real > a ) > ( a > complex ) > real ).
thf(tp_sK12_SV246,type,
sK12_SV246: real > ( real > a ) > ( a > complex ) > ( real > a ) > ( a > complex ) > real ).
thf(tp_sK13_SV265,type,
sK13_SV265: ( complex > a ) > ( complex > real ) > ( real > a ) > ( a > complex ) > ( real > a ) > ( a > complex ) > real ).
thf(tp_sK14_SV276,type,
sK14_SV276: ( a > complex ) > ( real > a ) > ( a > complex ) > ( complex > a ) > ( complex > real ) > ( real > a ) > complex ).
thf(tp_sK15_SV277,type,
sK15_SV277: ( a > complex ) > ( real > a ) > ( a > complex ) > ( complex > a ) > ( complex > real ) > ( real > a ) > complex ).
thf(tp_sK1_SV229,type,
sK1_SV229: ( a > complex ) > ( a > a ) > ( a > real ) > ( real > a ) > a ).
thf(tp_sK2_SV230,type,
sK2_SV230: ( real > complex ) > ( complex > complex ) > ( complex > a ) > ( a > complex ) > complex ).
thf(tp_sK3_SV231,type,
sK3_SV231: ( a > real ) > ( real > complex ) > ( real > a ) > ( a > complex ) > real ).
thf(tp_sK4_SV232,type,
sK4_SV232: ( complex > real ) > ( real > complex ) > ( real > a ) > ( a > complex ) > real ).
thf(tp_sK5_SV233,type,
sK5_SV233: ( real > a ) > ( a > complex ) > ( real > a ) > ( a > complex ) > real ).
thf(tp_sK6_SV234,type,
sK6_SV234: real > ( real > complex ) > ( real > a ) > ( a > complex ) > real ).
thf(tp_sK7_SV235,type,
sK7_SV235: ( a > complex ) > ( real > a ) > ( real > complex ) > ( complex > a ) > real ).
thf(tp_sK8_SV236,type,
sK8_SV236: ( real > a ) > ( a > complex ) > ( a > complex ) > ( complex > complex ) > a ).
thf(tp_sK9_SV237,type,
sK9_SV237: ( a > complex ) > ( complex > a ) > ( complex > real ) > ( real > a ) > complex ).
thf(tp_top_to1446257885l_real,type,
top_to1446257885l_real: set_real_real ).
thf(tp_top_to2109114701omplex,type,
top_to2109114701omplex: set_a_complex ).
thf(tp_top_to525076535plex_a,type,
top_to525076535plex_a: set_complex_a ).
thf(tp_top_top_a_o,type,
top_top_a_o: a > $o ).
thf(tp_top_top_complex_o,type,
top_top_complex_o: complex > $o ).
thf(tp_top_top_set_a,type,
top_top_set_a: set_a ).
thf(tp_top_top_set_a_a,type,
top_top_set_a_a: set_a_a ).
thf(tp_top_top_set_complex,type,
top_top_set_complex: set_complex ).
thf(tp_top_top_set_real,type,
top_top_set_real: set_real ).
thf(tp_top_top_set_real_a,type,
top_top_set_real_a: set_real_a ).
thf(tp_zero_zero_a,type,
zero_zero_a: a ).
thf(tp_zero_zero_complex,type,
zero_zero_complex: complex ).
thf(13,axiom,
! [A: a > complex,B: real > a,C: real > complex,V: real] :
( ( ( comp_a_complex_real @ A @ B )
= ( comp_c595887981x_real @ id_complex @ C ) )
=> ( ( A @ ( B @ V ) )
= ( C @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_comp__eq__id__dest) ).
thf(24,axiom,
! [F2: real > a,A2: set_real,A7: set_a,F3: a > complex,A8: set_complex] :
( ( bij_betw_real_a @ F2 @ A2 @ A7 )
=> ( ( bij_betw_a_complex @ F3 @ A7 @ A8 )
= ( bij_be122140626omplex @ ( comp_a_complex_real @ F3 @ F2 ) @ A2 @ A8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_bij__betw__comp__iff) ).
thf(34,axiom,
! [F2: real > a,A2: set_real,B3: set_a,G2: a > complex,C2: set_complex] :
( ( bij_betw_real_a @ F2 @ A2 @ B3 )
=> ( ( bij_betw_a_complex @ G2 @ B3 @ C2 )
=> ( bij_be122140626omplex @ ( comp_a_complex_real @ G2 @ F2 ) @ A2 @ C2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_bij__betw__trans) ).
thf(90,axiom,
! [M: complex > a,G2: real > complex,X2: real,N: a > a,H: real > a,F2: a > complex] :
( ( ( M @ ( G2 @ X2 ) )
= ( N @ ( H @ X2 ) ) )
=> ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ F2 @ M ) @ G2 @ X2 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_type__copy__map__cong0) ).
thf(91,axiom,
! [M: real > a,G2: a > real,X2: a,N: a > a,H: a > a,F2: a > complex] :
( ( ( M @ ( G2 @ X2 ) )
= ( N @ ( H @ X2 ) ) )
=> ( ( comp_real_complex_a @ ( comp_a_complex_real @ F2 @ M ) @ G2 @ X2 )
= ( comp_a_complex_a @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_type__copy__map__cong0) ).
thf(92,axiom,
! [M: real > a,G2: complex > real,X2: complex,N: a > a,H: complex > a,F2: a > complex] :
( ( ( M @ ( G2 @ X2 ) )
= ( N @ ( H @ X2 ) ) )
=> ( ( comp_r667767405omplex @ ( comp_a_complex_real @ F2 @ M ) @ G2 @ X2 )
= ( comp_a1063143865omplex @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_type__copy__map__cong0) ).
thf(93,axiom,
! [M: real > a,G2: real > real,X2: real,N: a > a,H: real > a,F2: a > complex] :
( ( ( M @ ( G2 @ X2 ) )
= ( N @ ( H @ X2 ) ) )
=> ( ( comp_r701421291x_real @ ( comp_a_complex_real @ F2 @ M ) @ G2 @ X2 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_type__copy__map__cong0) ).
thf(104,axiom,
bij_betw_a_complex @ poinca1910941596x_of_a @ top_top_set_a @ top_top_set_complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_complex__of__bij) ).
thf(106,axiom,
( ( comp_complex_a_a @ poinca837721858l_of_a @ poinca1910941596x_of_a )
= id_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_real__of__complex__of) ).
thf(107,axiom,
( ( comp_a1063143865omplex @ poinca1910941596x_of_a @ poinca837721858l_of_a )
= id_complex ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_complex__of__real__of) ).
thf(109,axiom,
! [G2: a > complex,F2: real > a,V: complex > real] :
( ( comp_a1063143865omplex @ G2 @ ( comp_real_a_complex @ F2 @ V ) )
= ( comp_r667767405omplex @ ( comp_a_complex_real @ G2 @ F2 ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_fun_Omap__comp) ).
thf(110,axiom,
! [G2: a > complex,F2: a > a,V: real > a] :
( ( comp_a_complex_real @ G2 @ ( comp_a_a_real @ F2 @ V ) )
= ( comp_a_complex_real @ ( comp_a_complex_a @ G2 @ F2 ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_fun_Omap__comp) ).
thf(111,axiom,
! [G2: a > complex,F2: real > a,V: real > real] :
( ( comp_a_complex_real @ G2 @ ( comp_real_a_real @ F2 @ V ) )
= ( comp_r701421291x_real @ ( comp_a_complex_real @ G2 @ F2 ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_fun_Omap__comp) ).
thf(112,axiom,
! [G2: a > complex,F2: complex > a,V: real > complex] :
( ( comp_a_complex_real @ G2 @ ( comp_complex_a_real @ F2 @ V ) )
= ( comp_c595887981x_real @ ( comp_a1063143865omplex @ G2 @ F2 ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_fun_Omap__comp) ).
thf(116,axiom,
! [G2: complex > a,F2: a > complex,V: real > a] :
( ( comp_complex_a_real @ G2 @ ( comp_a_complex_real @ F2 @ V ) )
= ( comp_a_a_real @ ( comp_complex_a_a @ G2 @ F2 ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_fun_Omap__comp) ).
thf(117,axiom,
! [G2: complex > complex,F2: a > complex,V: real > a] :
( ( comp_c595887981x_real @ G2 @ ( comp_a_complex_real @ F2 @ V ) )
= ( comp_a_complex_real @ ( comp_c124850173plex_a @ G2 @ F2 ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_fun_Omap__comp) ).
thf(118,axiom,
( path_arc_complex
= ( ^ [G: real > complex] :
( ( path_s36253918omplex @ G )
& ( ( path_p769714271omplex @ G )
!= ( path_p797330068omplex @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_arc__simple__path) ).
thf(120,axiom,
! [G2: real > complex] :
( ( path_s36253918omplex @ G2 )
=> ( ( path_arc_complex @ G2 )
| ( ( path_p769714271omplex @ G2 )
= ( path_p797330068omplex @ G2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_simple__path__cases) ).
thf(122,axiom,
! [G2: real > complex] :
( ( ( path_p769714271omplex @ G2 )
!= ( path_p797330068omplex @ G2 ) )
=> ( ( path_s36253918omplex @ G2 )
= ( path_arc_complex @ G2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_simple__path__eq__arc) ).
thf(124,axiom,
! [G2: real > complex] :
( ( path_s36253918omplex @ G2 )
=> ( ( ( path_p769714271omplex @ G2 )
!= ( path_p797330068omplex @ G2 ) )
=> ( path_arc_complex @ G2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_simple__path__imp__arc) ).
thf(133,axiom,
! [G2: real > complex] :
( ( path_arc_complex @ G2 )
=> ( ( path_p769714271omplex @ G2 )
!= ( path_p797330068omplex @ G2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_arc__distinct__ends) ).
thf(174,axiom,
! [F3: a > complex,F2: real > a,A2: set_real] :
( ( inj_on_real_complex @ ( comp_a_complex_real @ F3 @ F2 ) @ A2 )
=> ( inj_on_real_a @ F2 @ A2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_inj__on__imageI2) ).
thf(208,axiom,
! [F2: a > complex,G2: complex > a,L: complex > complex,H: real > complex] :
( ( ( comp_a1063143865omplex @ F2 @ G2 )
= L )
=> ( ( comp_a_complex_real @ F2 @ ( comp_complex_a_real @ G2 @ H ) )
= ( comp_c595887981x_real @ L @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_rewriteL__comp__comp) ).
thf(209,axiom,
! [F2: a > complex,G2: real > a,L: real > complex,H: a > real] :
( ( ( comp_a_complex_real @ F2 @ G2 )
= L )
=> ( ( comp_a_complex_a @ F2 @ ( comp_real_a_a @ G2 @ H ) )
= ( comp_real_complex_a @ L @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_rewriteL__comp__comp) ).
thf(210,axiom,
! [F2: a > complex,G2: real > a,L: real > complex,H: complex > real] :
( ( ( comp_a_complex_real @ F2 @ G2 )
= L )
=> ( ( comp_a1063143865omplex @ F2 @ ( comp_real_a_complex @ G2 @ H ) )
= ( comp_r667767405omplex @ L @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_rewriteL__comp__comp) ).
thf(211,axiom,
! [F2: a > complex,G2: real > a,L: real > complex,H: real > real] :
( ( ( comp_a_complex_real @ F2 @ G2 )
= L )
=> ( ( comp_a_complex_real @ F2 @ ( comp_real_a_real @ G2 @ H ) )
= ( comp_r701421291x_real @ L @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_rewriteL__comp__comp) ).
thf(216,axiom,
! [F2: complex > complex,G2: a > complex,L: a > complex,H: real > a] :
( ( ( comp_c124850173plex_a @ F2 @ G2 )
= L )
=> ( ( comp_c595887981x_real @ F2 @ ( comp_a_complex_real @ G2 @ H ) )
= ( comp_a_complex_real @ L @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_rewriteL__comp__comp) ).
thf(224,axiom,
! [G2: complex > a,H: real > complex,R: real > a,F2: a > complex] :
( ( ( comp_complex_a_real @ G2 @ H )
= R )
=> ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ F2 @ G2 ) @ H )
= ( comp_a_complex_real @ F2 @ R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_rewriteR__comp__comp) ).
thf(225,axiom,
! [G2: real > a,H: a > real,R: a > a,F2: a > complex] :
( ( ( comp_real_a_a @ G2 @ H )
= R )
=> ( ( comp_real_complex_a @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
= ( comp_a_complex_a @ F2 @ R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_rewriteR__comp__comp) ).
thf(226,axiom,
! [G2: real > a,H: complex > real,R: complex > a,F2: a > complex] :
( ( ( comp_real_a_complex @ G2 @ H )
= R )
=> ( ( comp_r667767405omplex @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
= ( comp_a1063143865omplex @ F2 @ R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_rewriteR__comp__comp) ).
thf(227,axiom,
! [F2: a > complex,G2: real > a,L1: a > complex,L2: real > a,H: complex > real,R: complex > a] :
( ( ( comp_a_complex_real @ F2 @ G2 )
= ( comp_a_complex_real @ L1 @ L2 ) )
=> ( ( ( comp_real_a_complex @ L2 @ H )
= R )
=> ( ( comp_a1063143865omplex @ F2 @ ( comp_real_a_complex @ G2 @ H ) )
= ( comp_a1063143865omplex @ L1 @ R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_rewriteL__comp__comp2) ).
thf(249,axiom,
! [A1: complex,A3: complex] :
( ( path_p797330068omplex @ ( path_rectpath @ A1 @ A3 ) )
= A1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_pathstart__rectpath) ).
thf(250,axiom,
! [A1: complex,A3: complex] :
( ( path_p769714271omplex @ ( path_rectpath @ A1 @ A3 ) )
= A1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_pathfinish__rectpath) ).
thf(258,axiom,
! [F2: real > a,G2: a > complex] :
( ( real_V779700657real_a @ F2 )
=> ( ( real_V1477106445omplex @ G2 )
=> ( real_V1948715323omplex @ ( comp_a_complex_real @ G2 @ F2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_linear__compose) ).
thf(266,axiom,
! [F2: complex > a,G2: real > complex] :
( ( real_V1327653935plex_a @ F2 )
=> ( ( path_pathfinish_a @ ( comp_complex_a_real @ F2 @ G2 ) )
= ( F2 @ ( path_p769714271omplex @ G2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_pathfinish__linear__image) ).
thf(267,axiom,
! [F2: a > complex,G2: real > a] :
( ( real_V1477106445omplex @ F2 )
=> ( ( path_p769714271omplex @ ( comp_a_complex_real @ F2 @ G2 ) )
= ( F2 @ ( path_pathfinish_a @ G2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_pathfinish__linear__image) ).
thf(270,axiom,
! [F2: complex > complex,G2: real > complex] :
( ( real_V670066493omplex @ F2 )
=> ( ( path_p769714271omplex @ ( comp_c595887981x_real @ F2 @ G2 ) )
= ( F2 @ ( path_p769714271omplex @ G2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_pathfinish__linear__image) ).
thf(271,axiom,
! [F2: complex > a,G2: real > complex] :
( ( real_V1327653935plex_a @ F2 )
=> ( ( path_pathstart_a @ ( comp_complex_a_real @ F2 @ G2 ) )
= ( F2 @ ( path_p797330068omplex @ G2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_pathstart__linear__image__eq) ).
thf(272,axiom,
! [F2: a > complex,G2: real > a] :
( ( real_V1477106445omplex @ F2 )
=> ( ( path_p797330068omplex @ ( comp_a_complex_real @ F2 @ G2 ) )
= ( F2 @ ( path_pathstart_a @ G2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_pathstart__linear__image__eq) ).
thf(275,axiom,
! [F2: complex > complex,G2: real > complex] :
( ( real_V670066493omplex @ F2 )
=> ( ( path_p797330068omplex @ ( comp_c595887981x_real @ F2 @ G2 ) )
= ( F2 @ ( path_p797330068omplex @ G2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_pathstart__linear__image__eq) ).
thf(283,axiom,
! [A: a > complex,B: real > a,C: real > complex,V: real] :
( ( ( comp_a_complex_real @ A @ B )
= C )
=> ( ( A @ ( B @ V ) )
= ( C @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_comp__eq__dest__lhs) ).
thf(290,axiom,
! [F2: a > complex,G2: complex > a,X2: complex,F3: a > complex,G3: real > a,X3: real] :
( ( ( F2 @ ( G2 @ X2 ) )
= ( F3 @ ( G3 @ X3 ) ) )
=> ( ( comp_a1063143865omplex @ F2 @ G2 @ X2 )
= ( comp_a_complex_real @ F3 @ G3 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_comp__cong) ).
thf(291,axiom,
! [F2: a > complex,G2: real > a,X2: real,F3: a > complex,G3: a > a,X3: a] :
( ( ( F2 @ ( G2 @ X2 ) )
= ( F3 @ ( G3 @ X3 ) ) )
=> ( ( comp_a_complex_real @ F2 @ G2 @ X2 )
= ( comp_a_complex_a @ F3 @ G3 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_comp__cong) ).
thf(292,axiom,
! [F2: a > complex,G2: real > a,X2: real,F3: a > complex,G3: complex > a,X3: complex] :
( ( ( F2 @ ( G2 @ X2 ) )
= ( F3 @ ( G3 @ X3 ) ) )
=> ( ( comp_a_complex_real @ F2 @ G2 @ X2 )
= ( comp_a1063143865omplex @ F3 @ G3 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_comp__cong) ).
thf(293,axiom,
! [F2: a > complex,G2: real > a,X2: real,F3: a > complex,G3: real > a,X3: real] :
( ( ( F2 @ ( G2 @ X2 ) )
= ( F3 @ ( G3 @ X3 ) ) )
=> ( ( comp_a_complex_real @ F2 @ G2 @ X2 )
= ( comp_a_complex_real @ F3 @ G3 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_comp__cong) ).
thf(303,axiom,
! [A: a > complex,B: real > a,C: a > complex,D: real > a] :
( ( ( comp_a_complex_real @ A @ B )
= ( comp_a_complex_real @ C @ D ) )
=> ! [V2: real] :
( ( A @ ( B @ V2 ) )
= ( C @ ( D @ V2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_comp__eq__elim) ).
thf(313,axiom,
! [A: a > complex,B: real > a,C: a > complex,D: real > a,V: real] :
( ( ( comp_a_complex_real @ A @ B )
= ( comp_a_complex_real @ C @ D ) )
=> ( ( A @ ( B @ V ) )
= ( C @ ( D @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_comp__eq__dest) ).
thf(314,axiom,
! [F2: a > complex,G2: a > a,H: real > a] :
( ( comp_a_complex_real @ ( comp_a_complex_a @ F2 @ G2 ) @ H )
= ( comp_a_complex_real @ F2 @ ( comp_a_a_real @ G2 @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_comp__assoc) ).
thf(315,axiom,
! [F2: complex > complex,G2: a > complex,H: real > a] :
( ( comp_a_complex_real @ ( comp_c124850173plex_a @ F2 @ G2 ) @ H )
= ( comp_c595887981x_real @ F2 @ ( comp_a_complex_real @ G2 @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_comp__assoc) ).
thf(318,axiom,
! [F2: complex > a,G2: a > complex,H: real > a] :
( ( comp_a_a_real @ ( comp_complex_a_a @ F2 @ G2 ) @ H )
= ( comp_complex_a_real @ F2 @ ( comp_a_complex_real @ G2 @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_comp__assoc) ).
thf(320,axiom,
! [F2: a > complex,G2: complex > a,H: real > complex] :
( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ F2 @ G2 ) @ H )
= ( comp_a_complex_real @ F2 @ ( comp_complex_a_real @ G2 @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_comp__assoc) ).
thf(322,axiom,
! [F2: a > complex,G2: real > a,H: complex > real] :
( ( comp_r667767405omplex @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
= ( comp_a1063143865omplex @ F2 @ ( comp_real_a_complex @ G2 @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_comp__assoc) ).
thf(323,axiom,
! [F2: a > complex,G2: real > a,H: real > real] :
( ( comp_r701421291x_real @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
= ( comp_a_complex_real @ F2 @ ( comp_real_a_real @ G2 @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_comp__assoc) ).
thf(326,axiom,
( comp_a_complex_real
= ( ^ [F: a > complex,G: real > a,X: real] : ( F @ ( G @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_comp__def) ).
thf(332,axiom,
real_V1477106445omplex @ poinca1910941596x_of_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_complex__of__linear) ).
thf(333,axiom,
real_V912435428omplex @ poinca1910941596x_of_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_complex__of__bounded__linear) ).
thf(335,axiom,
! [F2: complex > a,P: real > complex] :
( ( path_pathstart_a @ ( comp_complex_a_real @ F2 @ P ) )
= ( F2 @ ( path_p797330068omplex @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_pathstart__compose) ).
thf(336,axiom,
! [F2: a > complex,P: real > a] :
( ( path_p797330068omplex @ ( comp_a_complex_real @ F2 @ P ) )
= ( F2 @ ( path_pathstart_a @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_pathstart__compose) ).
thf(337,axiom,
! [F2: complex > complex,P: real > complex] :
( ( path_p797330068omplex @ ( comp_c595887981x_real @ F2 @ P ) )
= ( F2 @ ( path_p797330068omplex @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_pathstart__compose) ).
thf(340,axiom,
! [F2: complex > a,P: real > complex] :
( ( path_pathfinish_a @ ( comp_complex_a_real @ F2 @ P ) )
= ( F2 @ ( path_p769714271omplex @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_pathfinish__compose) ).
thf(341,axiom,
! [F2: a > complex,P: real > a] :
( ( path_p769714271omplex @ ( comp_a_complex_real @ F2 @ P ) )
= ( F2 @ ( path_pathfinish_a @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_pathfinish__compose) ).
thf(342,axiom,
! [F2: complex > complex,P: real > complex] :
( ( path_p769714271omplex @ ( comp_c595887981x_real @ F2 @ P ) )
= ( F2 @ ( path_p769714271omplex @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_pathfinish__compose) ).
thf(346,axiom,
( comp_a_complex_real
= ( ^ [F: a > complex,G: real > a,X: real] : ( F @ ( G @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_comp__apply) ).
thf(352,axiom,
path_s36253918omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_a1) ).
thf(353,axiom,
path_simple_path_a @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I1_J) ).
thf(354,axiom,
( ( path_pathfinish_a @ c )
= ( path_pathstart_a @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I2_J) ).
thf(355,conjecture,
( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
= ( path_p797330068omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(356,negated_conjecture,
( ( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
= ( path_p797330068omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[355]) ).
thf(357,plain,
( ( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
= ( path_p797330068omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) )
= $false ),
inference(unfold_def,[status(thm)],[356]) ).
thf(358,plain,
( ( ! [A: a > complex,B: real > a,C: real > complex,V: real] :
( ( ( comp_a_complex_real @ A @ B )
= ( comp_c595887981x_real @ id_complex @ C ) )
=> ( ( A @ ( B @ V ) )
= ( C @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(359,plain,
( ( ! [F2: real > a,A2: set_real,A7: set_a,F3: a > complex,A8: set_complex] :
( ( bij_betw_real_a @ F2 @ A2 @ A7 )
=> ( ( bij_betw_a_complex @ F3 @ A7 @ A8 )
= ( bij_be122140626omplex @ ( comp_a_complex_real @ F3 @ F2 ) @ A2 @ A8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(360,plain,
( ( ! [F2: real > a,A2: set_real,B3: set_a,G2: a > complex,C2: set_complex] :
( ( bij_betw_real_a @ F2 @ A2 @ B3 )
=> ( ( bij_betw_a_complex @ G2 @ B3 @ C2 )
=> ( bij_be122140626omplex @ ( comp_a_complex_real @ G2 @ F2 ) @ A2 @ C2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(361,plain,
( ( ! [M: complex > a,G2: real > complex,X2: real,N: a > a,H: real > a,F2: a > complex] :
( ( ( M @ ( G2 @ X2 ) )
= ( N @ ( H @ X2 ) ) )
=> ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ F2 @ M ) @ G2 @ X2 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(362,plain,
( ( ! [M: real > a,G2: a > real,X2: a,N: a > a,H: a > a,F2: a > complex] :
( ( ( M @ ( G2 @ X2 ) )
= ( N @ ( H @ X2 ) ) )
=> ( ( comp_real_complex_a @ ( comp_a_complex_real @ F2 @ M ) @ G2 @ X2 )
= ( comp_a_complex_a @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(363,plain,
( ( ! [M: real > a,G2: complex > real,X2: complex,N: a > a,H: complex > a,F2: a > complex] :
( ( ( M @ ( G2 @ X2 ) )
= ( N @ ( H @ X2 ) ) )
=> ( ( comp_r667767405omplex @ ( comp_a_complex_real @ F2 @ M ) @ G2 @ X2 )
= ( comp_a1063143865omplex @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(364,plain,
( ( ! [M: real > a,G2: real > real,X2: real,N: a > a,H: real > a,F2: a > complex] :
( ( ( M @ ( G2 @ X2 ) )
= ( N @ ( H @ X2 ) ) )
=> ( ( comp_r701421291x_real @ ( comp_a_complex_real @ F2 @ M ) @ G2 @ X2 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(365,plain,
( ( bij_betw_a_complex @ poinca1910941596x_of_a @ top_top_set_a @ top_top_set_complex )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(366,plain,
( ( ( comp_complex_a_a @ poinca837721858l_of_a @ poinca1910941596x_of_a )
= id_a )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(367,plain,
( ( ( comp_a1063143865omplex @ poinca1910941596x_of_a @ poinca837721858l_of_a )
= id_complex )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(368,plain,
( ( ! [G2: a > complex,F2: real > a,V: complex > real] :
( ( comp_a1063143865omplex @ G2 @ ( comp_real_a_complex @ F2 @ V ) )
= ( comp_r667767405omplex @ ( comp_a_complex_real @ G2 @ F2 ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(369,plain,
( ( ! [G2: a > complex,F2: a > a,V: real > a] :
( ( comp_a_complex_real @ G2 @ ( comp_a_a_real @ F2 @ V ) )
= ( comp_a_complex_real @ ( comp_a_complex_a @ G2 @ F2 ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(370,plain,
( ( ! [G2: a > complex,F2: real > a,V: real > real] :
( ( comp_a_complex_real @ G2 @ ( comp_real_a_real @ F2 @ V ) )
= ( comp_r701421291x_real @ ( comp_a_complex_real @ G2 @ F2 ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(371,plain,
( ( ! [G2: a > complex,F2: complex > a,V: real > complex] :
( ( comp_a_complex_real @ G2 @ ( comp_complex_a_real @ F2 @ V ) )
= ( comp_c595887981x_real @ ( comp_a1063143865omplex @ G2 @ F2 ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(372,plain,
( ( ! [G2: complex > a,F2: a > complex,V: real > a] :
( ( comp_complex_a_real @ G2 @ ( comp_a_complex_real @ F2 @ V ) )
= ( comp_a_a_real @ ( comp_complex_a_a @ G2 @ F2 ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(373,plain,
( ( ! [G2: complex > complex,F2: a > complex,V: real > a] :
( ( comp_c595887981x_real @ G2 @ ( comp_a_complex_real @ F2 @ V ) )
= ( comp_a_complex_real @ ( comp_c124850173plex_a @ G2 @ F2 ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(374,plain,
( ( path_arc_complex
= ( ^ [G: real > complex] :
( ( path_s36253918omplex @ G )
& ( ( path_p769714271omplex @ G )
!= ( path_p797330068omplex @ G ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(375,plain,
( ( ! [G2: real > complex] :
( ( path_s36253918omplex @ G2 )
=> ( ( path_arc_complex @ G2 )
| ( ( path_p769714271omplex @ G2 )
= ( path_p797330068omplex @ G2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(376,plain,
( ( ! [G2: real > complex] :
( ( ( path_p769714271omplex @ G2 )
!= ( path_p797330068omplex @ G2 ) )
=> ( ( path_s36253918omplex @ G2 )
= ( path_arc_complex @ G2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(377,plain,
( ( ! [G2: real > complex] :
( ( path_s36253918omplex @ G2 )
=> ( ( ( path_p769714271omplex @ G2 )
!= ( path_p797330068omplex @ G2 ) )
=> ( path_arc_complex @ G2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(378,plain,
( ( ! [G2: real > complex] :
( ( path_arc_complex @ G2 )
=> ( ( path_p769714271omplex @ G2 )
!= ( path_p797330068omplex @ G2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(379,plain,
( ( ! [F3: a > complex,F2: real > a,A2: set_real] :
( ( inj_on_real_complex @ ( comp_a_complex_real @ F3 @ F2 ) @ A2 )
=> ( inj_on_real_a @ F2 @ A2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(380,plain,
( ( ! [F2: a > complex,G2: complex > a,L: complex > complex,H: real > complex] :
( ( ( comp_a1063143865omplex @ F2 @ G2 )
= L )
=> ( ( comp_a_complex_real @ F2 @ ( comp_complex_a_real @ G2 @ H ) )
= ( comp_c595887981x_real @ L @ H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(381,plain,
( ( ! [F2: a > complex,G2: real > a,L: real > complex,H: a > real] :
( ( ( comp_a_complex_real @ F2 @ G2 )
= L )
=> ( ( comp_a_complex_a @ F2 @ ( comp_real_a_a @ G2 @ H ) )
= ( comp_real_complex_a @ L @ H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(382,plain,
( ( ! [F2: a > complex,G2: real > a,L: real > complex,H: complex > real] :
( ( ( comp_a_complex_real @ F2 @ G2 )
= L )
=> ( ( comp_a1063143865omplex @ F2 @ ( comp_real_a_complex @ G2 @ H ) )
= ( comp_r667767405omplex @ L @ H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(383,plain,
( ( ! [F2: a > complex,G2: real > a,L: real > complex,H: real > real] :
( ( ( comp_a_complex_real @ F2 @ G2 )
= L )
=> ( ( comp_a_complex_real @ F2 @ ( comp_real_a_real @ G2 @ H ) )
= ( comp_r701421291x_real @ L @ H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(384,plain,
( ( ! [F2: complex > complex,G2: a > complex,L: a > complex,H: real > a] :
( ( ( comp_c124850173plex_a @ F2 @ G2 )
= L )
=> ( ( comp_c595887981x_real @ F2 @ ( comp_a_complex_real @ G2 @ H ) )
= ( comp_a_complex_real @ L @ H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(385,plain,
( ( ! [G2: complex > a,H: real > complex,R: real > a,F2: a > complex] :
( ( ( comp_complex_a_real @ G2 @ H )
= R )
=> ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ F2 @ G2 ) @ H )
= ( comp_a_complex_real @ F2 @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(386,plain,
( ( ! [G2: real > a,H: a > real,R: a > a,F2: a > complex] :
( ( ( comp_real_a_a @ G2 @ H )
= R )
=> ( ( comp_real_complex_a @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
= ( comp_a_complex_a @ F2 @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(387,plain,
( ( ! [G2: real > a,H: complex > real,R: complex > a,F2: a > complex] :
( ( ( comp_real_a_complex @ G2 @ H )
= R )
=> ( ( comp_r667767405omplex @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
= ( comp_a1063143865omplex @ F2 @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(388,plain,
( ( ! [F2: a > complex,G2: real > a,L1: a > complex,L2: real > a,H: complex > real,R: complex > a] :
( ( ( comp_a_complex_real @ F2 @ G2 )
= ( comp_a_complex_real @ L1 @ L2 ) )
=> ( ( ( comp_real_a_complex @ L2 @ H )
= R )
=> ( ( comp_a1063143865omplex @ F2 @ ( comp_real_a_complex @ G2 @ H ) )
= ( comp_a1063143865omplex @ L1 @ R ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(389,plain,
( ( ! [A1: complex,A3: complex] :
( ( path_p797330068omplex @ ( path_rectpath @ A1 @ A3 ) )
= A1 ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(390,plain,
( ( ! [A1: complex,A3: complex] :
( ( path_p769714271omplex @ ( path_rectpath @ A1 @ A3 ) )
= A1 ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(391,plain,
( ( ! [F2: real > a,G2: a > complex] :
( ( real_V779700657real_a @ F2 )
=> ( ( real_V1477106445omplex @ G2 )
=> ( real_V1948715323omplex @ ( comp_a_complex_real @ G2 @ F2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(392,plain,
( ( ! [F2: complex > a,G2: real > complex] :
( ( real_V1327653935plex_a @ F2 )
=> ( ( path_pathfinish_a @ ( comp_complex_a_real @ F2 @ G2 ) )
= ( F2 @ ( path_p769714271omplex @ G2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(393,plain,
( ( ! [F2: a > complex,G2: real > a] :
( ( real_V1477106445omplex @ F2 )
=> ( ( path_p769714271omplex @ ( comp_a_complex_real @ F2 @ G2 ) )
= ( F2 @ ( path_pathfinish_a @ G2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(394,plain,
( ( ! [F2: complex > complex,G2: real > complex] :
( ( real_V670066493omplex @ F2 )
=> ( ( path_p769714271omplex @ ( comp_c595887981x_real @ F2 @ G2 ) )
= ( F2 @ ( path_p769714271omplex @ G2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(395,plain,
( ( ! [F2: complex > a,G2: real > complex] :
( ( real_V1327653935plex_a @ F2 )
=> ( ( path_pathstart_a @ ( comp_complex_a_real @ F2 @ G2 ) )
= ( F2 @ ( path_p797330068omplex @ G2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(396,plain,
( ( ! [F2: a > complex,G2: real > a] :
( ( real_V1477106445omplex @ F2 )
=> ( ( path_p797330068omplex @ ( comp_a_complex_real @ F2 @ G2 ) )
= ( F2 @ ( path_pathstart_a @ G2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(397,plain,
( ( ! [F2: complex > complex,G2: real > complex] :
( ( real_V670066493omplex @ F2 )
=> ( ( path_p797330068omplex @ ( comp_c595887981x_real @ F2 @ G2 ) )
= ( F2 @ ( path_p797330068omplex @ G2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(398,plain,
( ( ! [A: a > complex,B: real > a,C: real > complex,V: real] :
( ( ( comp_a_complex_real @ A @ B )
= C )
=> ( ( A @ ( B @ V ) )
= ( C @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(399,plain,
( ( ! [F2: a > complex,G2: complex > a,X2: complex,F3: a > complex,G3: real > a,X3: real] :
( ( ( F2 @ ( G2 @ X2 ) )
= ( F3 @ ( G3 @ X3 ) ) )
=> ( ( comp_a1063143865omplex @ F2 @ G2 @ X2 )
= ( comp_a_complex_real @ F3 @ G3 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(400,plain,
( ( ! [F2: a > complex,G2: real > a,X2: real,F3: a > complex,G3: a > a,X3: a] :
( ( ( F2 @ ( G2 @ X2 ) )
= ( F3 @ ( G3 @ X3 ) ) )
=> ( ( comp_a_complex_real @ F2 @ G2 @ X2 )
= ( comp_a_complex_a @ F3 @ G3 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(401,plain,
( ( ! [F2: a > complex,G2: real > a,X2: real,F3: a > complex,G3: complex > a,X3: complex] :
( ( ( F2 @ ( G2 @ X2 ) )
= ( F3 @ ( G3 @ X3 ) ) )
=> ( ( comp_a_complex_real @ F2 @ G2 @ X2 )
= ( comp_a1063143865omplex @ F3 @ G3 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(402,plain,
( ( ! [F2: a > complex,G2: real > a,X2: real,F3: a > complex,G3: real > a,X3: real] :
( ( ( F2 @ ( G2 @ X2 ) )
= ( F3 @ ( G3 @ X3 ) ) )
=> ( ( comp_a_complex_real @ F2 @ G2 @ X2 )
= ( comp_a_complex_real @ F3 @ G3 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(403,plain,
( ( ! [A: a > complex,B: real > a,C: a > complex,D: real > a] :
( ( ( comp_a_complex_real @ A @ B )
= ( comp_a_complex_real @ C @ D ) )
=> ! [V2: real] :
( ( A @ ( B @ V2 ) )
= ( C @ ( D @ V2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(404,plain,
( ( ! [A: a > complex,B: real > a,C: a > complex,D: real > a,V: real] :
( ( ( comp_a_complex_real @ A @ B )
= ( comp_a_complex_real @ C @ D ) )
=> ( ( A @ ( B @ V ) )
= ( C @ ( D @ V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(405,plain,
( ( ! [F2: a > complex,G2: a > a,H: real > a] :
( ( comp_a_complex_real @ ( comp_a_complex_a @ F2 @ G2 ) @ H )
= ( comp_a_complex_real @ F2 @ ( comp_a_a_real @ G2 @ H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(406,plain,
( ( ! [F2: complex > complex,G2: a > complex,H: real > a] :
( ( comp_a_complex_real @ ( comp_c124850173plex_a @ F2 @ G2 ) @ H )
= ( comp_c595887981x_real @ F2 @ ( comp_a_complex_real @ G2 @ H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(407,plain,
( ( ! [F2: complex > a,G2: a > complex,H: real > a] :
( ( comp_a_a_real @ ( comp_complex_a_a @ F2 @ G2 ) @ H )
= ( comp_complex_a_real @ F2 @ ( comp_a_complex_real @ G2 @ H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(408,plain,
( ( ! [F2: a > complex,G2: complex > a,H: real > complex] :
( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ F2 @ G2 ) @ H )
= ( comp_a_complex_real @ F2 @ ( comp_complex_a_real @ G2 @ H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(409,plain,
( ( ! [F2: a > complex,G2: real > a,H: complex > real] :
( ( comp_r667767405omplex @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
= ( comp_a1063143865omplex @ F2 @ ( comp_real_a_complex @ G2 @ H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(410,plain,
( ( ! [F2: a > complex,G2: real > a,H: real > real] :
( ( comp_r701421291x_real @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
= ( comp_a_complex_real @ F2 @ ( comp_real_a_real @ G2 @ H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(411,plain,
( ( comp_a_complex_real
= ( ^ [F: a > complex,G: real > a,X: real] : ( F @ ( G @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(412,plain,
( ( real_V1477106445omplex @ poinca1910941596x_of_a )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(413,plain,
( ( real_V912435428omplex @ poinca1910941596x_of_a )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(414,plain,
( ( ! [F2: complex > a,P: real > complex] :
( ( path_pathstart_a @ ( comp_complex_a_real @ F2 @ P ) )
= ( F2 @ ( path_p797330068omplex @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(415,plain,
( ( ! [F2: a > complex,P: real > a] :
( ( path_p797330068omplex @ ( comp_a_complex_real @ F2 @ P ) )
= ( F2 @ ( path_pathstart_a @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(416,plain,
( ( ! [F2: complex > complex,P: real > complex] :
( ( path_p797330068omplex @ ( comp_c595887981x_real @ F2 @ P ) )
= ( F2 @ ( path_p797330068omplex @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(417,plain,
( ( ! [F2: complex > a,P: real > complex] :
( ( path_pathfinish_a @ ( comp_complex_a_real @ F2 @ P ) )
= ( F2 @ ( path_p769714271omplex @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(418,plain,
( ( ! [F2: a > complex,P: real > a] :
( ( path_p769714271omplex @ ( comp_a_complex_real @ F2 @ P ) )
= ( F2 @ ( path_pathfinish_a @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(419,plain,
( ( ! [F2: complex > complex,P: real > complex] :
( ( path_p769714271omplex @ ( comp_c595887981x_real @ F2 @ P ) )
= ( F2 @ ( path_p769714271omplex @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(420,plain,
( ( comp_a_complex_real
= ( ^ [F: a > complex,G: real > a,X: real] : ( F @ ( G @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(421,plain,
( ( path_s36253918omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(422,plain,
( ( path_simple_path_a @ c )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(423,plain,
( ( ( path_pathfinish_a @ c )
= ( path_pathstart_a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(424,plain,
( ( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
!= ( path_p797330068omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[357]) ).
thf(425,plain,
( ( ( path_pathfinish_a @ c )
= ( path_pathstart_a @ c ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(426,plain,
( ( path_simple_path_a @ c )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(427,plain,
( ( path_s36253918omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(428,plain,
( ( comp_a_complex_real
= ( ^ [F: a > complex,G: real > a,X: real] : ( F @ ( G @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(429,plain,
( ( ! [F2: complex > complex,P: real > complex] :
( ( path_p769714271omplex @ ( comp_c595887981x_real @ F2 @ P ) )
= ( F2 @ ( path_p769714271omplex @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(430,plain,
( ( ! [F2: a > complex,P: real > a] :
( ( path_p769714271omplex @ ( comp_a_complex_real @ F2 @ P ) )
= ( F2 @ ( path_pathfinish_a @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(431,plain,
( ( ! [F2: complex > a,P: real > complex] :
( ( path_pathfinish_a @ ( comp_complex_a_real @ F2 @ P ) )
= ( F2 @ ( path_p769714271omplex @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(432,plain,
( ( ! [F2: complex > complex,P: real > complex] :
( ( path_p797330068omplex @ ( comp_c595887981x_real @ F2 @ P ) )
= ( F2 @ ( path_p797330068omplex @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(433,plain,
( ( ! [F2: a > complex,P: real > a] :
( ( path_p797330068omplex @ ( comp_a_complex_real @ F2 @ P ) )
= ( F2 @ ( path_pathstart_a @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(434,plain,
( ( ! [F2: complex > a,P: real > complex] :
( ( path_pathstart_a @ ( comp_complex_a_real @ F2 @ P ) )
= ( F2 @ ( path_p797330068omplex @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(435,plain,
( ( real_V912435428omplex @ poinca1910941596x_of_a )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(436,plain,
( ( real_V1477106445omplex @ poinca1910941596x_of_a )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(437,plain,
( ( comp_a_complex_real
= ( ^ [F: a > complex,G: real > a,X: real] : ( F @ ( G @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(438,plain,
( ( ! [F2: a > complex,G2: real > a,H: real > real] :
( ( comp_r701421291x_real @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
= ( comp_a_complex_real @ F2 @ ( comp_real_a_real @ G2 @ H ) ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(439,plain,
( ( ! [F2: a > complex,G2: real > a,H: complex > real] :
( ( comp_r667767405omplex @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
= ( comp_a1063143865omplex @ F2 @ ( comp_real_a_complex @ G2 @ H ) ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(440,plain,
( ( ! [F2: a > complex,G2: complex > a,H: real > complex] :
( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ F2 @ G2 ) @ H )
= ( comp_a_complex_real @ F2 @ ( comp_complex_a_real @ G2 @ H ) ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(441,plain,
( ( ! [F2: complex > a,G2: a > complex,H: real > a] :
( ( comp_a_a_real @ ( comp_complex_a_a @ F2 @ G2 ) @ H )
= ( comp_complex_a_real @ F2 @ ( comp_a_complex_real @ G2 @ H ) ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(442,plain,
( ( ! [F2: complex > complex,G2: a > complex,H: real > a] :
( ( comp_a_complex_real @ ( comp_c124850173plex_a @ F2 @ G2 ) @ H )
= ( comp_c595887981x_real @ F2 @ ( comp_a_complex_real @ G2 @ H ) ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(443,plain,
( ( ! [F2: a > complex,G2: a > a,H: real > a] :
( ( comp_a_complex_real @ ( comp_a_complex_a @ F2 @ G2 ) @ H )
= ( comp_a_complex_real @ F2 @ ( comp_a_a_real @ G2 @ H ) ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(444,plain,
( ( ! [A: a > complex,B: real > a,C: a > complex,D: real > a,V: real] :
( ( ( comp_a_complex_real @ A @ B )
= ( comp_a_complex_real @ C @ D ) )
=> ( ( A @ ( B @ V ) )
= ( C @ ( D @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(445,plain,
( ( ! [A: a > complex,B: real > a,C: a > complex,D: real > a] :
( ( ( comp_a_complex_real @ A @ B )
= ( comp_a_complex_real @ C @ D ) )
=> ! [V2: real] :
( ( A @ ( B @ V2 ) )
= ( C @ ( D @ V2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(446,plain,
( ( ! [F2: a > complex,G2: real > a,X2: real,F3: a > complex,G3: real > a,X3: real] :
( ( ( F2 @ ( G2 @ X2 ) )
= ( F3 @ ( G3 @ X3 ) ) )
=> ( ( comp_a_complex_real @ F2 @ G2 @ X2 )
= ( comp_a_complex_real @ F3 @ G3 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(447,plain,
( ( ! [F2: a > complex,G2: real > a,X2: real,F3: a > complex,G3: complex > a,X3: complex] :
( ( ( F2 @ ( G2 @ X2 ) )
= ( F3 @ ( G3 @ X3 ) ) )
=> ( ( comp_a_complex_real @ F2 @ G2 @ X2 )
= ( comp_a1063143865omplex @ F3 @ G3 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(448,plain,
( ( ! [F2: a > complex,G2: real > a,X2: real,F3: a > complex,G3: a > a,X3: a] :
( ( ( F2 @ ( G2 @ X2 ) )
= ( F3 @ ( G3 @ X3 ) ) )
=> ( ( comp_a_complex_real @ F2 @ G2 @ X2 )
= ( comp_a_complex_a @ F3 @ G3 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(449,plain,
( ( ! [F2: a > complex,G2: complex > a,X2: complex,F3: a > complex,G3: real > a,X3: real] :
( ( ( F2 @ ( G2 @ X2 ) )
= ( F3 @ ( G3 @ X3 ) ) )
=> ( ( comp_a1063143865omplex @ F2 @ G2 @ X2 )
= ( comp_a_complex_real @ F3 @ G3 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(450,plain,
( ( ! [A: a > complex,B: real > a,C: real > complex,V: real] :
( ( ( comp_a_complex_real @ A @ B )
= C )
=> ( ( A @ ( B @ V ) )
= ( C @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(451,plain,
( ( ! [F2: complex > complex,G2: real > complex] :
( ( real_V670066493omplex @ F2 )
=> ( ( path_p797330068omplex @ ( comp_c595887981x_real @ F2 @ G2 ) )
= ( F2 @ ( path_p797330068omplex @ G2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(452,plain,
( ( ! [F2: a > complex,G2: real > a] :
( ( real_V1477106445omplex @ F2 )
=> ( ( path_p797330068omplex @ ( comp_a_complex_real @ F2 @ G2 ) )
= ( F2 @ ( path_pathstart_a @ G2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(453,plain,
( ( ! [F2: complex > a,G2: real > complex] :
( ( real_V1327653935plex_a @ F2 )
=> ( ( path_pathstart_a @ ( comp_complex_a_real @ F2 @ G2 ) )
= ( F2 @ ( path_p797330068omplex @ G2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(454,plain,
( ( ! [F2: complex > complex,G2: real > complex] :
( ( real_V670066493omplex @ F2 )
=> ( ( path_p769714271omplex @ ( comp_c595887981x_real @ F2 @ G2 ) )
= ( F2 @ ( path_p769714271omplex @ G2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(455,plain,
( ( ! [F2: a > complex,G2: real > a] :
( ( real_V1477106445omplex @ F2 )
=> ( ( path_p769714271omplex @ ( comp_a_complex_real @ F2 @ G2 ) )
= ( F2 @ ( path_pathfinish_a @ G2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(456,plain,
( ( ! [F2: complex > a,G2: real > complex] :
( ( real_V1327653935plex_a @ F2 )
=> ( ( path_pathfinish_a @ ( comp_complex_a_real @ F2 @ G2 ) )
= ( F2 @ ( path_p769714271omplex @ G2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(457,plain,
( ( ! [F2: real > a,G2: a > complex] :
( ( real_V779700657real_a @ F2 )
=> ( ( real_V1477106445omplex @ G2 )
=> ( real_V1948715323omplex @ ( comp_a_complex_real @ G2 @ F2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(458,plain,
( ( ! [A1: complex,A3: complex] :
( ( path_p769714271omplex @ ( path_rectpath @ A1 @ A3 ) )
= A1 ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(459,plain,
( ( ! [A1: complex,A3: complex] :
( ( path_p797330068omplex @ ( path_rectpath @ A1 @ A3 ) )
= A1 ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(460,plain,
( ( ! [F2: a > complex,G2: real > a,L1: a > complex,L2: real > a,H: complex > real,R: complex > a] :
( ( ( comp_a_complex_real @ F2 @ G2 )
= ( comp_a_complex_real @ L1 @ L2 ) )
=> ( ( ( comp_real_a_complex @ L2 @ H )
= R )
=> ( ( comp_a1063143865omplex @ F2 @ ( comp_real_a_complex @ G2 @ H ) )
= ( comp_a1063143865omplex @ L1 @ R ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(461,plain,
( ( ! [G2: real > a,H: complex > real,R: complex > a,F2: a > complex] :
( ( ( comp_real_a_complex @ G2 @ H )
= R )
=> ( ( comp_r667767405omplex @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
= ( comp_a1063143865omplex @ F2 @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(462,plain,
( ( ! [G2: real > a,H: a > real,R: a > a,F2: a > complex] :
( ( ( comp_real_a_a @ G2 @ H )
= R )
=> ( ( comp_real_complex_a @ ( comp_a_complex_real @ F2 @ G2 ) @ H )
= ( comp_a_complex_a @ F2 @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(463,plain,
( ( ! [G2: complex > a,H: real > complex,R: real > a,F2: a > complex] :
( ( ( comp_complex_a_real @ G2 @ H )
= R )
=> ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ F2 @ G2 ) @ H )
= ( comp_a_complex_real @ F2 @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(464,plain,
( ( ! [F2: complex > complex,G2: a > complex,L: a > complex,H: real > a] :
( ( ( comp_c124850173plex_a @ F2 @ G2 )
= L )
=> ( ( comp_c595887981x_real @ F2 @ ( comp_a_complex_real @ G2 @ H ) )
= ( comp_a_complex_real @ L @ H ) ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(465,plain,
( ( ! [F2: a > complex,G2: real > a,L: real > complex,H: real > real] :
( ( ( comp_a_complex_real @ F2 @ G2 )
= L )
=> ( ( comp_a_complex_real @ F2 @ ( comp_real_a_real @ G2 @ H ) )
= ( comp_r701421291x_real @ L @ H ) ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(466,plain,
( ( ! [F2: a > complex,G2: real > a,L: real > complex,H: complex > real] :
( ( ( comp_a_complex_real @ F2 @ G2 )
= L )
=> ( ( comp_a1063143865omplex @ F2 @ ( comp_real_a_complex @ G2 @ H ) )
= ( comp_r667767405omplex @ L @ H ) ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(467,plain,
( ( ! [F2: a > complex,G2: real > a,L: real > complex,H: a > real] :
( ( ( comp_a_complex_real @ F2 @ G2 )
= L )
=> ( ( comp_a_complex_a @ F2 @ ( comp_real_a_a @ G2 @ H ) )
= ( comp_real_complex_a @ L @ H ) ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(468,plain,
( ( ! [F2: a > complex,G2: complex > a,L: complex > complex,H: real > complex] :
( ( ( comp_a1063143865omplex @ F2 @ G2 )
= L )
=> ( ( comp_a_complex_real @ F2 @ ( comp_complex_a_real @ G2 @ H ) )
= ( comp_c595887981x_real @ L @ H ) ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(469,plain,
( ( ! [F3: a > complex,F2: real > a,A2: set_real] :
( ( inj_on_real_complex @ ( comp_a_complex_real @ F3 @ F2 ) @ A2 )
=> ( inj_on_real_a @ F2 @ A2 ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(470,plain,
( ( ! [G2: real > complex] :
( ( path_arc_complex @ G2 )
=> ( ( path_p769714271omplex @ G2 )
!= ( path_p797330068omplex @ G2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(471,plain,
( ( ! [G2: real > complex] :
( ( path_s36253918omplex @ G2 )
=> ( ( ( path_p769714271omplex @ G2 )
!= ( path_p797330068omplex @ G2 ) )
=> ( path_arc_complex @ G2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(472,plain,
( ( ! [G2: real > complex] :
( ( ( path_p769714271omplex @ G2 )
!= ( path_p797330068omplex @ G2 ) )
=> ( ( path_s36253918omplex @ G2 )
= ( path_arc_complex @ G2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(473,plain,
( ( ! [G2: real > complex] :
( ( path_s36253918omplex @ G2 )
=> ( ( path_arc_complex @ G2 )
| ( ( path_p769714271omplex @ G2 )
= ( path_p797330068omplex @ G2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(474,plain,
( ( path_arc_complex
= ( ^ [G: real > complex] :
( ( path_s36253918omplex @ G )
& ( ( path_p769714271omplex @ G )
!= ( path_p797330068omplex @ G ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(475,plain,
( ( ! [G2: complex > complex,F2: a > complex,V: real > a] :
( ( comp_c595887981x_real @ G2 @ ( comp_a_complex_real @ F2 @ V ) )
= ( comp_a_complex_real @ ( comp_c124850173plex_a @ G2 @ F2 ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(476,plain,
( ( ! [G2: complex > a,F2: a > complex,V: real > a] :
( ( comp_complex_a_real @ G2 @ ( comp_a_complex_real @ F2 @ V ) )
= ( comp_a_a_real @ ( comp_complex_a_a @ G2 @ F2 ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(477,plain,
( ( ! [G2: a > complex,F2: complex > a,V: real > complex] :
( ( comp_a_complex_real @ G2 @ ( comp_complex_a_real @ F2 @ V ) )
= ( comp_c595887981x_real @ ( comp_a1063143865omplex @ G2 @ F2 ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(478,plain,
( ( ! [G2: a > complex,F2: real > a,V: real > real] :
( ( comp_a_complex_real @ G2 @ ( comp_real_a_real @ F2 @ V ) )
= ( comp_r701421291x_real @ ( comp_a_complex_real @ G2 @ F2 ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(479,plain,
( ( ! [G2: a > complex,F2: a > a,V: real > a] :
( ( comp_a_complex_real @ G2 @ ( comp_a_a_real @ F2 @ V ) )
= ( comp_a_complex_real @ ( comp_a_complex_a @ G2 @ F2 ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(480,plain,
( ( ! [G2: a > complex,F2: real > a,V: complex > real] :
( ( comp_a1063143865omplex @ G2 @ ( comp_real_a_complex @ F2 @ V ) )
= ( comp_r667767405omplex @ ( comp_a_complex_real @ G2 @ F2 ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(481,plain,
( ( ( comp_a1063143865omplex @ poinca1910941596x_of_a @ poinca837721858l_of_a )
= id_complex )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(482,plain,
( ( ( comp_complex_a_a @ poinca837721858l_of_a @ poinca1910941596x_of_a )
= id_a )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(483,plain,
( ( bij_betw_a_complex @ poinca1910941596x_of_a @ top_top_set_a @ top_top_set_complex )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(484,plain,
( ( ! [M: real > a,G2: real > real,X2: real,N: a > a,H: real > a,F2: a > complex] :
( ( ( M @ ( G2 @ X2 ) )
= ( N @ ( H @ X2 ) ) )
=> ( ( comp_r701421291x_real @ ( comp_a_complex_real @ F2 @ M ) @ G2 @ X2 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(485,plain,
( ( ! [M: real > a,G2: complex > real,X2: complex,N: a > a,H: complex > a,F2: a > complex] :
( ( ( M @ ( G2 @ X2 ) )
= ( N @ ( H @ X2 ) ) )
=> ( ( comp_r667767405omplex @ ( comp_a_complex_real @ F2 @ M ) @ G2 @ X2 )
= ( comp_a1063143865omplex @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(486,plain,
( ( ! [M: real > a,G2: a > real,X2: a,N: a > a,H: a > a,F2: a > complex] :
( ( ( M @ ( G2 @ X2 ) )
= ( N @ ( H @ X2 ) ) )
=> ( ( comp_real_complex_a @ ( comp_a_complex_real @ F2 @ M ) @ G2 @ X2 )
= ( comp_a_complex_a @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(487,plain,
( ( ! [M: complex > a,G2: real > complex,X2: real,N: a > a,H: real > a,F2: a > complex] :
( ( ( M @ ( G2 @ X2 ) )
= ( N @ ( H @ X2 ) ) )
=> ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ F2 @ M ) @ G2 @ X2 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ F2 @ N ) @ H @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(488,plain,
( ( ! [F2: real > a,A2: set_real,B3: set_a,G2: a > complex,C2: set_complex] :
( ( bij_betw_real_a @ F2 @ A2 @ B3 )
=> ( ( bij_betw_a_complex @ G2 @ B3 @ C2 )
=> ( bij_be122140626omplex @ ( comp_a_complex_real @ G2 @ F2 ) @ A2 @ C2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(489,plain,
( ( ! [F2: real > a,A2: set_real,A7: set_a,F3: a > complex,A8: set_complex] :
( ( bij_betw_real_a @ F2 @ A2 @ A7 )
=> ( ( bij_betw_a_complex @ F3 @ A7 @ A8 )
= ( bij_be122140626omplex @ ( comp_a_complex_real @ F3 @ F2 ) @ A2 @ A8 ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(490,plain,
( ( ! [A: a > complex,B: real > a,C: real > complex,V: real] :
( ( ( comp_a_complex_real @ A @ B )
= ( comp_c595887981x_real @ id_complex @ C ) )
=> ( ( A @ ( B @ V ) )
= ( C @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(491,plain,
( ( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
!= ( path_p797330068omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(492,plain,
( ( ! [SX0: complex > complex,SX1: real > complex] :
( ~ ( real_V670066493omplex @ SX0 )
| ( ( path_p797330068omplex @ ( comp_c595887981x_real @ SX0 @ SX1 ) )
= ( SX0 @ ( path_p797330068omplex @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(493,plain,
( ( ! [SX0: a > complex,SX1: real > a,SX2: set_real] :
( ~ ( inj_on_real_complex @ ( comp_a_complex_real @ SX0 @ SX1 ) @ SX2 )
| ( inj_on_real_a @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(494,plain,
( ( ! [SX0: real > a,SX1: a > real,SX2: a,SX3: a > a,SX4: a > a,SX5: a > complex] :
( ( ( SX0 @ ( SX1 @ SX2 ) )
!= ( SX3 @ ( SX4 @ SX2 ) ) )
| ( ( comp_real_complex_a @ ( comp_a_complex_real @ SX5 @ SX0 ) @ SX1 @ SX2 )
= ( comp_a_complex_a @ ( comp_a_complex_a @ SX5 @ SX3 ) @ SX4 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(495,plain,
( ( ! [SX0: a > complex,SX1: real > a] :
( ~ ( real_V1477106445omplex @ SX0 )
| ( ( path_p769714271omplex @ ( comp_a_complex_real @ SX0 @ SX1 ) )
= ( SX0 @ ( path_pathfinish_a @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(496,plain,
( ( ! [SX0: real > a,SX1: a > real,SX2: a > a,SX3: a > complex] :
( ( ( comp_real_a_a @ SX0 @ SX1 )
!= SX2 )
| ( ( comp_real_complex_a @ ( comp_a_complex_real @ SX3 @ SX0 ) @ SX1 )
= ( comp_a_complex_a @ SX3 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(497,plain,
( ( ! [SX0: a > complex,SX1: complex > a,SX2: complex > complex,SX3: real > complex] :
( ( ( comp_a1063143865omplex @ SX0 @ SX1 )
!= SX2 )
| ( ( comp_a_complex_real @ SX0 @ ( comp_complex_a_real @ SX1 @ SX3 ) )
= ( comp_c595887981x_real @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(498,plain,
( ( ! [SX0: real > complex] :
( ~ ( path_s36253918omplex @ SX0 )
| ~ ( ( ( path_p769714271omplex @ SX0 )
!= ( path_p797330068omplex @ SX0 ) ) )
| ( path_arc_complex @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(499,plain,
( ( ! [SX0: real > complex] :
( ~ ( ( ( path_p769714271omplex @ SX0 )
!= ( path_p797330068omplex @ SX0 ) ) )
| ( ( path_s36253918omplex @ SX0 )
= ( path_arc_complex @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(500,plain,
( ( ! [SX0: a > complex,SX1: real > a,SX2: real > complex,SX3: a > real] :
( ( ( comp_a_complex_real @ SX0 @ SX1 )
!= SX2 )
| ( ( comp_a_complex_a @ SX0 @ ( comp_real_a_a @ SX1 @ SX3 ) )
= ( comp_real_complex_a @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(501,plain,
( ( ! [SX0: a > complex,SX1: real > a,SX2: real > complex,SX3: complex > real] :
( ( ( comp_a_complex_real @ SX0 @ SX1 )
!= SX2 )
| ( ( comp_a1063143865omplex @ SX0 @ ( comp_real_a_complex @ SX1 @ SX3 ) )
= ( comp_r667767405omplex @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(502,plain,
( ( ! [SX0: a > complex,SX1: real > a,SX2: a > complex,SX3: real > a] :
( ( ( comp_a_complex_real @ SX0 @ SX1 )
!= ( comp_a_complex_real @ SX2 @ SX3 ) )
| ! [SX4: real] :
( ( SX0 @ ( SX1 @ SX4 ) )
= ( SX2 @ ( SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(503,plain,
( ( ! [SX0: real > complex] :
( ~ ( path_s36253918omplex @ SX0 )
| ( path_arc_complex @ SX0 )
| ( ( path_p769714271omplex @ SX0 )
= ( path_p797330068omplex @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(504,plain,
( ( ! [SX0: a > complex,SX1: real > a,SX2: real > complex,SX3: real] :
( ( ( comp_a_complex_real @ SX0 @ SX1 )
!= SX2 )
| ( ( SX0 @ ( SX1 @ SX3 ) )
= ( SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(505,plain,
( ( ! [SX0: complex > a,SX1: real > complex] :
( ~ ( real_V1327653935plex_a @ SX0 )
| ( ( path_pathfinish_a @ ( comp_complex_a_real @ SX0 @ SX1 ) )
= ( SX0 @ ( path_p769714271omplex @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(506,plain,
( ( ! [SX0: complex > complex,SX1: real > complex] :
( ~ ( real_V670066493omplex @ SX0 )
| ( ( path_p769714271omplex @ ( comp_c595887981x_real @ SX0 @ SX1 ) )
= ( SX0 @ ( path_p769714271omplex @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(507,plain,
( ( ! [SX0: complex > a,SX1: real > complex,SX2: real > a,SX3: a > complex] :
( ( ( comp_complex_a_real @ SX0 @ SX1 )
!= SX2 )
| ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SX3 @ SX0 ) @ SX1 )
= ( comp_a_complex_real @ SX3 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(508,plain,
( ( ! [SX0: a > complex,SX1: real > a,SX2: real,SX3: a > complex,SX4: a > a,SX5: a] :
( ( ( SX0 @ ( SX1 @ SX2 ) )
!= ( SX3 @ ( SX4 @ SX5 ) ) )
| ( ( comp_a_complex_real @ SX0 @ SX1 @ SX2 )
= ( comp_a_complex_a @ SX3 @ SX4 @ SX5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(509,plain,
( ( path_arc_complex
= ( ^ [SX0: real > complex] :
~ ( ~ ( path_s36253918omplex @ SX0 )
| ~ ( ( ( path_p769714271omplex @ SX0 )
!= ( path_p797330068omplex @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(510,plain,
( ( ! [SX0: real > a,SX1: set_real,SX2: set_a,SX3: a > complex,SX4: set_complex] :
( ~ ( bij_betw_real_a @ SX0 @ SX1 @ SX2 )
| ( ( bij_betw_a_complex @ SX3 @ SX2 @ SX4 )
= ( bij_be122140626omplex @ ( comp_a_complex_real @ SX3 @ SX0 ) @ SX1 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(511,plain,
( ( ! [SX0: a > complex,SX1: real > a,SX2: a > complex,SX3: real > a,SX4: real] :
( ( ( comp_a_complex_real @ SX0 @ SX1 )
!= ( comp_a_complex_real @ SX2 @ SX3 ) )
| ( ( SX0 @ ( SX1 @ SX4 ) )
= ( SX2 @ ( SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(512,plain,
( ( ! [SX0: complex > a,SX1: real > complex] :
( ~ ( real_V1327653935plex_a @ SX0 )
| ( ( path_pathstart_a @ ( comp_complex_a_real @ SX0 @ SX1 ) )
= ( SX0 @ ( path_p797330068omplex @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(513,plain,
( ( ! [SX0: a > complex,SX1: real > a] :
( ~ ( real_V1477106445omplex @ SX0 )
| ( ( path_p797330068omplex @ ( comp_a_complex_real @ SX0 @ SX1 ) )
= ( SX0 @ ( path_pathstart_a @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(514,plain,
( ( ! [SX0: complex > complex,SX1: a > complex,SX2: a > complex,SX3: real > a] :
( ( ( comp_c124850173plex_a @ SX0 @ SX1 )
!= SX2 )
| ( ( comp_c595887981x_real @ SX0 @ ( comp_a_complex_real @ SX1 @ SX3 ) )
= ( comp_a_complex_real @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(515,plain,
( ( ! [SX0: a > complex,SX1: real > a,SX2: real,SX3: a > complex,SX4: complex > a,SX5: complex] :
( ( ( SX0 @ ( SX1 @ SX2 ) )
!= ( SX3 @ ( SX4 @ SX5 ) ) )
| ( ( comp_a_complex_real @ SX0 @ SX1 @ SX2 )
= ( comp_a1063143865omplex @ SX3 @ SX4 @ SX5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(516,plain,
( ( ! [SX0: real > a,SX1: complex > real,SX2: complex > a,SX3: a > complex] :
( ( ( comp_real_a_complex @ SX0 @ SX1 )
!= SX2 )
| ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SX3 @ SX0 ) @ SX1 )
= ( comp_a1063143865omplex @ SX3 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(517,plain,
( ( ! [SX0: real > a,SX1: a > complex] :
( ~ ( real_V779700657real_a @ SX0 )
| ~ ( real_V1477106445omplex @ SX1 )
| ( real_V1948715323omplex @ ( comp_a_complex_real @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(518,plain,
( ( ! [SX0: real > a,SX1: complex > real,SX2: complex,SX3: a > a,SX4: complex > a,SX5: a > complex] :
( ( ( SX0 @ ( SX1 @ SX2 ) )
!= ( SX3 @ ( SX4 @ SX2 ) ) )
| ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SX5 @ SX0 ) @ SX1 @ SX2 )
= ( comp_a1063143865omplex @ ( comp_a_complex_a @ SX5 @ SX3 ) @ SX4 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(519,plain,
( ( ! [SX0: real > complex] :
( ~ ( path_arc_complex @ SX0 )
| ( ( path_p769714271omplex @ SX0 )
!= ( path_p797330068omplex @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(520,plain,
( ( ! [SX0: complex > a,SX1: real > complex,SX2: real,SX3: a > a,SX4: real > a,SX5: a > complex] :
( ( ( SX0 @ ( SX1 @ SX2 ) )
!= ( SX3 @ ( SX4 @ SX2 ) ) )
| ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SX5 @ SX0 ) @ SX1 @ SX2 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SX5 @ SX3 ) @ SX4 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(521,plain,
( ( ! [SX0: a > complex,SX1: real > a,SX2: real,SX3: a > complex,SX4: real > a,SX5: real] :
( ( ( SX0 @ ( SX1 @ SX2 ) )
!= ( SX3 @ ( SX4 @ SX5 ) ) )
| ( ( comp_a_complex_real @ SX0 @ SX1 @ SX2 )
= ( comp_a_complex_real @ SX3 @ SX4 @ SX5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(522,plain,
( ( ! [SX0: a > complex,SX1: real > a,SX2: real > complex,SX3: real] :
( ( ( comp_a_complex_real @ SX0 @ SX1 )
!= ( comp_c595887981x_real @ id_complex @ SX2 ) )
| ( ( SX0 @ ( SX1 @ SX3 ) )
= ( SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(523,plain,
( ( ! [SX0: a > complex,SX1: real > a,SX2: a > complex,SX3: real > a,SX4: complex > real,SX5: complex > a] :
( ( ( comp_a_complex_real @ SX0 @ SX1 )
!= ( comp_a_complex_real @ SX2 @ SX3 ) )
| ( ( comp_real_a_complex @ SX3 @ SX4 )
!= SX5 )
| ( ( comp_a1063143865omplex @ SX0 @ ( comp_real_a_complex @ SX1 @ SX4 ) )
= ( comp_a1063143865omplex @ SX2 @ SX5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(524,plain,
( ( ! [SX0: real > a,SX1: real > real,SX2: real,SX3: a > a,SX4: real > a,SX5: a > complex] :
( ( ( SX0 @ ( SX1 @ SX2 ) )
!= ( SX3 @ ( SX4 @ SX2 ) ) )
| ( ( comp_r701421291x_real @ ( comp_a_complex_real @ SX5 @ SX0 ) @ SX1 @ SX2 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SX5 @ SX3 ) @ SX4 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(525,plain,
( ( ! [SX0: a > complex,SX1: complex > a,SX2: complex,SX3: a > complex,SX4: real > a,SX5: real] :
( ( ( SX0 @ ( SX1 @ SX2 ) )
!= ( SX3 @ ( SX4 @ SX5 ) ) )
| ( ( comp_a1063143865omplex @ SX0 @ SX1 @ SX2 )
= ( comp_a_complex_real @ SX3 @ SX4 @ SX5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(526,plain,
( ( ! [SX0: a > complex,SX1: real > a,SX2: real > complex,SX3: real > real] :
( ( ( comp_a_complex_real @ SX0 @ SX1 )
!= SX2 )
| ( ( comp_a_complex_real @ SX0 @ ( comp_real_a_real @ SX1 @ SX3 ) )
= ( comp_r701421291x_real @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(527,plain,
( ( ! [SX0: real > a,SX1: set_real,SX2: set_a,SX3: a > complex,SX4: set_complex] :
( ~ ( bij_betw_real_a @ SX0 @ SX1 @ SX2 )
| ~ ( bij_betw_a_complex @ SX3 @ SX2 @ SX4 )
| ( bij_be122140626omplex @ ( comp_a_complex_real @ SX3 @ SX0 ) @ SX1 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(528,plain,
( ( ! [SV1: a > complex] :
( ( comp_a_complex_real @ SV1 )
= ( ^ [SY194: real > a,SY195: real] : ( SV1 @ ( SY194 @ SY195 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[428]) ).
thf(529,plain,
( ( comp_a_complex_real
= ( ^ [F: a > complex,G: real > a,X: real] : ( F @ ( G @ X ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[428]) ).
thf(530,plain,
! [SV2: complex > complex] :
( ( ! [SY196: real > complex] :
( ( path_p769714271omplex @ ( comp_c595887981x_real @ SV2 @ SY196 ) )
= ( SV2 @ ( path_p769714271omplex @ SY196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(531,plain,
! [SV3: a > complex] :
( ( ! [SY197: real > a] :
( ( path_p769714271omplex @ ( comp_a_complex_real @ SV3 @ SY197 ) )
= ( SV3 @ ( path_pathfinish_a @ SY197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(532,plain,
! [SV4: complex > a] :
( ( ! [SY198: real > complex] :
( ( path_pathfinish_a @ ( comp_complex_a_real @ SV4 @ SY198 ) )
= ( SV4 @ ( path_p769714271omplex @ SY198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(533,plain,
! [SV5: complex > complex] :
( ( ! [SY199: real > complex] :
( ( path_p797330068omplex @ ( comp_c595887981x_real @ SV5 @ SY199 ) )
= ( SV5 @ ( path_p797330068omplex @ SY199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(534,plain,
! [SV6: a > complex] :
( ( ! [SY200: real > a] :
( ( path_p797330068omplex @ ( comp_a_complex_real @ SV6 @ SY200 ) )
= ( SV6 @ ( path_pathstart_a @ SY200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(535,plain,
! [SV7: complex > a] :
( ( ! [SY201: real > complex] :
( ( path_pathstart_a @ ( comp_complex_a_real @ SV7 @ SY201 ) )
= ( SV7 @ ( path_p797330068omplex @ SY201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(536,plain,
( ( ! [SV8: a > complex] :
( ( comp_a_complex_real @ SV8 )
= ( ^ [SY202: real > a,SY203: real] : ( SV8 @ ( SY202 @ SY203 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[437]) ).
thf(537,plain,
( ( comp_a_complex_real
= ( ^ [F: a > complex,G: real > a,X: real] : ( F @ ( G @ X ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[437]) ).
thf(538,plain,
! [SV9: a > complex] :
( ( ! [SY204: real > a,SY205: real > real] :
( ( comp_r701421291x_real @ ( comp_a_complex_real @ SV9 @ SY204 ) @ SY205 )
= ( comp_a_complex_real @ SV9 @ ( comp_real_a_real @ SY204 @ SY205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(539,plain,
! [SV10: a > complex] :
( ( ! [SY206: real > a,SY207: complex > real] :
( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV10 @ SY206 ) @ SY207 )
= ( comp_a1063143865omplex @ SV10 @ ( comp_real_a_complex @ SY206 @ SY207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(540,plain,
! [SV11: a > complex] :
( ( ! [SY208: complex > a,SY209: real > complex] :
( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV11 @ SY208 ) @ SY209 )
= ( comp_a_complex_real @ SV11 @ ( comp_complex_a_real @ SY208 @ SY209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(541,plain,
! [SV12: complex > a] :
( ( ! [SY210: a > complex,SY211: real > a] :
( ( comp_a_a_real @ ( comp_complex_a_a @ SV12 @ SY210 ) @ SY211 )
= ( comp_complex_a_real @ SV12 @ ( comp_a_complex_real @ SY210 @ SY211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(542,plain,
! [SV13: complex > complex] :
( ( ! [SY212: a > complex,SY213: real > a] :
( ( comp_a_complex_real @ ( comp_c124850173plex_a @ SV13 @ SY212 ) @ SY213 )
= ( comp_c595887981x_real @ SV13 @ ( comp_a_complex_real @ SY212 @ SY213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(543,plain,
! [SV14: a > complex] :
( ( ! [SY214: a > a,SY215: real > a] :
( ( comp_a_complex_real @ ( comp_a_complex_a @ SV14 @ SY214 ) @ SY215 )
= ( comp_a_complex_real @ SV14 @ ( comp_a_a_real @ SY214 @ SY215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(544,plain,
! [SV15: complex] :
( ( ! [SY216: complex] :
( ( path_p769714271omplex @ ( path_rectpath @ SV15 @ SY216 ) )
= SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(545,plain,
! [SV16: complex] :
( ( ! [SY217: complex] :
( ( path_p797330068omplex @ ( path_rectpath @ SV16 @ SY217 ) )
= SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(546,plain,
! [SV17: complex > complex] :
( ( ! [SY218: a > complex,SY219: real > a] :
( ( comp_c595887981x_real @ SV17 @ ( comp_a_complex_real @ SY218 @ SY219 ) )
= ( comp_a_complex_real @ ( comp_c124850173plex_a @ SV17 @ SY218 ) @ SY219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(547,plain,
! [SV18: complex > a] :
( ( ! [SY220: a > complex,SY221: real > a] :
( ( comp_complex_a_real @ SV18 @ ( comp_a_complex_real @ SY220 @ SY221 ) )
= ( comp_a_a_real @ ( comp_complex_a_a @ SV18 @ SY220 ) @ SY221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(548,plain,
! [SV19: a > complex] :
( ( ! [SY222: complex > a,SY223: real > complex] :
( ( comp_a_complex_real @ SV19 @ ( comp_complex_a_real @ SY222 @ SY223 ) )
= ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV19 @ SY222 ) @ SY223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(549,plain,
! [SV20: a > complex] :
( ( ! [SY224: real > a,SY225: real > real] :
( ( comp_a_complex_real @ SV20 @ ( comp_real_a_real @ SY224 @ SY225 ) )
= ( comp_r701421291x_real @ ( comp_a_complex_real @ SV20 @ SY224 ) @ SY225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(550,plain,
! [SV21: a > complex] :
( ( ! [SY226: a > a,SY227: real > a] :
( ( comp_a_complex_real @ SV21 @ ( comp_a_a_real @ SY226 @ SY227 ) )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SV21 @ SY226 ) @ SY227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(551,plain,
! [SV22: a > complex] :
( ( ! [SY228: real > a,SY229: complex > real] :
( ( comp_a1063143865omplex @ SV22 @ ( comp_real_a_complex @ SY228 @ SY229 ) )
= ( comp_r667767405omplex @ ( comp_a_complex_real @ SV22 @ SY228 ) @ SY229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(552,plain,
( ( ! [SV23: complex] :
( ( comp_a1063143865omplex @ poinca1910941596x_of_a @ poinca837721858l_of_a @ SV23 )
= ( id_complex @ SV23 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[481]) ).
thf(553,plain,
( ( ( comp_a1063143865omplex @ poinca1910941596x_of_a @ poinca837721858l_of_a )
= id_complex )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[481]) ).
thf(554,plain,
( ( ! [SV24: a] :
( ( comp_complex_a_a @ poinca837721858l_of_a @ poinca1910941596x_of_a @ SV24 )
= ( id_a @ SV24 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[482]) ).
thf(555,plain,
( ( ( comp_complex_a_a @ poinca837721858l_of_a @ poinca1910941596x_of_a )
= id_a )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[482]) ).
thf(556,plain,
( ( ( path_p769714271omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) )
= ( path_p797330068omplex @ ( comp_a_complex_real @ poinca1910941596x_of_a @ c ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(557,plain,
! [SV25: complex > complex] :
( ( ! [SY230: real > complex] :
( ~ ( real_V670066493omplex @ SV25 )
| ( ( path_p797330068omplex @ ( comp_c595887981x_real @ SV25 @ SY230 ) )
= ( SV25 @ ( path_p797330068omplex @ SY230 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(558,plain,
! [SV26: a > complex] :
( ( ! [SY231: real > a,SY232: set_real] :
( ~ ( inj_on_real_complex @ ( comp_a_complex_real @ SV26 @ SY231 ) @ SY232 )
| ( inj_on_real_a @ SY231 @ SY232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(559,plain,
! [SV27: real > a] :
( ( ! [SY233: a > real,SY234: a,SY235: a > a,SY236: a > a,SY237: a > complex] :
( ( ( SV27 @ ( SY233 @ SY234 ) )
!= ( SY235 @ ( SY236 @ SY234 ) ) )
| ( ( comp_real_complex_a @ ( comp_a_complex_real @ SY237 @ SV27 ) @ SY233 @ SY234 )
= ( comp_a_complex_a @ ( comp_a_complex_a @ SY237 @ SY235 ) @ SY236 @ SY234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(560,plain,
! [SV28: a > complex] :
( ( ! [SY238: real > a] :
( ~ ( real_V1477106445omplex @ SV28 )
| ( ( path_p769714271omplex @ ( comp_a_complex_real @ SV28 @ SY238 ) )
= ( SV28 @ ( path_pathfinish_a @ SY238 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(561,plain,
! [SV29: real > a] :
( ( ! [SY239: a > real,SY240: a > a,SY241: a > complex] :
( ( ( comp_real_a_a @ SV29 @ SY239 )
!= SY240 )
| ( ( comp_real_complex_a @ ( comp_a_complex_real @ SY241 @ SV29 ) @ SY239 )
= ( comp_a_complex_a @ SY241 @ SY240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(562,plain,
! [SV30: a > complex] :
( ( ! [SY242: complex > a,SY243: complex > complex,SY244: real > complex] :
( ( ( comp_a1063143865omplex @ SV30 @ SY242 )
!= SY243 )
| ( ( comp_a_complex_real @ SV30 @ ( comp_complex_a_real @ SY242 @ SY244 ) )
= ( comp_c595887981x_real @ SY243 @ SY244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(563,plain,
! [SV31: real > complex] :
( ( ~ ( path_s36253918omplex @ SV31 )
| ~ ( ( ( path_p769714271omplex @ SV31 )
!= ( path_p797330068omplex @ SV31 ) ) )
| ( path_arc_complex @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(564,plain,
! [SV32: real > complex] :
( ( ~ ( ( ( path_p769714271omplex @ SV32 )
!= ( path_p797330068omplex @ SV32 ) ) )
| ( ( path_s36253918omplex @ SV32 )
= ( path_arc_complex @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(565,plain,
! [SV33: a > complex] :
( ( ! [SY245: real > a,SY246: real > complex,SY247: a > real] :
( ( ( comp_a_complex_real @ SV33 @ SY245 )
!= SY246 )
| ( ( comp_a_complex_a @ SV33 @ ( comp_real_a_a @ SY245 @ SY247 ) )
= ( comp_real_complex_a @ SY246 @ SY247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(566,plain,
! [SV34: a > complex] :
( ( ! [SY248: real > a,SY249: real > complex,SY250: complex > real] :
( ( ( comp_a_complex_real @ SV34 @ SY248 )
!= SY249 )
| ( ( comp_a1063143865omplex @ SV34 @ ( comp_real_a_complex @ SY248 @ SY250 ) )
= ( comp_r667767405omplex @ SY249 @ SY250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(567,plain,
! [SV35: a > complex] :
( ( ! [SY251: real > a,SY252: a > complex,SY253: real > a] :
( ( ( comp_a_complex_real @ SV35 @ SY251 )
!= ( comp_a_complex_real @ SY252 @ SY253 ) )
| ! [SY254: real] :
( ( SV35 @ ( SY251 @ SY254 ) )
= ( SY252 @ ( SY253 @ SY254 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(568,plain,
! [SV36: real > complex] :
( ( ~ ( path_s36253918omplex @ SV36 )
| ( path_arc_complex @ SV36 )
| ( ( path_p769714271omplex @ SV36 )
= ( path_p797330068omplex @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(569,plain,
! [SV37: a > complex] :
( ( ! [SY255: real > a,SY256: real > complex,SY257: real] :
( ( ( comp_a_complex_real @ SV37 @ SY255 )
!= SY256 )
| ( ( SV37 @ ( SY255 @ SY257 ) )
= ( SY256 @ SY257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(570,plain,
! [SV38: complex > a] :
( ( ! [SY258: real > complex] :
( ~ ( real_V1327653935plex_a @ SV38 )
| ( ( path_pathfinish_a @ ( comp_complex_a_real @ SV38 @ SY258 ) )
= ( SV38 @ ( path_p769714271omplex @ SY258 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(571,plain,
! [SV39: complex > complex] :
( ( ! [SY259: real > complex] :
( ~ ( real_V670066493omplex @ SV39 )
| ( ( path_p769714271omplex @ ( comp_c595887981x_real @ SV39 @ SY259 ) )
= ( SV39 @ ( path_p769714271omplex @ SY259 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(572,plain,
! [SV40: complex > a] :
( ( ! [SY260: real > complex,SY261: real > a,SY262: a > complex] :
( ( ( comp_complex_a_real @ SV40 @ SY260 )
!= SY261 )
| ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SY262 @ SV40 ) @ SY260 )
= ( comp_a_complex_real @ SY262 @ SY261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(573,plain,
! [SV41: a > complex] :
( ( ! [SY263: real > a,SY264: real,SY265: a > complex,SY266: a > a,SY267: a] :
( ( ( SV41 @ ( SY263 @ SY264 ) )
!= ( SY265 @ ( SY266 @ SY267 ) ) )
| ( ( comp_a_complex_real @ SV41 @ SY263 @ SY264 )
= ( comp_a_complex_a @ SY265 @ SY266 @ SY267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(574,plain,
( ( ! [SV42: real > complex] :
( ( path_arc_complex @ SV42 )
= ( ~ ( ~ ( path_s36253918omplex @ SV42 )
| ~ ( ( ( path_p769714271omplex @ SV42 )
!= ( path_p797330068omplex @ SV42 ) ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[509]) ).
thf(575,plain,
( ( path_arc_complex
= ( ^ [SX0: real > complex] :
~ ( ~ ( path_s36253918omplex @ SX0 )
| ~ ( ( ( path_p769714271omplex @ SX0 )
!= ( path_p797330068omplex @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[509]) ).
thf(576,plain,
! [SV43: real > a] :
( ( ! [SY268: set_real,SY269: set_a,SY270: a > complex,SY271: set_complex] :
( ~ ( bij_betw_real_a @ SV43 @ SY268 @ SY269 )
| ( ( bij_betw_a_complex @ SY270 @ SY269 @ SY271 )
= ( bij_be122140626omplex @ ( comp_a_complex_real @ SY270 @ SV43 ) @ SY268 @ SY271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(577,plain,
! [SV44: a > complex] :
( ( ! [SY272: real > a,SY273: a > complex,SY274: real > a,SY275: real] :
( ( ( comp_a_complex_real @ SV44 @ SY272 )
!= ( comp_a_complex_real @ SY273 @ SY274 ) )
| ( ( SV44 @ ( SY272 @ SY275 ) )
= ( SY273 @ ( SY274 @ SY275 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(578,plain,
! [SV45: complex > a] :
( ( ! [SY276: real > complex] :
( ~ ( real_V1327653935plex_a @ SV45 )
| ( ( path_pathstart_a @ ( comp_complex_a_real @ SV45 @ SY276 ) )
= ( SV45 @ ( path_p797330068omplex @ SY276 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(579,plain,
! [SV46: a > complex] :
( ( ! [SY277: real > a] :
( ~ ( real_V1477106445omplex @ SV46 )
| ( ( path_p797330068omplex @ ( comp_a_complex_real @ SV46 @ SY277 ) )
= ( SV46 @ ( path_pathstart_a @ SY277 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(580,plain,
! [SV47: complex > complex] :
( ( ! [SY278: a > complex,SY279: a > complex,SY280: real > a] :
( ( ( comp_c124850173plex_a @ SV47 @ SY278 )
!= SY279 )
| ( ( comp_c595887981x_real @ SV47 @ ( comp_a_complex_real @ SY278 @ SY280 ) )
= ( comp_a_complex_real @ SY279 @ SY280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(581,plain,
! [SV48: a > complex] :
( ( ! [SY281: real > a,SY282: real,SY283: a > complex,SY284: complex > a,SY285: complex] :
( ( ( SV48 @ ( SY281 @ SY282 ) )
!= ( SY283 @ ( SY284 @ SY285 ) ) )
| ( ( comp_a_complex_real @ SV48 @ SY281 @ SY282 )
= ( comp_a1063143865omplex @ SY283 @ SY284 @ SY285 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(582,plain,
! [SV49: real > a] :
( ( ! [SY286: complex > real,SY287: complex > a,SY288: a > complex] :
( ( ( comp_real_a_complex @ SV49 @ SY286 )
!= SY287 )
| ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SY288 @ SV49 ) @ SY286 )
= ( comp_a1063143865omplex @ SY288 @ SY287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(583,plain,
! [SV50: real > a] :
( ( ! [SY289: a > complex] :
( ~ ( real_V779700657real_a @ SV50 )
| ~ ( real_V1477106445omplex @ SY289 )
| ( real_V1948715323omplex @ ( comp_a_complex_real @ SY289 @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(584,plain,
! [SV51: real > a] :
( ( ! [SY290: complex > real,SY291: complex,SY292: a > a,SY293: complex > a,SY294: a > complex] :
( ( ( SV51 @ ( SY290 @ SY291 ) )
!= ( SY292 @ ( SY293 @ SY291 ) ) )
| ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SY294 @ SV51 ) @ SY290 @ SY291 )
= ( comp_a1063143865omplex @ ( comp_a_complex_a @ SY294 @ SY292 ) @ SY293 @ SY291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(585,plain,
! [SV52: real > complex] :
( ( ~ ( path_arc_complex @ SV52 )
| ( ( path_p769714271omplex @ SV52 )
!= ( path_p797330068omplex @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(586,plain,
! [SV53: complex > a] :
( ( ! [SY295: real > complex,SY296: real,SY297: a > a,SY298: real > a,SY299: a > complex] :
( ( ( SV53 @ ( SY295 @ SY296 ) )
!= ( SY297 @ ( SY298 @ SY296 ) ) )
| ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SY299 @ SV53 ) @ SY295 @ SY296 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SY299 @ SY297 ) @ SY298 @ SY296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(587,plain,
! [SV54: a > complex] :
( ( ! [SY300: real > a,SY301: real,SY302: a > complex,SY303: real > a,SY304: real] :
( ( ( SV54 @ ( SY300 @ SY301 ) )
!= ( SY302 @ ( SY303 @ SY304 ) ) )
| ( ( comp_a_complex_real @ SV54 @ SY300 @ SY301 )
= ( comp_a_complex_real @ SY302 @ SY303 @ SY304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(588,plain,
! [SV55: a > complex] :
( ( ! [SY305: real > a,SY306: real > complex,SY307: real] :
( ( ( comp_a_complex_real @ SV55 @ SY305 )
!= ( comp_c595887981x_real @ id_complex @ SY306 ) )
| ( ( SV55 @ ( SY305 @ SY307 ) )
= ( SY306 @ SY307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(589,plain,
! [SV56: a > complex] :
( ( ! [SY308: real > a,SY309: a > complex,SY310: real > a,SY311: complex > real,SY312: complex > a] :
( ( ( comp_a_complex_real @ SV56 @ SY308 )
!= ( comp_a_complex_real @ SY309 @ SY310 ) )
| ( ( comp_real_a_complex @ SY310 @ SY311 )
!= SY312 )
| ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SY308 @ SY311 ) )
= ( comp_a1063143865omplex @ SY309 @ SY312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(590,plain,
! [SV57: real > a] :
( ( ! [SY313: real > real,SY314: real,SY315: a > a,SY316: real > a,SY317: a > complex] :
( ( ( SV57 @ ( SY313 @ SY314 ) )
!= ( SY315 @ ( SY316 @ SY314 ) ) )
| ( ( comp_r701421291x_real @ ( comp_a_complex_real @ SY317 @ SV57 ) @ SY313 @ SY314 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SY317 @ SY315 ) @ SY316 @ SY314 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(591,plain,
! [SV58: a > complex] :
( ( ! [SY318: complex > a,SY319: complex,SY320: a > complex,SY321: real > a,SY322: real] :
( ( ( SV58 @ ( SY318 @ SY319 ) )
!= ( SY320 @ ( SY321 @ SY322 ) ) )
| ( ( comp_a1063143865omplex @ SV58 @ SY318 @ SY319 )
= ( comp_a_complex_real @ SY320 @ SY321 @ SY322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(592,plain,
! [SV59: a > complex] :
( ( ! [SY323: real > a,SY324: real > complex,SY325: real > real] :
( ( ( comp_a_complex_real @ SV59 @ SY323 )
!= SY324 )
| ( ( comp_a_complex_real @ SV59 @ ( comp_real_a_real @ SY323 @ SY325 ) )
= ( comp_r701421291x_real @ SY324 @ SY325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(593,plain,
! [SV60: real > a] :
( ( ! [SY326: set_real,SY327: set_a,SY328: a > complex,SY329: set_complex] :
( ~ ( bij_betw_real_a @ SV60 @ SY326 @ SY327 )
| ~ ( bij_betw_a_complex @ SY328 @ SY327 @ SY329 )
| ( bij_be122140626omplex @ ( comp_a_complex_real @ SY328 @ SV60 ) @ SY326 @ SY329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(594,plain,
! [SV61: a > complex] :
( ( ( comp_a_complex_real @ SV61 )
= ( ^ [SY330: real > a,SY331: real] : ( SV61 @ ( SY330 @ SY331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(595,plain,
! [SV62: real > complex,SV2: complex > complex] :
( ( ( path_p769714271omplex @ ( comp_c595887981x_real @ SV2 @ SV62 ) )
= ( SV2 @ ( path_p769714271omplex @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(596,plain,
! [SV63: real > a,SV3: a > complex] :
( ( ( path_p769714271omplex @ ( comp_a_complex_real @ SV3 @ SV63 ) )
= ( SV3 @ ( path_pathfinish_a @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(597,plain,
! [SV64: real > complex,SV4: complex > a] :
( ( ( path_pathfinish_a @ ( comp_complex_a_real @ SV4 @ SV64 ) )
= ( SV4 @ ( path_p769714271omplex @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(598,plain,
! [SV65: real > complex,SV5: complex > complex] :
( ( ( path_p797330068omplex @ ( comp_c595887981x_real @ SV5 @ SV65 ) )
= ( SV5 @ ( path_p797330068omplex @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(599,plain,
! [SV66: real > a,SV6: a > complex] :
( ( ( path_p797330068omplex @ ( comp_a_complex_real @ SV6 @ SV66 ) )
= ( SV6 @ ( path_pathstart_a @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(600,plain,
! [SV67: real > complex,SV7: complex > a] :
( ( ( path_pathstart_a @ ( comp_complex_a_real @ SV7 @ SV67 ) )
= ( SV7 @ ( path_p797330068omplex @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(601,plain,
! [SV68: a > complex] :
( ( ( comp_a_complex_real @ SV68 )
= ( ^ [SY332: real > a,SY333: real] : ( SV68 @ ( SY332 @ SY333 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(602,plain,
! [SV69: real > a,SV9: a > complex] :
( ( ! [SY334: real > real] :
( ( comp_r701421291x_real @ ( comp_a_complex_real @ SV9 @ SV69 ) @ SY334 )
= ( comp_a_complex_real @ SV9 @ ( comp_real_a_real @ SV69 @ SY334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(603,plain,
! [SV70: real > a,SV10: a > complex] :
( ( ! [SY335: complex > real] :
( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV10 @ SV70 ) @ SY335 )
= ( comp_a1063143865omplex @ SV10 @ ( comp_real_a_complex @ SV70 @ SY335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(604,plain,
! [SV71: complex > a,SV11: a > complex] :
( ( ! [SY336: real > complex] :
( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV11 @ SV71 ) @ SY336 )
= ( comp_a_complex_real @ SV11 @ ( comp_complex_a_real @ SV71 @ SY336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(605,plain,
! [SV72: a > complex,SV12: complex > a] :
( ( ! [SY337: real > a] :
( ( comp_a_a_real @ ( comp_complex_a_a @ SV12 @ SV72 ) @ SY337 )
= ( comp_complex_a_real @ SV12 @ ( comp_a_complex_real @ SV72 @ SY337 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(606,plain,
! [SV73: a > complex,SV13: complex > complex] :
( ( ! [SY338: real > a] :
( ( comp_a_complex_real @ ( comp_c124850173plex_a @ SV13 @ SV73 ) @ SY338 )
= ( comp_c595887981x_real @ SV13 @ ( comp_a_complex_real @ SV73 @ SY338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(607,plain,
! [SV74: a > a,SV14: a > complex] :
( ( ! [SY339: real > a] :
( ( comp_a_complex_real @ ( comp_a_complex_a @ SV14 @ SV74 ) @ SY339 )
= ( comp_a_complex_real @ SV14 @ ( comp_a_a_real @ SV74 @ SY339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(608,plain,
! [SV75: complex,SV15: complex] :
( ( ( path_p769714271omplex @ ( path_rectpath @ SV15 @ SV75 ) )
= SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(609,plain,
! [SV76: complex,SV16: complex] :
( ( ( path_p797330068omplex @ ( path_rectpath @ SV16 @ SV76 ) )
= SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(610,plain,
! [SV77: a > complex,SV17: complex > complex] :
( ( ! [SY340: real > a] :
( ( comp_c595887981x_real @ SV17 @ ( comp_a_complex_real @ SV77 @ SY340 ) )
= ( comp_a_complex_real @ ( comp_c124850173plex_a @ SV17 @ SV77 ) @ SY340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(611,plain,
! [SV78: a > complex,SV18: complex > a] :
( ( ! [SY341: real > a] :
( ( comp_complex_a_real @ SV18 @ ( comp_a_complex_real @ SV78 @ SY341 ) )
= ( comp_a_a_real @ ( comp_complex_a_a @ SV18 @ SV78 ) @ SY341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(612,plain,
! [SV79: complex > a,SV19: a > complex] :
( ( ! [SY342: real > complex] :
( ( comp_a_complex_real @ SV19 @ ( comp_complex_a_real @ SV79 @ SY342 ) )
= ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV19 @ SV79 ) @ SY342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(613,plain,
! [SV80: real > a,SV20: a > complex] :
( ( ! [SY343: real > real] :
( ( comp_a_complex_real @ SV20 @ ( comp_real_a_real @ SV80 @ SY343 ) )
= ( comp_r701421291x_real @ ( comp_a_complex_real @ SV20 @ SV80 ) @ SY343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(614,plain,
! [SV81: a > a,SV21: a > complex] :
( ( ! [SY344: real > a] :
( ( comp_a_complex_real @ SV21 @ ( comp_a_a_real @ SV81 @ SY344 ) )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SV21 @ SV81 ) @ SY344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(615,plain,
! [SV82: real > a,SV22: a > complex] :
( ( ! [SY345: complex > real] :
( ( comp_a1063143865omplex @ SV22 @ ( comp_real_a_complex @ SV82 @ SY345 ) )
= ( comp_r667767405omplex @ ( comp_a_complex_real @ SV22 @ SV82 ) @ SY345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(616,plain,
! [SV83: complex] :
( ( ( comp_a1063143865omplex @ poinca1910941596x_of_a @ poinca837721858l_of_a @ SV83 )
= ( id_complex @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(617,plain,
! [SV84: a] :
( ( ( comp_complex_a_a @ poinca837721858l_of_a @ poinca1910941596x_of_a @ SV84 )
= ( id_a @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(618,plain,
! [SV85: real > complex,SV25: complex > complex] :
( ( ~ ( real_V670066493omplex @ SV25 )
| ( ( path_p797330068omplex @ ( comp_c595887981x_real @ SV25 @ SV85 ) )
= ( SV25 @ ( path_p797330068omplex @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(619,plain,
! [SV86: real > a,SV26: a > complex] :
( ( ! [SY346: set_real] :
( ~ ( inj_on_real_complex @ ( comp_a_complex_real @ SV26 @ SV86 ) @ SY346 )
| ( inj_on_real_a @ SV86 @ SY346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(620,plain,
! [SV87: a > real,SV27: real > a] :
( ( ! [SY347: a,SY348: a > a,SY349: a > a,SY350: a > complex] :
( ( ( SV27 @ ( SV87 @ SY347 ) )
!= ( SY348 @ ( SY349 @ SY347 ) ) )
| ( ( comp_real_complex_a @ ( comp_a_complex_real @ SY350 @ SV27 ) @ SV87 @ SY347 )
= ( comp_a_complex_a @ ( comp_a_complex_a @ SY350 @ SY348 ) @ SY349 @ SY347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(621,plain,
! [SV88: real > a,SV28: a > complex] :
( ( ~ ( real_V1477106445omplex @ SV28 )
| ( ( path_p769714271omplex @ ( comp_a_complex_real @ SV28 @ SV88 ) )
= ( SV28 @ ( path_pathfinish_a @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(622,plain,
! [SV89: a > real,SV29: real > a] :
( ( ! [SY351: a > a,SY352: a > complex] :
( ( ( comp_real_a_a @ SV29 @ SV89 )
!= SY351 )
| ( ( comp_real_complex_a @ ( comp_a_complex_real @ SY352 @ SV29 ) @ SV89 )
= ( comp_a_complex_a @ SY352 @ SY351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(623,plain,
! [SV90: complex > a,SV30: a > complex] :
( ( ! [SY353: complex > complex,SY354: real > complex] :
( ( ( comp_a1063143865omplex @ SV30 @ SV90 )
!= SY353 )
| ( ( comp_a_complex_real @ SV30 @ ( comp_complex_a_real @ SV90 @ SY354 ) )
= ( comp_c595887981x_real @ SY353 @ SY354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(624,plain,
! [SV31: real > complex] :
( ( ( ~ ( path_s36253918omplex @ SV31 ) )
= $true )
| ( ( ~ ( ( ( path_p769714271omplex @ SV31 )
!= ( path_p797330068omplex @ SV31 ) ) )
| ( path_arc_complex @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[563]) ).
thf(625,plain,
! [SV32: real > complex] :
( ( ( ~ ( ( ( path_p769714271omplex @ SV32 )
!= ( path_p797330068omplex @ SV32 ) ) ) )
= $true )
| ( ( ( path_s36253918omplex @ SV32 )
= ( path_arc_complex @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(626,plain,
! [SV91: real > a,SV33: a > complex] :
( ( ! [SY355: real > complex,SY356: a > real] :
( ( ( comp_a_complex_real @ SV33 @ SV91 )
!= SY355 )
| ( ( comp_a_complex_a @ SV33 @ ( comp_real_a_a @ SV91 @ SY356 ) )
= ( comp_real_complex_a @ SY355 @ SY356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(627,plain,
! [SV92: real > a,SV34: a > complex] :
( ( ! [SY357: real > complex,SY358: complex > real] :
( ( ( comp_a_complex_real @ SV34 @ SV92 )
!= SY357 )
| ( ( comp_a1063143865omplex @ SV34 @ ( comp_real_a_complex @ SV92 @ SY358 ) )
= ( comp_r667767405omplex @ SY357 @ SY358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(628,plain,
! [SV93: real > a,SV35: a > complex] :
( ( ! [SY359: a > complex,SY360: real > a] :
( ( ( comp_a_complex_real @ SV35 @ SV93 )
!= ( comp_a_complex_real @ SY359 @ SY360 ) )
| ! [SY361: real] :
( ( SV35 @ ( SV93 @ SY361 ) )
= ( SY359 @ ( SY360 @ SY361 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(629,plain,
! [SV36: real > complex] :
( ( ( ~ ( path_s36253918omplex @ SV36 ) )
= $true )
| ( ( ( path_arc_complex @ SV36 )
| ( ( path_p769714271omplex @ SV36 )
= ( path_p797330068omplex @ SV36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[568]) ).
thf(630,plain,
! [SV94: real > a,SV37: a > complex] :
( ( ! [SY362: real > complex,SY363: real] :
( ( ( comp_a_complex_real @ SV37 @ SV94 )
!= SY362 )
| ( ( SV37 @ ( SV94 @ SY363 ) )
= ( SY362 @ SY363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(631,plain,
! [SV95: real > complex,SV38: complex > a] :
( ( ~ ( real_V1327653935plex_a @ SV38 )
| ( ( path_pathfinish_a @ ( comp_complex_a_real @ SV38 @ SV95 ) )
= ( SV38 @ ( path_p769714271omplex @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(632,plain,
! [SV96: real > complex,SV39: complex > complex] :
( ( ~ ( real_V670066493omplex @ SV39 )
| ( ( path_p769714271omplex @ ( comp_c595887981x_real @ SV39 @ SV96 ) )
= ( SV39 @ ( path_p769714271omplex @ SV96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(633,plain,
! [SV97: real > complex,SV40: complex > a] :
( ( ! [SY364: real > a,SY365: a > complex] :
( ( ( comp_complex_a_real @ SV40 @ SV97 )
!= SY364 )
| ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SY365 @ SV40 ) @ SV97 )
= ( comp_a_complex_real @ SY365 @ SY364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(634,plain,
! [SV98: real > a,SV41: a > complex] :
( ( ! [SY366: real,SY367: a > complex,SY368: a > a,SY369: a] :
( ( ( SV41 @ ( SV98 @ SY366 ) )
!= ( SY367 @ ( SY368 @ SY369 ) ) )
| ( ( comp_a_complex_real @ SV41 @ SV98 @ SY366 )
= ( comp_a_complex_a @ SY367 @ SY368 @ SY369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(635,plain,
! [SV99: real > complex] :
( ( ( path_arc_complex @ SV99 )
= ( ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(636,plain,
! [SV100: set_real,SV43: real > a] :
( ( ! [SY370: set_a,SY371: a > complex,SY372: set_complex] :
( ~ ( bij_betw_real_a @ SV43 @ SV100 @ SY370 )
| ( ( bij_betw_a_complex @ SY371 @ SY370 @ SY372 )
= ( bij_be122140626omplex @ ( comp_a_complex_real @ SY371 @ SV43 ) @ SV100 @ SY372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(637,plain,
! [SV101: real > a,SV44: a > complex] :
( ( ! [SY373: a > complex,SY374: real > a,SY375: real] :
( ( ( comp_a_complex_real @ SV44 @ SV101 )
!= ( comp_a_complex_real @ SY373 @ SY374 ) )
| ( ( SV44 @ ( SV101 @ SY375 ) )
= ( SY373 @ ( SY374 @ SY375 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(638,plain,
! [SV102: real > complex,SV45: complex > a] :
( ( ~ ( real_V1327653935plex_a @ SV45 )
| ( ( path_pathstart_a @ ( comp_complex_a_real @ SV45 @ SV102 ) )
= ( SV45 @ ( path_p797330068omplex @ SV102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(639,plain,
! [SV103: real > a,SV46: a > complex] :
( ( ~ ( real_V1477106445omplex @ SV46 )
| ( ( path_p797330068omplex @ ( comp_a_complex_real @ SV46 @ SV103 ) )
= ( SV46 @ ( path_pathstart_a @ SV103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(640,plain,
! [SV104: a > complex,SV47: complex > complex] :
( ( ! [SY376: a > complex,SY377: real > a] :
( ( ( comp_c124850173plex_a @ SV47 @ SV104 )
!= SY376 )
| ( ( comp_c595887981x_real @ SV47 @ ( comp_a_complex_real @ SV104 @ SY377 ) )
= ( comp_a_complex_real @ SY376 @ SY377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(641,plain,
! [SV105: real > a,SV48: a > complex] :
( ( ! [SY378: real,SY379: a > complex,SY380: complex > a,SY381: complex] :
( ( ( SV48 @ ( SV105 @ SY378 ) )
!= ( SY379 @ ( SY380 @ SY381 ) ) )
| ( ( comp_a_complex_real @ SV48 @ SV105 @ SY378 )
= ( comp_a1063143865omplex @ SY379 @ SY380 @ SY381 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(642,plain,
! [SV106: complex > real,SV49: real > a] :
( ( ! [SY382: complex > a,SY383: a > complex] :
( ( ( comp_real_a_complex @ SV49 @ SV106 )
!= SY382 )
| ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SY383 @ SV49 ) @ SV106 )
= ( comp_a1063143865omplex @ SY383 @ SY382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(643,plain,
! [SV107: a > complex,SV50: real > a] :
( ( ~ ( real_V779700657real_a @ SV50 )
| ~ ( real_V1477106445omplex @ SV107 )
| ( real_V1948715323omplex @ ( comp_a_complex_real @ SV107 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(644,plain,
! [SV108: complex > real,SV51: real > a] :
( ( ! [SY384: complex,SY385: a > a,SY386: complex > a,SY387: a > complex] :
( ( ( SV51 @ ( SV108 @ SY384 ) )
!= ( SY385 @ ( SY386 @ SY384 ) ) )
| ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SY387 @ SV51 ) @ SV108 @ SY384 )
= ( comp_a1063143865omplex @ ( comp_a_complex_a @ SY387 @ SY385 ) @ SY386 @ SY384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(645,plain,
! [SV52: real > complex] :
( ( ( ~ ( path_arc_complex @ SV52 ) )
= $true )
| ( ( ( path_p769714271omplex @ SV52 )
!= ( path_p797330068omplex @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(646,plain,
! [SV109: real > complex,SV53: complex > a] :
( ( ! [SY388: real,SY389: a > a,SY390: real > a,SY391: a > complex] :
( ( ( SV53 @ ( SV109 @ SY388 ) )
!= ( SY389 @ ( SY390 @ SY388 ) ) )
| ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SY391 @ SV53 ) @ SV109 @ SY388 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SY391 @ SY389 ) @ SY390 @ SY388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(647,plain,
! [SV110: real > a,SV54: a > complex] :
( ( ! [SY392: real,SY393: a > complex,SY394: real > a,SY395: real] :
( ( ( SV54 @ ( SV110 @ SY392 ) )
!= ( SY393 @ ( SY394 @ SY395 ) ) )
| ( ( comp_a_complex_real @ SV54 @ SV110 @ SY392 )
= ( comp_a_complex_real @ SY393 @ SY394 @ SY395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(648,plain,
! [SV111: real > a,SV55: a > complex] :
( ( ! [SY396: real > complex,SY397: real] :
( ( ( comp_a_complex_real @ SV55 @ SV111 )
!= ( comp_c595887981x_real @ id_complex @ SY396 ) )
| ( ( SV55 @ ( SV111 @ SY397 ) )
= ( SY396 @ SY397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(649,plain,
! [SV112: real > a,SV56: a > complex] :
( ( ! [SY398: a > complex,SY399: real > a,SY400: complex > real,SY401: complex > a] :
( ( ( comp_a_complex_real @ SV56 @ SV112 )
!= ( comp_a_complex_real @ SY398 @ SY399 ) )
| ( ( comp_real_a_complex @ SY399 @ SY400 )
!= SY401 )
| ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SY400 ) )
= ( comp_a1063143865omplex @ SY398 @ SY401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(650,plain,
! [SV113: real > real,SV57: real > a] :
( ( ! [SY402: real,SY403: a > a,SY404: real > a,SY405: a > complex] :
( ( ( SV57 @ ( SV113 @ SY402 ) )
!= ( SY403 @ ( SY404 @ SY402 ) ) )
| ( ( comp_r701421291x_real @ ( comp_a_complex_real @ SY405 @ SV57 ) @ SV113 @ SY402 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SY405 @ SY403 ) @ SY404 @ SY402 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(651,plain,
! [SV114: complex > a,SV58: a > complex] :
( ( ! [SY406: complex,SY407: a > complex,SY408: real > a,SY409: real] :
( ( ( SV58 @ ( SV114 @ SY406 ) )
!= ( SY407 @ ( SY408 @ SY409 ) ) )
| ( ( comp_a1063143865omplex @ SV58 @ SV114 @ SY406 )
= ( comp_a_complex_real @ SY407 @ SY408 @ SY409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(652,plain,
! [SV115: real > a,SV59: a > complex] :
( ( ! [SY410: real > complex,SY411: real > real] :
( ( ( comp_a_complex_real @ SV59 @ SV115 )
!= SY410 )
| ( ( comp_a_complex_real @ SV59 @ ( comp_real_a_real @ SV115 @ SY411 ) )
= ( comp_r701421291x_real @ SY410 @ SY411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(653,plain,
! [SV116: set_real,SV60: real > a] :
( ( ! [SY412: set_a,SY413: a > complex,SY414: set_complex] :
( ~ ( bij_betw_real_a @ SV60 @ SV116 @ SY412 )
| ~ ( bij_betw_a_complex @ SY413 @ SY412 @ SY414 )
| ( bij_be122140626omplex @ ( comp_a_complex_real @ SY413 @ SV60 ) @ SV116 @ SY414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(654,plain,
! [SV61: a > complex] :
( ( ! [SV117: real > a] :
( ( comp_a_complex_real @ SV61 @ SV117 )
= ( ^ [SY415: real] : ( SV61 @ ( SV117 @ SY415 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[594]) ).
thf(655,plain,
! [SV61: a > complex] :
( ( ( comp_a_complex_real @ SV61 )
= ( ^ [SY330: real > a,SY331: real] : ( SV61 @ ( SY330 @ SY331 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[594]) ).
thf(656,plain,
! [SV68: a > complex] :
( ( ! [SV118: real > a] :
( ( comp_a_complex_real @ SV68 @ SV118 )
= ( ^ [SY416: real] : ( SV68 @ ( SV118 @ SY416 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[601]) ).
thf(657,plain,
! [SV68: a > complex] :
( ( ( comp_a_complex_real @ SV68 )
= ( ^ [SY332: real > a,SY333: real] : ( SV68 @ ( SY332 @ SY333 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[601]) ).
thf(658,plain,
! [SV119: real > real,SV69: real > a,SV9: a > complex] :
( ( ( comp_r701421291x_real @ ( comp_a_complex_real @ SV9 @ SV69 ) @ SV119 )
= ( comp_a_complex_real @ SV9 @ ( comp_real_a_real @ SV69 @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(659,plain,
! [SV120: complex > real,SV70: real > a,SV10: a > complex] :
( ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV10 @ SV70 ) @ SV120 )
= ( comp_a1063143865omplex @ SV10 @ ( comp_real_a_complex @ SV70 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(660,plain,
! [SV121: real > complex,SV71: complex > a,SV11: a > complex] :
( ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV11 @ SV71 ) @ SV121 )
= ( comp_a_complex_real @ SV11 @ ( comp_complex_a_real @ SV71 @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(661,plain,
! [SV122: real > a,SV72: a > complex,SV12: complex > a] :
( ( ( comp_a_a_real @ ( comp_complex_a_a @ SV12 @ SV72 ) @ SV122 )
= ( comp_complex_a_real @ SV12 @ ( comp_a_complex_real @ SV72 @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(662,plain,
! [SV123: real > a,SV73: a > complex,SV13: complex > complex] :
( ( ( comp_a_complex_real @ ( comp_c124850173plex_a @ SV13 @ SV73 ) @ SV123 )
= ( comp_c595887981x_real @ SV13 @ ( comp_a_complex_real @ SV73 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(663,plain,
! [SV124: real > a,SV74: a > a,SV14: a > complex] :
( ( ( comp_a_complex_real @ ( comp_a_complex_a @ SV14 @ SV74 ) @ SV124 )
= ( comp_a_complex_real @ SV14 @ ( comp_a_a_real @ SV74 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(664,plain,
! [SV125: real > a,SV77: a > complex,SV17: complex > complex] :
( ( ( comp_c595887981x_real @ SV17 @ ( comp_a_complex_real @ SV77 @ SV125 ) )
= ( comp_a_complex_real @ ( comp_c124850173plex_a @ SV17 @ SV77 ) @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(665,plain,
! [SV126: real > a,SV78: a > complex,SV18: complex > a] :
( ( ( comp_complex_a_real @ SV18 @ ( comp_a_complex_real @ SV78 @ SV126 ) )
= ( comp_a_a_real @ ( comp_complex_a_a @ SV18 @ SV78 ) @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(666,plain,
! [SV127: real > complex,SV79: complex > a,SV19: a > complex] :
( ( ( comp_a_complex_real @ SV19 @ ( comp_complex_a_real @ SV79 @ SV127 ) )
= ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV19 @ SV79 ) @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(667,plain,
! [SV128: real > real,SV80: real > a,SV20: a > complex] :
( ( ( comp_a_complex_real @ SV20 @ ( comp_real_a_real @ SV80 @ SV128 ) )
= ( comp_r701421291x_real @ ( comp_a_complex_real @ SV20 @ SV80 ) @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(668,plain,
! [SV129: real > a,SV81: a > a,SV21: a > complex] :
( ( ( comp_a_complex_real @ SV21 @ ( comp_a_a_real @ SV81 @ SV129 ) )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SV21 @ SV81 ) @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(669,plain,
! [SV130: complex > real,SV82: real > a,SV22: a > complex] :
( ( ( comp_a1063143865omplex @ SV22 @ ( comp_real_a_complex @ SV82 @ SV130 ) )
= ( comp_r667767405omplex @ ( comp_a_complex_real @ SV22 @ SV82 ) @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(670,plain,
! [SV85: real > complex,SV25: complex > complex] :
( ( ( ~ ( real_V670066493omplex @ SV25 ) )
= $true )
| ( ( ( path_p797330068omplex @ ( comp_c595887981x_real @ SV25 @ SV85 ) )
= ( SV25 @ ( path_p797330068omplex @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(671,plain,
! [SV131: set_real,SV86: real > a,SV26: a > complex] :
( ( ~ ( inj_on_real_complex @ ( comp_a_complex_real @ SV26 @ SV86 ) @ SV131 )
| ( inj_on_real_a @ SV86 @ SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(672,plain,
! [SV132: a,SV87: a > real,SV27: real > a] :
( ( ! [SY417: a > a,SY418: a > a,SY419: a > complex] :
( ( ( SV27 @ ( SV87 @ SV132 ) )
!= ( SY417 @ ( SY418 @ SV132 ) ) )
| ( ( comp_real_complex_a @ ( comp_a_complex_real @ SY419 @ SV27 ) @ SV87 @ SV132 )
= ( comp_a_complex_a @ ( comp_a_complex_a @ SY419 @ SY417 ) @ SY418 @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(673,plain,
! [SV88: real > a,SV28: a > complex] :
( ( ( ~ ( real_V1477106445omplex @ SV28 ) )
= $true )
| ( ( ( path_p769714271omplex @ ( comp_a_complex_real @ SV28 @ SV88 ) )
= ( SV28 @ ( path_pathfinish_a @ SV88 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(674,plain,
! [SV133: a > a,SV89: a > real,SV29: real > a] :
( ( ! [SY420: a > complex] :
( ( ( comp_real_a_a @ SV29 @ SV89 )
!= SV133 )
| ( ( comp_real_complex_a @ ( comp_a_complex_real @ SY420 @ SV29 ) @ SV89 )
= ( comp_a_complex_a @ SY420 @ SV133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(675,plain,
! [SV134: complex > complex,SV90: complex > a,SV30: a > complex] :
( ( ! [SY421: real > complex] :
( ( ( comp_a1063143865omplex @ SV30 @ SV90 )
!= SV134 )
| ( ( comp_a_complex_real @ SV30 @ ( comp_complex_a_real @ SV90 @ SY421 ) )
= ( comp_c595887981x_real @ SV134 @ SY421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(676,plain,
! [SV31: real > complex] :
( ( ( path_s36253918omplex @ SV31 )
= $false )
| ( ( ~ ( ( ( path_p769714271omplex @ SV31 )
!= ( path_p797330068omplex @ SV31 ) ) )
| ( path_arc_complex @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(677,plain,
! [SV32: real > complex] :
( ( ( ( path_p769714271omplex @ SV32 )
!= ( path_p797330068omplex @ SV32 ) )
= $false )
| ( ( ( path_s36253918omplex @ SV32 )
= ( path_arc_complex @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(678,plain,
! [SV135: real > complex,SV91: real > a,SV33: a > complex] :
( ( ! [SY422: a > real] :
( ( ( comp_a_complex_real @ SV33 @ SV91 )
!= SV135 )
| ( ( comp_a_complex_a @ SV33 @ ( comp_real_a_a @ SV91 @ SY422 ) )
= ( comp_real_complex_a @ SV135 @ SY422 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(679,plain,
! [SV136: real > complex,SV92: real > a,SV34: a > complex] :
( ( ! [SY423: complex > real] :
( ( ( comp_a_complex_real @ SV34 @ SV92 )
!= SV136 )
| ( ( comp_a1063143865omplex @ SV34 @ ( comp_real_a_complex @ SV92 @ SY423 ) )
= ( comp_r667767405omplex @ SV136 @ SY423 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(680,plain,
! [SV137: a > complex,SV93: real > a,SV35: a > complex] :
( ( ! [SY424: real > a] :
( ( ( comp_a_complex_real @ SV35 @ SV93 )
!= ( comp_a_complex_real @ SV137 @ SY424 ) )
| ! [SY425: real] :
( ( SV35 @ ( SV93 @ SY425 ) )
= ( SV137 @ ( SY424 @ SY425 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(681,plain,
! [SV36: real > complex] :
( ( ( path_s36253918omplex @ SV36 )
= $false )
| ( ( ( path_arc_complex @ SV36 )
| ( ( path_p769714271omplex @ SV36 )
= ( path_p797330068omplex @ SV36 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(682,plain,
! [SV138: real > complex,SV94: real > a,SV37: a > complex] :
( ( ! [SY426: real] :
( ( ( comp_a_complex_real @ SV37 @ SV94 )
!= SV138 )
| ( ( SV37 @ ( SV94 @ SY426 ) )
= ( SV138 @ SY426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(683,plain,
! [SV95: real > complex,SV38: complex > a] :
( ( ( ~ ( real_V1327653935plex_a @ SV38 ) )
= $true )
| ( ( ( path_pathfinish_a @ ( comp_complex_a_real @ SV38 @ SV95 ) )
= ( SV38 @ ( path_p769714271omplex @ SV95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[631]) ).
thf(684,plain,
! [SV96: real > complex,SV39: complex > complex] :
( ( ( ~ ( real_V670066493omplex @ SV39 ) )
= $true )
| ( ( ( path_p769714271omplex @ ( comp_c595887981x_real @ SV39 @ SV96 ) )
= ( SV39 @ ( path_p769714271omplex @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[632]) ).
thf(685,plain,
! [SV139: real > a,SV97: real > complex,SV40: complex > a] :
( ( ! [SY427: a > complex] :
( ( ( comp_complex_a_real @ SV40 @ SV97 )
!= SV139 )
| ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SY427 @ SV40 ) @ SV97 )
= ( comp_a_complex_real @ SY427 @ SV139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(686,plain,
! [SV140: real,SV98: real > a,SV41: a > complex] :
( ( ! [SY428: a > complex,SY429: a > a,SY430: a] :
( ( ( SV41 @ ( SV98 @ SV140 ) )
!= ( SY428 @ ( SY429 @ SY430 ) ) )
| ( ( comp_a_complex_real @ SV41 @ SV98 @ SV140 )
= ( comp_a_complex_a @ SY428 @ SY429 @ SY430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(687,plain,
! [SV99: real > complex] :
( ( ~ ( ( path_arc_complex @ SV99 )
| ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) )
| ~ ( ~ ( path_arc_complex @ SV99 )
| ~ ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[635]) ).
thf(688,plain,
! [SV99: real > complex] :
( ( ( path_arc_complex @ SV99 )
= ( ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[635]) ).
thf(689,plain,
! [SV141: set_a,SV100: set_real,SV43: real > a] :
( ( ! [SY431: a > complex,SY432: set_complex] :
( ~ ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
| ( ( bij_betw_a_complex @ SY431 @ SV141 @ SY432 )
= ( bij_be122140626omplex @ ( comp_a_complex_real @ SY431 @ SV43 ) @ SV100 @ SY432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(690,plain,
! [SV142: a > complex,SV101: real > a,SV44: a > complex] :
( ( ! [SY433: real > a,SY434: real] :
( ( ( comp_a_complex_real @ SV44 @ SV101 )
!= ( comp_a_complex_real @ SV142 @ SY433 ) )
| ( ( SV44 @ ( SV101 @ SY434 ) )
= ( SV142 @ ( SY433 @ SY434 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(691,plain,
! [SV102: real > complex,SV45: complex > a] :
( ( ( ~ ( real_V1327653935plex_a @ SV45 ) )
= $true )
| ( ( ( path_pathstart_a @ ( comp_complex_a_real @ SV45 @ SV102 ) )
= ( SV45 @ ( path_p797330068omplex @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(692,plain,
! [SV103: real > a,SV46: a > complex] :
( ( ( ~ ( real_V1477106445omplex @ SV46 ) )
= $true )
| ( ( ( path_p797330068omplex @ ( comp_a_complex_real @ SV46 @ SV103 ) )
= ( SV46 @ ( path_pathstart_a @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(693,plain,
! [SV143: a > complex,SV104: a > complex,SV47: complex > complex] :
( ( ! [SY435: real > a] :
( ( ( comp_c124850173plex_a @ SV47 @ SV104 )
!= SV143 )
| ( ( comp_c595887981x_real @ SV47 @ ( comp_a_complex_real @ SV104 @ SY435 ) )
= ( comp_a_complex_real @ SV143 @ SY435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(694,plain,
! [SV144: real,SV105: real > a,SV48: a > complex] :
( ( ! [SY436: a > complex,SY437: complex > a,SY438: complex] :
( ( ( SV48 @ ( SV105 @ SV144 ) )
!= ( SY436 @ ( SY437 @ SY438 ) ) )
| ( ( comp_a_complex_real @ SV48 @ SV105 @ SV144 )
= ( comp_a1063143865omplex @ SY436 @ SY437 @ SY438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(695,plain,
! [SV145: complex > a,SV106: complex > real,SV49: real > a] :
( ( ! [SY439: a > complex] :
( ( ( comp_real_a_complex @ SV49 @ SV106 )
!= SV145 )
| ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SY439 @ SV49 ) @ SV106 )
= ( comp_a1063143865omplex @ SY439 @ SV145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(696,plain,
! [SV107: a > complex,SV50: real > a] :
( ( ( ~ ( real_V779700657real_a @ SV50 ) )
= $true )
| ( ( ~ ( real_V1477106445omplex @ SV107 )
| ( real_V1948715323omplex @ ( comp_a_complex_real @ SV107 @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(697,plain,
! [SV146: complex,SV108: complex > real,SV51: real > a] :
( ( ! [SY440: a > a,SY441: complex > a,SY442: a > complex] :
( ( ( SV51 @ ( SV108 @ SV146 ) )
!= ( SY440 @ ( SY441 @ SV146 ) ) )
| ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SY442 @ SV51 ) @ SV108 @ SV146 )
= ( comp_a1063143865omplex @ ( comp_a_complex_a @ SY442 @ SY440 ) @ SY441 @ SV146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(698,plain,
! [SV52: real > complex] :
( ( ( path_arc_complex @ SV52 )
= $false )
| ( ( ( path_p769714271omplex @ SV52 )
!= ( path_p797330068omplex @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(699,plain,
! [SV147: real,SV109: real > complex,SV53: complex > a] :
( ( ! [SY443: a > a,SY444: real > a,SY445: a > complex] :
( ( ( SV53 @ ( SV109 @ SV147 ) )
!= ( SY443 @ ( SY444 @ SV147 ) ) )
| ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SY445 @ SV53 ) @ SV109 @ SV147 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SY445 @ SY443 ) @ SY444 @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(700,plain,
! [SV148: real,SV110: real > a,SV54: a > complex] :
( ( ! [SY446: a > complex,SY447: real > a,SY448: real] :
( ( ( SV54 @ ( SV110 @ SV148 ) )
!= ( SY446 @ ( SY447 @ SY448 ) ) )
| ( ( comp_a_complex_real @ SV54 @ SV110 @ SV148 )
= ( comp_a_complex_real @ SY446 @ SY447 @ SY448 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(701,plain,
! [SV149: real > complex,SV111: real > a,SV55: a > complex] :
( ( ! [SY449: real] :
( ( ( comp_a_complex_real @ SV55 @ SV111 )
!= ( comp_c595887981x_real @ id_complex @ SV149 ) )
| ( ( SV55 @ ( SV111 @ SY449 ) )
= ( SV149 @ SY449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(702,plain,
! [SV150: a > complex,SV112: real > a,SV56: a > complex] :
( ( ! [SY450: real > a,SY451: complex > real,SY452: complex > a] :
( ( ( comp_a_complex_real @ SV56 @ SV112 )
!= ( comp_a_complex_real @ SV150 @ SY450 ) )
| ( ( comp_real_a_complex @ SY450 @ SY451 )
!= SY452 )
| ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SY451 ) )
= ( comp_a1063143865omplex @ SV150 @ SY452 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(703,plain,
! [SV151: real,SV113: real > real,SV57: real > a] :
( ( ! [SY453: a > a,SY454: real > a,SY455: a > complex] :
( ( ( SV57 @ ( SV113 @ SV151 ) )
!= ( SY453 @ ( SY454 @ SV151 ) ) )
| ( ( comp_r701421291x_real @ ( comp_a_complex_real @ SY455 @ SV57 ) @ SV113 @ SV151 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SY455 @ SY453 ) @ SY454 @ SV151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(704,plain,
! [SV152: complex,SV114: complex > a,SV58: a > complex] :
( ( ! [SY456: a > complex,SY457: real > a,SY458: real] :
( ( ( SV58 @ ( SV114 @ SV152 ) )
!= ( SY456 @ ( SY457 @ SY458 ) ) )
| ( ( comp_a1063143865omplex @ SV58 @ SV114 @ SV152 )
= ( comp_a_complex_real @ SY456 @ SY457 @ SY458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(705,plain,
! [SV153: real > complex,SV115: real > a,SV59: a > complex] :
( ( ! [SY459: real > real] :
( ( ( comp_a_complex_real @ SV59 @ SV115 )
!= SV153 )
| ( ( comp_a_complex_real @ SV59 @ ( comp_real_a_real @ SV115 @ SY459 ) )
= ( comp_r701421291x_real @ SV153 @ SY459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(706,plain,
! [SV154: set_a,SV116: set_real,SV60: real > a] :
( ( ! [SY460: a > complex,SY461: set_complex] :
( ~ ( bij_betw_real_a @ SV60 @ SV116 @ SV154 )
| ~ ( bij_betw_a_complex @ SY460 @ SV154 @ SY461 )
| ( bij_be122140626omplex @ ( comp_a_complex_real @ SY460 @ SV60 ) @ SV116 @ SY461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(707,plain,
! [SV155: real > a,SV61: a > complex] :
( ( ( comp_a_complex_real @ SV61 @ SV155 )
= ( ^ [SY462: real] : ( SV61 @ ( SV155 @ SY462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(708,plain,
! [SV156: real > a,SV68: a > complex] :
( ( ( comp_a_complex_real @ SV68 @ SV156 )
= ( ^ [SY463: real] : ( SV68 @ ( SV156 @ SY463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(709,plain,
! [SV119: real > real,SV69: real > a,SV9: a > complex] :
( ( ! [SV157: real] :
( ( comp_r701421291x_real @ ( comp_a_complex_real @ SV9 @ SV69 ) @ SV119 @ SV157 )
= ( comp_a_complex_real @ SV9 @ ( comp_real_a_real @ SV69 @ SV119 ) @ SV157 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[658]) ).
thf(710,plain,
! [SV119: real > real,SV69: real > a,SV9: a > complex] :
( ( ( comp_r701421291x_real @ ( comp_a_complex_real @ SV9 @ SV69 ) @ SV119 )
= ( comp_a_complex_real @ SV9 @ ( comp_real_a_real @ SV69 @ SV119 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[658]) ).
thf(711,plain,
! [SV120: complex > real,SV70: real > a,SV10: a > complex] :
( ( ! [SV158: complex] :
( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV10 @ SV70 ) @ SV120 @ SV158 )
= ( comp_a1063143865omplex @ SV10 @ ( comp_real_a_complex @ SV70 @ SV120 ) @ SV158 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[659]) ).
thf(712,plain,
! [SV120: complex > real,SV70: real > a,SV10: a > complex] :
( ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV10 @ SV70 ) @ SV120 )
= ( comp_a1063143865omplex @ SV10 @ ( comp_real_a_complex @ SV70 @ SV120 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[659]) ).
thf(713,plain,
! [SV121: real > complex,SV71: complex > a,SV11: a > complex] :
( ( ! [SV159: real] :
( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV11 @ SV71 ) @ SV121 @ SV159 )
= ( comp_a_complex_real @ SV11 @ ( comp_complex_a_real @ SV71 @ SV121 ) @ SV159 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[660]) ).
thf(714,plain,
! [SV121: real > complex,SV71: complex > a,SV11: a > complex] :
( ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV11 @ SV71 ) @ SV121 )
= ( comp_a_complex_real @ SV11 @ ( comp_complex_a_real @ SV71 @ SV121 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[660]) ).
thf(715,plain,
! [SV122: real > a,SV72: a > complex,SV12: complex > a] :
( ( ! [SV160: real] :
( ( comp_a_a_real @ ( comp_complex_a_a @ SV12 @ SV72 ) @ SV122 @ SV160 )
= ( comp_complex_a_real @ SV12 @ ( comp_a_complex_real @ SV72 @ SV122 ) @ SV160 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[661]) ).
thf(716,plain,
! [SV122: real > a,SV72: a > complex,SV12: complex > a] :
( ( ( comp_a_a_real @ ( comp_complex_a_a @ SV12 @ SV72 ) @ SV122 )
= ( comp_complex_a_real @ SV12 @ ( comp_a_complex_real @ SV72 @ SV122 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[661]) ).
thf(717,plain,
! [SV123: real > a,SV73: a > complex,SV13: complex > complex] :
( ( ! [SV161: real] :
( ( comp_a_complex_real @ ( comp_c124850173plex_a @ SV13 @ SV73 ) @ SV123 @ SV161 )
= ( comp_c595887981x_real @ SV13 @ ( comp_a_complex_real @ SV73 @ SV123 ) @ SV161 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[662]) ).
thf(718,plain,
! [SV123: real > a,SV73: a > complex,SV13: complex > complex] :
( ( ( comp_a_complex_real @ ( comp_c124850173plex_a @ SV13 @ SV73 ) @ SV123 )
= ( comp_c595887981x_real @ SV13 @ ( comp_a_complex_real @ SV73 @ SV123 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[662]) ).
thf(719,plain,
! [SV124: real > a,SV74: a > a,SV14: a > complex] :
( ( ! [SV162: real] :
( ( comp_a_complex_real @ ( comp_a_complex_a @ SV14 @ SV74 ) @ SV124 @ SV162 )
= ( comp_a_complex_real @ SV14 @ ( comp_a_a_real @ SV74 @ SV124 ) @ SV162 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[663]) ).
thf(720,plain,
! [SV124: real > a,SV74: a > a,SV14: a > complex] :
( ( ( comp_a_complex_real @ ( comp_a_complex_a @ SV14 @ SV74 ) @ SV124 )
= ( comp_a_complex_real @ SV14 @ ( comp_a_a_real @ SV74 @ SV124 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[663]) ).
thf(721,plain,
! [SV125: real > a,SV77: a > complex,SV17: complex > complex] :
( ( ! [SV163: real] :
( ( comp_c595887981x_real @ SV17 @ ( comp_a_complex_real @ SV77 @ SV125 ) @ SV163 )
= ( comp_a_complex_real @ ( comp_c124850173plex_a @ SV17 @ SV77 ) @ SV125 @ SV163 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[664]) ).
thf(722,plain,
! [SV125: real > a,SV77: a > complex,SV17: complex > complex] :
( ( ( comp_c595887981x_real @ SV17 @ ( comp_a_complex_real @ SV77 @ SV125 ) )
= ( comp_a_complex_real @ ( comp_c124850173plex_a @ SV17 @ SV77 ) @ SV125 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[664]) ).
thf(723,plain,
! [SV126: real > a,SV78: a > complex,SV18: complex > a] :
( ( ! [SV164: real] :
( ( comp_complex_a_real @ SV18 @ ( comp_a_complex_real @ SV78 @ SV126 ) @ SV164 )
= ( comp_a_a_real @ ( comp_complex_a_a @ SV18 @ SV78 ) @ SV126 @ SV164 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[665]) ).
thf(724,plain,
! [SV126: real > a,SV78: a > complex,SV18: complex > a] :
( ( ( comp_complex_a_real @ SV18 @ ( comp_a_complex_real @ SV78 @ SV126 ) )
= ( comp_a_a_real @ ( comp_complex_a_a @ SV18 @ SV78 ) @ SV126 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[665]) ).
thf(725,plain,
! [SV127: real > complex,SV79: complex > a,SV19: a > complex] :
( ( ! [SV165: real] :
( ( comp_a_complex_real @ SV19 @ ( comp_complex_a_real @ SV79 @ SV127 ) @ SV165 )
= ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV19 @ SV79 ) @ SV127 @ SV165 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[666]) ).
thf(726,plain,
! [SV127: real > complex,SV79: complex > a,SV19: a > complex] :
( ( ( comp_a_complex_real @ SV19 @ ( comp_complex_a_real @ SV79 @ SV127 ) )
= ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV19 @ SV79 ) @ SV127 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[666]) ).
thf(727,plain,
! [SV128: real > real,SV80: real > a,SV20: a > complex] :
( ( ! [SV166: real] :
( ( comp_a_complex_real @ SV20 @ ( comp_real_a_real @ SV80 @ SV128 ) @ SV166 )
= ( comp_r701421291x_real @ ( comp_a_complex_real @ SV20 @ SV80 ) @ SV128 @ SV166 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[667]) ).
thf(728,plain,
! [SV128: real > real,SV80: real > a,SV20: a > complex] :
( ( ( comp_a_complex_real @ SV20 @ ( comp_real_a_real @ SV80 @ SV128 ) )
= ( comp_r701421291x_real @ ( comp_a_complex_real @ SV20 @ SV80 ) @ SV128 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[667]) ).
thf(729,plain,
! [SV129: real > a,SV81: a > a,SV21: a > complex] :
( ( ! [SV167: real] :
( ( comp_a_complex_real @ SV21 @ ( comp_a_a_real @ SV81 @ SV129 ) @ SV167 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SV21 @ SV81 ) @ SV129 @ SV167 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[668]) ).
thf(730,plain,
! [SV129: real > a,SV81: a > a,SV21: a > complex] :
( ( ( comp_a_complex_real @ SV21 @ ( comp_a_a_real @ SV81 @ SV129 ) )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SV21 @ SV81 ) @ SV129 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[668]) ).
thf(731,plain,
! [SV130: complex > real,SV82: real > a,SV22: a > complex] :
( ( ! [SV168: complex] :
( ( comp_a1063143865omplex @ SV22 @ ( comp_real_a_complex @ SV82 @ SV130 ) @ SV168 )
= ( comp_r667767405omplex @ ( comp_a_complex_real @ SV22 @ SV82 ) @ SV130 @ SV168 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[669]) ).
thf(732,plain,
! [SV130: complex > real,SV82: real > a,SV22: a > complex] :
( ( ( comp_a1063143865omplex @ SV22 @ ( comp_real_a_complex @ SV82 @ SV130 ) )
= ( comp_r667767405omplex @ ( comp_a_complex_real @ SV22 @ SV82 ) @ SV130 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[669]) ).
thf(733,plain,
! [SV85: real > complex,SV25: complex > complex] :
( ( ( real_V670066493omplex @ SV25 )
= $false )
| ( ( ( path_p797330068omplex @ ( comp_c595887981x_real @ SV25 @ SV85 ) )
= ( SV25 @ ( path_p797330068omplex @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(734,plain,
! [SV131: set_real,SV86: real > a,SV26: a > complex] :
( ( ( ~ ( inj_on_real_complex @ ( comp_a_complex_real @ SV26 @ SV86 ) @ SV131 ) )
= $true )
| ( ( inj_on_real_a @ SV86 @ SV131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[671]) ).
thf(735,plain,
! [SV169: a > a,SV132: a,SV87: a > real,SV27: real > a] :
( ( ! [SY464: a > a,SY465: a > complex] :
( ( ( SV27 @ ( SV87 @ SV132 ) )
!= ( SV169 @ ( SY464 @ SV132 ) ) )
| ( ( comp_real_complex_a @ ( comp_a_complex_real @ SY465 @ SV27 ) @ SV87 @ SV132 )
= ( comp_a_complex_a @ ( comp_a_complex_a @ SY465 @ SV169 ) @ SY464 @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(736,plain,
! [SV88: real > a,SV28: a > complex] :
( ( ( real_V1477106445omplex @ SV28 )
= $false )
| ( ( ( path_p769714271omplex @ ( comp_a_complex_real @ SV28 @ SV88 ) )
= ( SV28 @ ( path_pathfinish_a @ SV88 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(737,plain,
! [SV170: a > complex,SV133: a > a,SV89: a > real,SV29: real > a] :
( ( ( ( comp_real_a_a @ SV29 @ SV89 )
!= SV133 )
| ( ( comp_real_complex_a @ ( comp_a_complex_real @ SV170 @ SV29 ) @ SV89 )
= ( comp_a_complex_a @ SV170 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(738,plain,
! [SV171: real > complex,SV134: complex > complex,SV90: complex > a,SV30: a > complex] :
( ( ( ( comp_a1063143865omplex @ SV30 @ SV90 )
!= SV134 )
| ( ( comp_a_complex_real @ SV30 @ ( comp_complex_a_real @ SV90 @ SV171 ) )
= ( comp_c595887981x_real @ SV134 @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(739,plain,
! [SV31: real > complex] :
( ( ( ~ ( ( ( path_p769714271omplex @ SV31 )
!= ( path_p797330068omplex @ SV31 ) ) ) )
= $true )
| ( ( path_arc_complex @ SV31 )
= $true )
| ( ( path_s36253918omplex @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(740,plain,
! [SV32: real > complex] :
( ( ( ( path_p769714271omplex @ SV32 )
= ( path_p797330068omplex @ SV32 ) )
= $true )
| ( ( ( path_s36253918omplex @ SV32 )
= ( path_arc_complex @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[677]) ).
thf(741,plain,
! [SV172: a > real,SV135: real > complex,SV91: real > a,SV33: a > complex] :
( ( ( ( comp_a_complex_real @ SV33 @ SV91 )
!= SV135 )
| ( ( comp_a_complex_a @ SV33 @ ( comp_real_a_a @ SV91 @ SV172 ) )
= ( comp_real_complex_a @ SV135 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(742,plain,
! [SV173: complex > real,SV136: real > complex,SV92: real > a,SV34: a > complex] :
( ( ( ( comp_a_complex_real @ SV34 @ SV92 )
!= SV136 )
| ( ( comp_a1063143865omplex @ SV34 @ ( comp_real_a_complex @ SV92 @ SV173 ) )
= ( comp_r667767405omplex @ SV136 @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(743,plain,
! [SV174: real > a,SV137: a > complex,SV93: real > a,SV35: a > complex] :
( ( ( ( comp_a_complex_real @ SV35 @ SV93 )
!= ( comp_a_complex_real @ SV137 @ SV174 ) )
| ! [SY466: real] :
( ( SV35 @ ( SV93 @ SY466 ) )
= ( SV137 @ ( SV174 @ SY466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(744,plain,
! [SV36: real > complex] :
( ( ( path_arc_complex @ SV36 )
= $true )
| ( ( ( path_p769714271omplex @ SV36 )
= ( path_p797330068omplex @ SV36 ) )
= $true )
| ( ( path_s36253918omplex @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(745,plain,
! [SV175: real,SV138: real > complex,SV94: real > a,SV37: a > complex] :
( ( ( ( comp_a_complex_real @ SV37 @ SV94 )
!= SV138 )
| ( ( SV37 @ ( SV94 @ SV175 ) )
= ( SV138 @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(746,plain,
! [SV95: real > complex,SV38: complex > a] :
( ( ( real_V1327653935plex_a @ SV38 )
= $false )
| ( ( ( path_pathfinish_a @ ( comp_complex_a_real @ SV38 @ SV95 ) )
= ( SV38 @ ( path_p769714271omplex @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(747,plain,
! [SV96: real > complex,SV39: complex > complex] :
( ( ( real_V670066493omplex @ SV39 )
= $false )
| ( ( ( path_p769714271omplex @ ( comp_c595887981x_real @ SV39 @ SV96 ) )
= ( SV39 @ ( path_p769714271omplex @ SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(748,plain,
! [SV176: a > complex,SV139: real > a,SV97: real > complex,SV40: complex > a] :
( ( ( ( comp_complex_a_real @ SV40 @ SV97 )
!= SV139 )
| ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV176 @ SV40 ) @ SV97 )
= ( comp_a_complex_real @ SV176 @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(749,plain,
! [SV177: a > complex,SV140: real,SV98: real > a,SV41: a > complex] :
( ( ! [SY467: a > a,SY468: a] :
( ( ( SV41 @ ( SV98 @ SV140 ) )
!= ( SV177 @ ( SY467 @ SY468 ) ) )
| ( ( comp_a_complex_real @ SV41 @ SV98 @ SV140 )
= ( comp_a_complex_a @ SV177 @ SY467 @ SY468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(750,plain,
! [SV99: real > complex] :
( ( ( ~ ( ( path_arc_complex @ SV99 )
| ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( path_arc_complex @ SV99 )
| ~ ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(751,plain,
! [SV178: a > complex,SV141: set_a,SV100: set_real,SV43: real > a] :
( ( ! [SY469: set_complex] :
( ~ ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
| ( ( bij_betw_a_complex @ SV178 @ SV141 @ SY469 )
= ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SY469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(752,plain,
! [SV179: real > a,SV142: a > complex,SV101: real > a,SV44: a > complex] :
( ( ! [SY470: real] :
( ( ( comp_a_complex_real @ SV44 @ SV101 )
!= ( comp_a_complex_real @ SV142 @ SV179 ) )
| ( ( SV44 @ ( SV101 @ SY470 ) )
= ( SV142 @ ( SV179 @ SY470 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(753,plain,
! [SV102: real > complex,SV45: complex > a] :
( ( ( real_V1327653935plex_a @ SV45 )
= $false )
| ( ( ( path_pathstart_a @ ( comp_complex_a_real @ SV45 @ SV102 ) )
= ( SV45 @ ( path_p797330068omplex @ SV102 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(754,plain,
! [SV103: real > a,SV46: a > complex] :
( ( ( real_V1477106445omplex @ SV46 )
= $false )
| ( ( ( path_p797330068omplex @ ( comp_a_complex_real @ SV46 @ SV103 ) )
= ( SV46 @ ( path_pathstart_a @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(755,plain,
! [SV180: real > a,SV143: a > complex,SV104: a > complex,SV47: complex > complex] :
( ( ( ( comp_c124850173plex_a @ SV47 @ SV104 )
!= SV143 )
| ( ( comp_c595887981x_real @ SV47 @ ( comp_a_complex_real @ SV104 @ SV180 ) )
= ( comp_a_complex_real @ SV143 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(756,plain,
! [SV181: a > complex,SV144: real,SV105: real > a,SV48: a > complex] :
( ( ! [SY471: complex > a,SY472: complex] :
( ( ( SV48 @ ( SV105 @ SV144 ) )
!= ( SV181 @ ( SY471 @ SY472 ) ) )
| ( ( comp_a_complex_real @ SV48 @ SV105 @ SV144 )
= ( comp_a1063143865omplex @ SV181 @ SY471 @ SY472 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(757,plain,
! [SV182: a > complex,SV145: complex > a,SV106: complex > real,SV49: real > a] :
( ( ( ( comp_real_a_complex @ SV49 @ SV106 )
!= SV145 )
| ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV182 @ SV49 ) @ SV106 )
= ( comp_a1063143865omplex @ SV182 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(758,plain,
! [SV107: a > complex,SV50: real > a] :
( ( ( real_V779700657real_a @ SV50 )
= $false )
| ( ( ~ ( real_V1477106445omplex @ SV107 )
| ( real_V1948715323omplex @ ( comp_a_complex_real @ SV107 @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[696]) ).
thf(759,plain,
! [SV183: a > a,SV146: complex,SV108: complex > real,SV51: real > a] :
( ( ! [SY473: complex > a,SY474: a > complex] :
( ( ( SV51 @ ( SV108 @ SV146 ) )
!= ( SV183 @ ( SY473 @ SV146 ) ) )
| ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SY474 @ SV51 ) @ SV108 @ SV146 )
= ( comp_a1063143865omplex @ ( comp_a_complex_a @ SY474 @ SV183 ) @ SY473 @ SV146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(760,plain,
! [SV52: real > complex] :
( ( ( ( path_p769714271omplex @ SV52 )
= ( path_p797330068omplex @ SV52 ) )
= $false )
| ( ( path_arc_complex @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(761,plain,
! [SV184: a > a,SV147: real,SV109: real > complex,SV53: complex > a] :
( ( ! [SY475: real > a,SY476: a > complex] :
( ( ( SV53 @ ( SV109 @ SV147 ) )
!= ( SV184 @ ( SY475 @ SV147 ) ) )
| ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SY476 @ SV53 ) @ SV109 @ SV147 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SY476 @ SV184 ) @ SY475 @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(762,plain,
! [SV185: a > complex,SV148: real,SV110: real > a,SV54: a > complex] :
( ( ! [SY477: real > a,SY478: real] :
( ( ( SV54 @ ( SV110 @ SV148 ) )
!= ( SV185 @ ( SY477 @ SY478 ) ) )
| ( ( comp_a_complex_real @ SV54 @ SV110 @ SV148 )
= ( comp_a_complex_real @ SV185 @ SY477 @ SY478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(763,plain,
! [SV186: real,SV149: real > complex,SV111: real > a,SV55: a > complex] :
( ( ( ( comp_a_complex_real @ SV55 @ SV111 )
!= ( comp_c595887981x_real @ id_complex @ SV149 ) )
| ( ( SV55 @ ( SV111 @ SV186 ) )
= ( SV149 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(764,plain,
! [SV187: real > a,SV150: a > complex,SV112: real > a,SV56: a > complex] :
( ( ! [SY479: complex > real,SY480: complex > a] :
( ( ( comp_a_complex_real @ SV56 @ SV112 )
!= ( comp_a_complex_real @ SV150 @ SV187 ) )
| ( ( comp_real_a_complex @ SV187 @ SY479 )
!= SY480 )
| ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SY479 ) )
= ( comp_a1063143865omplex @ SV150 @ SY480 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(765,plain,
! [SV188: a > a,SV151: real,SV113: real > real,SV57: real > a] :
( ( ! [SY481: real > a,SY482: a > complex] :
( ( ( SV57 @ ( SV113 @ SV151 ) )
!= ( SV188 @ ( SY481 @ SV151 ) ) )
| ( ( comp_r701421291x_real @ ( comp_a_complex_real @ SY482 @ SV57 ) @ SV113 @ SV151 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SY482 @ SV188 ) @ SY481 @ SV151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(766,plain,
! [SV189: a > complex,SV152: complex,SV114: complex > a,SV58: a > complex] :
( ( ! [SY483: real > a,SY484: real] :
( ( ( SV58 @ ( SV114 @ SV152 ) )
!= ( SV189 @ ( SY483 @ SY484 ) ) )
| ( ( comp_a1063143865omplex @ SV58 @ SV114 @ SV152 )
= ( comp_a_complex_real @ SV189 @ SY483 @ SY484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(767,plain,
! [SV190: real > real,SV153: real > complex,SV115: real > a,SV59: a > complex] :
( ( ( ( comp_a_complex_real @ SV59 @ SV115 )
!= SV153 )
| ( ( comp_a_complex_real @ SV59 @ ( comp_real_a_real @ SV115 @ SV190 ) )
= ( comp_r701421291x_real @ SV153 @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(768,plain,
! [SV191: a > complex,SV154: set_a,SV116: set_real,SV60: real > a] :
( ( ! [SY485: set_complex] :
( ~ ( bij_betw_real_a @ SV60 @ SV116 @ SV154 )
| ~ ( bij_betw_a_complex @ SV191 @ SV154 @ SY485 )
| ( bij_be122140626omplex @ ( comp_a_complex_real @ SV191 @ SV60 ) @ SV116 @ SY485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(769,plain,
! [SV155: real > a,SV61: a > complex] :
( ( ! [SV192: real] :
( ( comp_a_complex_real @ SV61 @ SV155 @ SV192 )
= ( SV61 @ ( SV155 @ SV192 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[707]) ).
thf(770,plain,
! [SV155: real > a,SV61: a > complex] :
( ( ( comp_a_complex_real @ SV61 @ SV155 )
= ( ^ [SY462: real] : ( SV61 @ ( SV155 @ SY462 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[707]) ).
thf(771,plain,
! [SV156: real > a,SV68: a > complex] :
( ( ! [SV193: real] :
( ( comp_a_complex_real @ SV68 @ SV156 @ SV193 )
= ( SV68 @ ( SV156 @ SV193 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[708]) ).
thf(772,plain,
! [SV156: real > a,SV68: a > complex] :
( ( ( comp_a_complex_real @ SV68 @ SV156 )
= ( ^ [SY463: real] : ( SV68 @ ( SV156 @ SY463 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[708]) ).
thf(773,plain,
! [SV194: real,SV119: real > real,SV69: real > a,SV9: a > complex] :
( ( ( comp_r701421291x_real @ ( comp_a_complex_real @ SV9 @ SV69 ) @ SV119 @ SV194 )
= ( comp_a_complex_real @ SV9 @ ( comp_real_a_real @ SV69 @ SV119 ) @ SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(774,plain,
! [SV195: complex,SV120: complex > real,SV70: real > a,SV10: a > complex] :
( ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV10 @ SV70 ) @ SV120 @ SV195 )
= ( comp_a1063143865omplex @ SV10 @ ( comp_real_a_complex @ SV70 @ SV120 ) @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(775,plain,
! [SV196: real,SV121: real > complex,SV71: complex > a,SV11: a > complex] :
( ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV11 @ SV71 ) @ SV121 @ SV196 )
= ( comp_a_complex_real @ SV11 @ ( comp_complex_a_real @ SV71 @ SV121 ) @ SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(776,plain,
! [SV197: real,SV122: real > a,SV72: a > complex,SV12: complex > a] :
( ( ( comp_a_a_real @ ( comp_complex_a_a @ SV12 @ SV72 ) @ SV122 @ SV197 )
= ( comp_complex_a_real @ SV12 @ ( comp_a_complex_real @ SV72 @ SV122 ) @ SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(777,plain,
! [SV198: real,SV123: real > a,SV73: a > complex,SV13: complex > complex] :
( ( ( comp_a_complex_real @ ( comp_c124850173plex_a @ SV13 @ SV73 ) @ SV123 @ SV198 )
= ( comp_c595887981x_real @ SV13 @ ( comp_a_complex_real @ SV73 @ SV123 ) @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(778,plain,
! [SV199: real,SV124: real > a,SV74: a > a,SV14: a > complex] :
( ( ( comp_a_complex_real @ ( comp_a_complex_a @ SV14 @ SV74 ) @ SV124 @ SV199 )
= ( comp_a_complex_real @ SV14 @ ( comp_a_a_real @ SV74 @ SV124 ) @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(779,plain,
! [SV200: real,SV125: real > a,SV77: a > complex,SV17: complex > complex] :
( ( ( comp_c595887981x_real @ SV17 @ ( comp_a_complex_real @ SV77 @ SV125 ) @ SV200 )
= ( comp_a_complex_real @ ( comp_c124850173plex_a @ SV17 @ SV77 ) @ SV125 @ SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(780,plain,
! [SV201: real,SV126: real > a,SV78: a > complex,SV18: complex > a] :
( ( ( comp_complex_a_real @ SV18 @ ( comp_a_complex_real @ SV78 @ SV126 ) @ SV201 )
= ( comp_a_a_real @ ( comp_complex_a_a @ SV18 @ SV78 ) @ SV126 @ SV201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(781,plain,
! [SV202: real,SV127: real > complex,SV79: complex > a,SV19: a > complex] :
( ( ( comp_a_complex_real @ SV19 @ ( comp_complex_a_real @ SV79 @ SV127 ) @ SV202 )
= ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV19 @ SV79 ) @ SV127 @ SV202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(782,plain,
! [SV203: real,SV128: real > real,SV80: real > a,SV20: a > complex] :
( ( ( comp_a_complex_real @ SV20 @ ( comp_real_a_real @ SV80 @ SV128 ) @ SV203 )
= ( comp_r701421291x_real @ ( comp_a_complex_real @ SV20 @ SV80 ) @ SV128 @ SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(783,plain,
! [SV204: real,SV129: real > a,SV81: a > a,SV21: a > complex] :
( ( ( comp_a_complex_real @ SV21 @ ( comp_a_a_real @ SV81 @ SV129 ) @ SV204 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SV21 @ SV81 ) @ SV129 @ SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(784,plain,
! [SV205: complex,SV130: complex > real,SV82: real > a,SV22: a > complex] :
( ( ( comp_a1063143865omplex @ SV22 @ ( comp_real_a_complex @ SV82 @ SV130 ) @ SV205 )
= ( comp_r667767405omplex @ ( comp_a_complex_real @ SV22 @ SV82 ) @ SV130 @ SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(785,plain,
! [SV131: set_real,SV86: real > a,SV26: a > complex] :
( ( ( inj_on_real_complex @ ( comp_a_complex_real @ SV26 @ SV86 ) @ SV131 )
= $false )
| ( ( inj_on_real_a @ SV86 @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(786,plain,
! [SV206: a > a,SV169: a > a,SV132: a,SV87: a > real,SV27: real > a] :
( ( ! [SY486: a > complex] :
( ( ( SV27 @ ( SV87 @ SV132 ) )
!= ( SV169 @ ( SV206 @ SV132 ) ) )
| ( ( comp_real_complex_a @ ( comp_a_complex_real @ SY486 @ SV27 ) @ SV87 @ SV132 )
= ( comp_a_complex_a @ ( comp_a_complex_a @ SY486 @ SV169 ) @ SV206 @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(787,plain,
! [SV170: a > complex,SV133: a > a,SV89: a > real,SV29: real > a] :
( ( ( ( comp_real_a_a @ SV29 @ SV89 )
!= SV133 )
= $true )
| ( ( ( comp_real_complex_a @ ( comp_a_complex_real @ SV170 @ SV29 ) @ SV89 )
= ( comp_a_complex_a @ SV170 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(788,plain,
! [SV171: real > complex,SV134: complex > complex,SV90: complex > a,SV30: a > complex] :
( ( ( ( comp_a1063143865omplex @ SV30 @ SV90 )
!= SV134 )
= $true )
| ( ( ( comp_a_complex_real @ SV30 @ ( comp_complex_a_real @ SV90 @ SV171 ) )
= ( comp_c595887981x_real @ SV134 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[738]) ).
thf(789,plain,
! [SV31: real > complex] :
( ( ( ( path_p769714271omplex @ SV31 )
!= ( path_p797330068omplex @ SV31 ) )
= $false )
| ( ( path_arc_complex @ SV31 )
= $true )
| ( ( path_s36253918omplex @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(790,plain,
! [SV32: real > complex] :
( ( ( ~ ( ( path_s36253918omplex @ SV32 )
| ( path_arc_complex @ SV32 ) )
| ~ ( ~ ( path_s36253918omplex @ SV32 )
| ~ ( path_arc_complex @ SV32 ) ) )
= $true )
| ( ( ( path_p769714271omplex @ SV32 )
= ( path_p797330068omplex @ SV32 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[740]) ).
thf(791,plain,
! [SV32: real > complex] :
( ( ( ( path_s36253918omplex @ SV32 )
= ( path_arc_complex @ SV32 ) )
= $true )
| ( ( ( path_p769714271omplex @ SV32 )
= ( path_p797330068omplex @ SV32 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[740]) ).
thf(792,plain,
! [SV172: a > real,SV135: real > complex,SV91: real > a,SV33: a > complex] :
( ( ( ( comp_a_complex_real @ SV33 @ SV91 )
!= SV135 )
= $true )
| ( ( ( comp_a_complex_a @ SV33 @ ( comp_real_a_a @ SV91 @ SV172 ) )
= ( comp_real_complex_a @ SV135 @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[741]) ).
thf(793,plain,
! [SV173: complex > real,SV136: real > complex,SV92: real > a,SV34: a > complex] :
( ( ( ( comp_a_complex_real @ SV34 @ SV92 )
!= SV136 )
= $true )
| ( ( ( comp_a1063143865omplex @ SV34 @ ( comp_real_a_complex @ SV92 @ SV173 ) )
= ( comp_r667767405omplex @ SV136 @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(794,plain,
! [SV174: real > a,SV137: a > complex,SV93: real > a,SV35: a > complex] :
( ( ( ( comp_a_complex_real @ SV35 @ SV93 )
!= ( comp_a_complex_real @ SV137 @ SV174 ) )
= $true )
| ( ( ! [SY466: real] :
( ( SV35 @ ( SV93 @ SY466 ) )
= ( SV137 @ ( SV174 @ SY466 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(795,plain,
! [SV175: real,SV138: real > complex,SV94: real > a,SV37: a > complex] :
( ( ( ( comp_a_complex_real @ SV37 @ SV94 )
!= SV138 )
= $true )
| ( ( ( SV37 @ ( SV94 @ SV175 ) )
= ( SV138 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(796,plain,
! [SV176: a > complex,SV139: real > a,SV97: real > complex,SV40: complex > a] :
( ( ( ( comp_complex_a_real @ SV40 @ SV97 )
!= SV139 )
= $true )
| ( ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV176 @ SV40 ) @ SV97 )
= ( comp_a_complex_real @ SV176 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(797,plain,
! [SV207: a > a,SV177: a > complex,SV140: real,SV98: real > a,SV41: a > complex] :
( ( ! [SY487: a] :
( ( ( SV41 @ ( SV98 @ SV140 ) )
!= ( SV177 @ ( SV207 @ SY487 ) ) )
| ( ( comp_a_complex_real @ SV41 @ SV98 @ SV140 )
= ( comp_a_complex_a @ SV177 @ SV207 @ SY487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(798,plain,
! [SV99: real > complex] :
( ( ( ( path_arc_complex @ SV99 )
| ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( path_arc_complex @ SV99 )
| ~ ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(799,plain,
! [SV208: set_complex,SV178: a > complex,SV141: set_a,SV100: set_real,SV43: real > a] :
( ( ~ ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
| ( ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
= ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(800,plain,
! [SV209: real,SV179: real > a,SV142: a > complex,SV101: real > a,SV44: a > complex] :
( ( ( ( comp_a_complex_real @ SV44 @ SV101 )
!= ( comp_a_complex_real @ SV142 @ SV179 ) )
| ( ( SV44 @ ( SV101 @ SV209 ) )
= ( SV142 @ ( SV179 @ SV209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(801,plain,
! [SV180: real > a,SV143: a > complex,SV104: a > complex,SV47: complex > complex] :
( ( ( ( comp_c124850173plex_a @ SV47 @ SV104 )
!= SV143 )
= $true )
| ( ( ( comp_c595887981x_real @ SV47 @ ( comp_a_complex_real @ SV104 @ SV180 ) )
= ( comp_a_complex_real @ SV143 @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(802,plain,
! [SV210: complex > a,SV181: a > complex,SV144: real,SV105: real > a,SV48: a > complex] :
( ( ! [SY488: complex] :
( ( ( SV48 @ ( SV105 @ SV144 ) )
!= ( SV181 @ ( SV210 @ SY488 ) ) )
| ( ( comp_a_complex_real @ SV48 @ SV105 @ SV144 )
= ( comp_a1063143865omplex @ SV181 @ SV210 @ SY488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(803,plain,
! [SV182: a > complex,SV145: complex > a,SV106: complex > real,SV49: real > a] :
( ( ( ( comp_real_a_complex @ SV49 @ SV106 )
!= SV145 )
= $true )
| ( ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV182 @ SV49 ) @ SV106 )
= ( comp_a1063143865omplex @ SV182 @ SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(804,plain,
! [SV50: real > a,SV107: a > complex] :
( ( ( ~ ( real_V1477106445omplex @ SV107 ) )
= $true )
| ( ( real_V1948715323omplex @ ( comp_a_complex_real @ SV107 @ SV50 ) )
= $true )
| ( ( real_V779700657real_a @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[758]) ).
thf(805,plain,
! [SV211: complex > a,SV183: a > a,SV146: complex,SV108: complex > real,SV51: real > a] :
( ( ! [SY489: a > complex] :
( ( ( SV51 @ ( SV108 @ SV146 ) )
!= ( SV183 @ ( SV211 @ SV146 ) ) )
| ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SY489 @ SV51 ) @ SV108 @ SV146 )
= ( comp_a1063143865omplex @ ( comp_a_complex_a @ SY489 @ SV183 ) @ SV211 @ SV146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(806,plain,
! [SV212: real > a,SV184: a > a,SV147: real,SV109: real > complex,SV53: complex > a] :
( ( ! [SY490: a > complex] :
( ( ( SV53 @ ( SV109 @ SV147 ) )
!= ( SV184 @ ( SV212 @ SV147 ) ) )
| ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SY490 @ SV53 ) @ SV109 @ SV147 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SY490 @ SV184 ) @ SV212 @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(807,plain,
! [SV213: real > a,SV185: a > complex,SV148: real,SV110: real > a,SV54: a > complex] :
( ( ! [SY491: real] :
( ( ( SV54 @ ( SV110 @ SV148 ) )
!= ( SV185 @ ( SV213 @ SY491 ) ) )
| ( ( comp_a_complex_real @ SV54 @ SV110 @ SV148 )
= ( comp_a_complex_real @ SV185 @ SV213 @ SY491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(808,plain,
! [SV186: real,SV149: real > complex,SV111: real > a,SV55: a > complex] :
( ( ( ( comp_a_complex_real @ SV55 @ SV111 )
!= ( comp_c595887981x_real @ id_complex @ SV149 ) )
= $true )
| ( ( ( SV55 @ ( SV111 @ SV186 ) )
= ( SV149 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(809,plain,
! [SV214: complex > real,SV187: real > a,SV150: a > complex,SV112: real > a,SV56: a > complex] :
( ( ! [SY492: complex > a] :
( ( ( comp_a_complex_real @ SV56 @ SV112 )
!= ( comp_a_complex_real @ SV150 @ SV187 ) )
| ( ( comp_real_a_complex @ SV187 @ SV214 )
!= SY492 )
| ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SY492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(810,plain,
! [SV215: real > a,SV188: a > a,SV151: real,SV113: real > real,SV57: real > a] :
( ( ! [SY493: a > complex] :
( ( ( SV57 @ ( SV113 @ SV151 ) )
!= ( SV188 @ ( SV215 @ SV151 ) ) )
| ( ( comp_r701421291x_real @ ( comp_a_complex_real @ SY493 @ SV57 ) @ SV113 @ SV151 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SY493 @ SV188 ) @ SV215 @ SV151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(811,plain,
! [SV216: real > a,SV189: a > complex,SV152: complex,SV114: complex > a,SV58: a > complex] :
( ( ! [SY494: real] :
( ( ( SV58 @ ( SV114 @ SV152 ) )
!= ( SV189 @ ( SV216 @ SY494 ) ) )
| ( ( comp_a1063143865omplex @ SV58 @ SV114 @ SV152 )
= ( comp_a_complex_real @ SV189 @ SV216 @ SY494 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(812,plain,
! [SV190: real > real,SV153: real > complex,SV115: real > a,SV59: a > complex] :
( ( ( ( comp_a_complex_real @ SV59 @ SV115 )
!= SV153 )
= $true )
| ( ( ( comp_a_complex_real @ SV59 @ ( comp_real_a_real @ SV115 @ SV190 ) )
= ( comp_r701421291x_real @ SV153 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(813,plain,
! [SV217: set_complex,SV191: a > complex,SV154: set_a,SV116: set_real,SV60: real > a] :
( ( ~ ( bij_betw_real_a @ SV60 @ SV116 @ SV154 )
| ~ ( bij_betw_a_complex @ SV191 @ SV154 @ SV217 )
| ( bij_be122140626omplex @ ( comp_a_complex_real @ SV191 @ SV60 ) @ SV116 @ SV217 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(814,plain,
! [SV218: real,SV155: real > a,SV61: a > complex] :
( ( ( comp_a_complex_real @ SV61 @ SV155 @ SV218 )
= ( SV61 @ ( SV155 @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(815,plain,
! [SV219: real,SV156: real > a,SV68: a > complex] :
( ( ( comp_a_complex_real @ SV68 @ SV156 @ SV219 )
= ( SV68 @ ( SV156 @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(816,plain,
! [SV220: a > complex,SV206: a > a,SV169: a > a,SV132: a,SV87: a > real,SV27: real > a] :
( ( ( ( SV27 @ ( SV87 @ SV132 ) )
!= ( SV169 @ ( SV206 @ SV132 ) ) )
| ( ( comp_real_complex_a @ ( comp_a_complex_real @ SV220 @ SV27 ) @ SV87 @ SV132 )
= ( comp_a_complex_a @ ( comp_a_complex_a @ SV220 @ SV169 ) @ SV206 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(817,plain,
! [SV170: a > complex,SV133: a > a,SV89: a > real,SV29: real > a] :
( ( ( ( comp_real_a_a @ SV29 @ SV89 )
= SV133 )
= $false )
| ( ( ( comp_real_complex_a @ ( comp_a_complex_real @ SV170 @ SV29 ) @ SV89 )
= ( comp_a_complex_a @ SV170 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(818,plain,
! [SV171: real > complex,SV134: complex > complex,SV90: complex > a,SV30: a > complex] :
( ( ( ( comp_a1063143865omplex @ SV30 @ SV90 )
= SV134 )
= $false )
| ( ( ( comp_a_complex_real @ SV30 @ ( comp_complex_a_real @ SV90 @ SV171 ) )
= ( comp_c595887981x_real @ SV134 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(819,plain,
! [SV31: real > complex] :
( ( ( ( path_p769714271omplex @ SV31 )
= ( path_p797330068omplex @ SV31 ) )
= $true )
| ( ( path_arc_complex @ SV31 )
= $true )
| ( ( path_s36253918omplex @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(820,plain,
! [SV32: real > complex] :
( ( ( ~ ( ( path_s36253918omplex @ SV32 )
| ( path_arc_complex @ SV32 ) ) )
= $true )
| ( ( ~ ( ~ ( path_s36253918omplex @ SV32 )
| ~ ( path_arc_complex @ SV32 ) ) )
= $true )
| ( ( ( path_p769714271omplex @ SV32 )
= ( path_p797330068omplex @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[790]) ).
thf(821,plain,
! [SV172: a > real,SV135: real > complex,SV91: real > a,SV33: a > complex] :
( ( ( ( comp_a_complex_real @ SV33 @ SV91 )
= SV135 )
= $false )
| ( ( ( comp_a_complex_a @ SV33 @ ( comp_real_a_a @ SV91 @ SV172 ) )
= ( comp_real_complex_a @ SV135 @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(822,plain,
! [SV173: complex > real,SV136: real > complex,SV92: real > a,SV34: a > complex] :
( ( ( ( comp_a_complex_real @ SV34 @ SV92 )
= SV136 )
= $false )
| ( ( ( comp_a1063143865omplex @ SV34 @ ( comp_real_a_complex @ SV92 @ SV173 ) )
= ( comp_r667767405omplex @ SV136 @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(823,plain,
! [SV174: real > a,SV137: a > complex,SV93: real > a,SV35: a > complex] :
( ( ( ( comp_a_complex_real @ SV35 @ SV93 )
= ( comp_a_complex_real @ SV137 @ SV174 ) )
= $false )
| ( ( ! [SY466: real] :
( ( SV35 @ ( SV93 @ SY466 ) )
= ( SV137 @ ( SV174 @ SY466 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(824,plain,
! [SV175: real,SV138: real > complex,SV94: real > a,SV37: a > complex] :
( ( ( ( comp_a_complex_real @ SV37 @ SV94 )
= SV138 )
= $false )
| ( ( ( SV37 @ ( SV94 @ SV175 ) )
= ( SV138 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(825,plain,
! [SV176: a > complex,SV139: real > a,SV97: real > complex,SV40: complex > a] :
( ( ( ( comp_complex_a_real @ SV40 @ SV97 )
= SV139 )
= $false )
| ( ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV176 @ SV40 ) @ SV97 )
= ( comp_a_complex_real @ SV176 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(826,plain,
! [SV221: a,SV207: a > a,SV177: a > complex,SV140: real,SV98: real > a,SV41: a > complex] :
( ( ( ( SV41 @ ( SV98 @ SV140 ) )
!= ( SV177 @ ( SV207 @ SV221 ) ) )
| ( ( comp_a_complex_real @ SV41 @ SV98 @ SV140 )
= ( comp_a_complex_a @ SV177 @ SV207 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(827,plain,
! [SV99: real > complex] :
( ( ( path_arc_complex @ SV99 )
= $false )
| ( ( ~ ( ~ ( path_arc_complex @ SV99 )
| ~ ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(828,plain,
! [SV99: real > complex] :
( ( ( ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( path_arc_complex @ SV99 )
| ~ ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(829,plain,
! [SV208: set_complex,SV178: a > complex,SV141: set_a,SV100: set_real,SV43: real > a] :
( ( ( ~ ( bij_betw_real_a @ SV43 @ SV100 @ SV141 ) )
= $true )
| ( ( ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
= ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(830,plain,
! [SV209: real,SV179: real > a,SV142: a > complex,SV101: real > a,SV44: a > complex] :
( ( ( ( comp_a_complex_real @ SV44 @ SV101 )
!= ( comp_a_complex_real @ SV142 @ SV179 ) )
= $true )
| ( ( ( SV44 @ ( SV101 @ SV209 ) )
= ( SV142 @ ( SV179 @ SV209 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[800]) ).
thf(831,plain,
! [SV180: real > a,SV143: a > complex,SV104: a > complex,SV47: complex > complex] :
( ( ( ( comp_c124850173plex_a @ SV47 @ SV104 )
= SV143 )
= $false )
| ( ( ( comp_c595887981x_real @ SV47 @ ( comp_a_complex_real @ SV104 @ SV180 ) )
= ( comp_a_complex_real @ SV143 @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[801]) ).
thf(832,plain,
! [SV222: complex,SV210: complex > a,SV181: a > complex,SV144: real,SV105: real > a,SV48: a > complex] :
( ( ( ( SV48 @ ( SV105 @ SV144 ) )
!= ( SV181 @ ( SV210 @ SV222 ) ) )
| ( ( comp_a_complex_real @ SV48 @ SV105 @ SV144 )
= ( comp_a1063143865omplex @ SV181 @ SV210 @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(833,plain,
! [SV182: a > complex,SV145: complex > a,SV106: complex > real,SV49: real > a] :
( ( ( ( comp_real_a_complex @ SV49 @ SV106 )
= SV145 )
= $false )
| ( ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV182 @ SV49 ) @ SV106 )
= ( comp_a1063143865omplex @ SV182 @ SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(834,plain,
! [SV50: real > a,SV107: a > complex] :
( ( ( real_V1477106445omplex @ SV107 )
= $false )
| ( ( real_V1948715323omplex @ ( comp_a_complex_real @ SV107 @ SV50 ) )
= $true )
| ( ( real_V779700657real_a @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(835,plain,
! [SV223: a > complex,SV211: complex > a,SV183: a > a,SV146: complex,SV108: complex > real,SV51: real > a] :
( ( ( ( SV51 @ ( SV108 @ SV146 ) )
!= ( SV183 @ ( SV211 @ SV146 ) ) )
| ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV223 @ SV51 ) @ SV108 @ SV146 )
= ( comp_a1063143865omplex @ ( comp_a_complex_a @ SV223 @ SV183 ) @ SV211 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(836,plain,
! [SV224: a > complex,SV212: real > a,SV184: a > a,SV147: real,SV109: real > complex,SV53: complex > a] :
( ( ( ( SV53 @ ( SV109 @ SV147 ) )
!= ( SV184 @ ( SV212 @ SV147 ) ) )
| ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV224 @ SV53 ) @ SV109 @ SV147 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SV224 @ SV184 ) @ SV212 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(837,plain,
! [SV225: real,SV213: real > a,SV185: a > complex,SV148: real,SV110: real > a,SV54: a > complex] :
( ( ( ( SV54 @ ( SV110 @ SV148 ) )
!= ( SV185 @ ( SV213 @ SV225 ) ) )
| ( ( comp_a_complex_real @ SV54 @ SV110 @ SV148 )
= ( comp_a_complex_real @ SV185 @ SV213 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(838,plain,
! [SV186: real,SV149: real > complex,SV111: real > a,SV55: a > complex] :
( ( ( ( comp_a_complex_real @ SV55 @ SV111 )
= ( comp_c595887981x_real @ id_complex @ SV149 ) )
= $false )
| ( ( ( SV55 @ ( SV111 @ SV186 ) )
= ( SV149 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(839,plain,
! [SV226: complex > a,SV214: complex > real,SV187: real > a,SV150: a > complex,SV112: real > a,SV56: a > complex] :
( ( ( ( comp_a_complex_real @ SV56 @ SV112 )
!= ( comp_a_complex_real @ SV150 @ SV187 ) )
| ( ( comp_real_a_complex @ SV187 @ SV214 )
!= SV226 )
| ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(840,plain,
! [SV227: a > complex,SV215: real > a,SV188: a > a,SV151: real,SV113: real > real,SV57: real > a] :
( ( ( ( SV57 @ ( SV113 @ SV151 ) )
!= ( SV188 @ ( SV215 @ SV151 ) ) )
| ( ( comp_r701421291x_real @ ( comp_a_complex_real @ SV227 @ SV57 ) @ SV113 @ SV151 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SV227 @ SV188 ) @ SV215 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(841,plain,
! [SV228: real,SV216: real > a,SV189: a > complex,SV152: complex,SV114: complex > a,SV58: a > complex] :
( ( ( ( SV58 @ ( SV114 @ SV152 ) )
!= ( SV189 @ ( SV216 @ SV228 ) ) )
| ( ( comp_a1063143865omplex @ SV58 @ SV114 @ SV152 )
= ( comp_a_complex_real @ SV189 @ SV216 @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(842,plain,
! [SV190: real > real,SV153: real > complex,SV115: real > a,SV59: a > complex] :
( ( ( ( comp_a_complex_real @ SV59 @ SV115 )
= SV153 )
= $false )
| ( ( ( comp_a_complex_real @ SV59 @ ( comp_real_a_real @ SV115 @ SV190 ) )
= ( comp_r701421291x_real @ SV153 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(843,plain,
! [SV217: set_complex,SV191: a > complex,SV154: set_a,SV116: set_real,SV60: real > a] :
( ( ( ~ ( bij_betw_real_a @ SV60 @ SV116 @ SV154 ) )
= $true )
| ( ( ~ ( bij_betw_a_complex @ SV191 @ SV154 @ SV217 )
| ( bij_be122140626omplex @ ( comp_a_complex_real @ SV191 @ SV60 ) @ SV116 @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[813]) ).
thf(844,plain,
! [SV220: a > complex,SV206: a > a,SV169: a > a,SV132: a,SV87: a > real,SV27: real > a] :
( ( ( ( SV27 @ ( SV87 @ SV132 ) )
!= ( SV169 @ ( SV206 @ SV132 ) ) )
= $true )
| ( ( ( comp_real_complex_a @ ( comp_a_complex_real @ SV220 @ SV27 ) @ SV87 @ SV132 )
= ( comp_a_complex_a @ ( comp_a_complex_a @ SV220 @ SV169 ) @ SV206 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[816]) ).
thf(845,plain,
! [SV170: a > complex,SV133: a > a,SV89: a > real,SV29: real > a] :
( ( ( ! [SV229: a] :
( ( comp_real_a_a @ SV29 @ SV89 @ SV229 )
= ( SV133 @ SV229 ) ) )
= $false )
| ( ( ( comp_real_complex_a @ ( comp_a_complex_real @ SV170 @ SV29 ) @ SV89 )
= ( comp_a_complex_a @ SV170 @ SV133 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[817]) ).
thf(846,plain,
! [SV170: a > complex,SV133: a > a,SV89: a > real,SV29: real > a] :
( ( ( ( comp_real_a_a @ SV29 @ SV89 )
= SV133 )
= $false )
| ( ( ( comp_real_complex_a @ ( comp_a_complex_real @ SV170 @ SV29 ) @ SV89 )
= ( comp_a_complex_a @ SV170 @ SV133 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[817]) ).
thf(847,plain,
! [SV171: real > complex,SV134: complex > complex,SV90: complex > a,SV30: a > complex] :
( ( ( ! [SV230: complex] :
( ( comp_a1063143865omplex @ SV30 @ SV90 @ SV230 )
= ( SV134 @ SV230 ) ) )
= $false )
| ( ( ( comp_a_complex_real @ SV30 @ ( comp_complex_a_real @ SV90 @ SV171 ) )
= ( comp_c595887981x_real @ SV134 @ SV171 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[818]) ).
thf(848,plain,
! [SV171: real > complex,SV134: complex > complex,SV90: complex > a,SV30: a > complex] :
( ( ( ( comp_a1063143865omplex @ SV30 @ SV90 )
= SV134 )
= $false )
| ( ( ( comp_a_complex_real @ SV30 @ ( comp_complex_a_real @ SV90 @ SV171 ) )
= ( comp_c595887981x_real @ SV134 @ SV171 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[818]) ).
thf(849,plain,
! [SV32: real > complex] :
( ( ( ( path_s36253918omplex @ SV32 )
| ( path_arc_complex @ SV32 ) )
= $false )
| ( ( ~ ( ~ ( path_s36253918omplex @ SV32 )
| ~ ( path_arc_complex @ SV32 ) ) )
= $true )
| ( ( ( path_p769714271omplex @ SV32 )
= ( path_p797330068omplex @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(850,plain,
! [SV172: a > real,SV135: real > complex,SV91: real > a,SV33: a > complex] :
( ( ( ! [SV231: real] :
( ( comp_a_complex_real @ SV33 @ SV91 @ SV231 )
= ( SV135 @ SV231 ) ) )
= $false )
| ( ( ( comp_a_complex_a @ SV33 @ ( comp_real_a_a @ SV91 @ SV172 ) )
= ( comp_real_complex_a @ SV135 @ SV172 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[821]) ).
thf(851,plain,
! [SV172: a > real,SV135: real > complex,SV91: real > a,SV33: a > complex] :
( ( ( ( comp_a_complex_real @ SV33 @ SV91 )
= SV135 )
= $false )
| ( ( ( comp_a_complex_a @ SV33 @ ( comp_real_a_a @ SV91 @ SV172 ) )
= ( comp_real_complex_a @ SV135 @ SV172 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[821]) ).
thf(852,plain,
! [SV173: complex > real,SV136: real > complex,SV92: real > a,SV34: a > complex] :
( ( ( ! [SV232: real] :
( ( comp_a_complex_real @ SV34 @ SV92 @ SV232 )
= ( SV136 @ SV232 ) ) )
= $false )
| ( ( ( comp_a1063143865omplex @ SV34 @ ( comp_real_a_complex @ SV92 @ SV173 ) )
= ( comp_r667767405omplex @ SV136 @ SV173 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[822]) ).
thf(853,plain,
! [SV173: complex > real,SV136: real > complex,SV92: real > a,SV34: a > complex] :
( ( ( ( comp_a_complex_real @ SV34 @ SV92 )
= SV136 )
= $false )
| ( ( ( comp_a1063143865omplex @ SV34 @ ( comp_real_a_complex @ SV92 @ SV173 ) )
= ( comp_r667767405omplex @ SV136 @ SV173 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[822]) ).
thf(854,plain,
! [SV174: real > a,SV137: a > complex,SV93: real > a,SV35: a > complex] :
( ( ( ! [SV233: real] :
( ( comp_a_complex_real @ SV35 @ SV93 @ SV233 )
= ( comp_a_complex_real @ SV137 @ SV174 @ SV233 ) ) )
= $false )
| ( ( ! [SY466: real] :
( ( SV35 @ ( SV93 @ SY466 ) )
= ( SV137 @ ( SV174 @ SY466 ) ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[823]) ).
thf(855,plain,
! [SV174: real > a,SV137: a > complex,SV93: real > a,SV35: a > complex] :
( ( ( ( comp_a_complex_real @ SV35 @ SV93 )
= ( comp_a_complex_real @ SV137 @ SV174 ) )
= $false )
| ( ( ! [SY466: real] :
( ( SV35 @ ( SV93 @ SY466 ) )
= ( SV137 @ ( SV174 @ SY466 ) ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[823]) ).
thf(856,plain,
! [SV175: real,SV138: real > complex,SV94: real > a,SV37: a > complex] :
( ( ( ! [SV234: real] :
( ( comp_a_complex_real @ SV37 @ SV94 @ SV234 )
= ( SV138 @ SV234 ) ) )
= $false )
| ( ( ( SV37 @ ( SV94 @ SV175 ) )
= ( SV138 @ SV175 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[824]) ).
thf(857,plain,
! [SV175: real,SV138: real > complex,SV94: real > a,SV37: a > complex] :
( ( ( ( comp_a_complex_real @ SV37 @ SV94 )
= SV138 )
= $false )
| ( ( ( SV37 @ ( SV94 @ SV175 ) )
= ( SV138 @ SV175 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[824]) ).
thf(858,plain,
! [SV176: a > complex,SV139: real > a,SV97: real > complex,SV40: complex > a] :
( ( ( ! [SV235: real] :
( ( comp_complex_a_real @ SV40 @ SV97 @ SV235 )
= ( SV139 @ SV235 ) ) )
= $false )
| ( ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV176 @ SV40 ) @ SV97 )
= ( comp_a_complex_real @ SV176 @ SV139 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[825]) ).
thf(859,plain,
! [SV176: a > complex,SV139: real > a,SV97: real > complex,SV40: complex > a] :
( ( ( ( comp_complex_a_real @ SV40 @ SV97 )
= SV139 )
= $false )
| ( ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV176 @ SV40 ) @ SV97 )
= ( comp_a_complex_real @ SV176 @ SV139 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[825]) ).
thf(860,plain,
! [SV221: a,SV207: a > a,SV177: a > complex,SV140: real,SV98: real > a,SV41: a > complex] :
( ( ( ( SV41 @ ( SV98 @ SV140 ) )
!= ( SV177 @ ( SV207 @ SV221 ) ) )
= $true )
| ( ( ( comp_a_complex_real @ SV41 @ SV98 @ SV140 )
= ( comp_a_complex_a @ SV177 @ SV207 @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(861,plain,
! [SV99: real > complex] :
( ( ( ~ ( path_arc_complex @ SV99 )
| ~ ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) )
= $false )
| ( ( path_arc_complex @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(862,plain,
! [SV99: real > complex] :
( ( ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) )
= $true )
| ( ( ~ ( ~ ( path_arc_complex @ SV99 )
| ~ ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[828]) ).
thf(863,plain,
! [SV208: set_complex,SV178: a > complex,SV141: set_a,SV100: set_real,SV43: real > a] :
( ( ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
= $false )
| ( ( ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
= ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[829]) ).
thf(864,plain,
! [SV209: real,SV179: real > a,SV142: a > complex,SV101: real > a,SV44: a > complex] :
( ( ( ( comp_a_complex_real @ SV44 @ SV101 )
= ( comp_a_complex_real @ SV142 @ SV179 ) )
= $false )
| ( ( ( SV44 @ ( SV101 @ SV209 ) )
= ( SV142 @ ( SV179 @ SV209 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(865,plain,
! [SV180: real > a,SV143: a > complex,SV104: a > complex,SV47: complex > complex] :
( ( ( ! [SV236: a] :
( ( comp_c124850173plex_a @ SV47 @ SV104 @ SV236 )
= ( SV143 @ SV236 ) ) )
= $false )
| ( ( ( comp_c595887981x_real @ SV47 @ ( comp_a_complex_real @ SV104 @ SV180 ) )
= ( comp_a_complex_real @ SV143 @ SV180 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[831]) ).
thf(866,plain,
! [SV180: real > a,SV143: a > complex,SV104: a > complex,SV47: complex > complex] :
( ( ( ( comp_c124850173plex_a @ SV47 @ SV104 )
= SV143 )
= $false )
| ( ( ( comp_c595887981x_real @ SV47 @ ( comp_a_complex_real @ SV104 @ SV180 ) )
= ( comp_a_complex_real @ SV143 @ SV180 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[831]) ).
thf(867,plain,
! [SV222: complex,SV210: complex > a,SV181: a > complex,SV144: real,SV105: real > a,SV48: a > complex] :
( ( ( ( SV48 @ ( SV105 @ SV144 ) )
!= ( SV181 @ ( SV210 @ SV222 ) ) )
= $true )
| ( ( ( comp_a_complex_real @ SV48 @ SV105 @ SV144 )
= ( comp_a1063143865omplex @ SV181 @ SV210 @ SV222 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[832]) ).
thf(868,plain,
! [SV182: a > complex,SV145: complex > a,SV106: complex > real,SV49: real > a] :
( ( ( ! [SV237: complex] :
( ( comp_real_a_complex @ SV49 @ SV106 @ SV237 )
= ( SV145 @ SV237 ) ) )
= $false )
| ( ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV182 @ SV49 ) @ SV106 )
= ( comp_a1063143865omplex @ SV182 @ SV145 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[833]) ).
thf(869,plain,
! [SV182: a > complex,SV145: complex > a,SV106: complex > real,SV49: real > a] :
( ( ( ( comp_real_a_complex @ SV49 @ SV106 )
= SV145 )
= $false )
| ( ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV182 @ SV49 ) @ SV106 )
= ( comp_a1063143865omplex @ SV182 @ SV145 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[833]) ).
thf(870,plain,
! [SV223: a > complex,SV211: complex > a,SV183: a > a,SV146: complex,SV108: complex > real,SV51: real > a] :
( ( ( ( SV51 @ ( SV108 @ SV146 ) )
!= ( SV183 @ ( SV211 @ SV146 ) ) )
= $true )
| ( ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV223 @ SV51 ) @ SV108 @ SV146 )
= ( comp_a1063143865omplex @ ( comp_a_complex_a @ SV223 @ SV183 ) @ SV211 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(871,plain,
! [SV224: a > complex,SV212: real > a,SV184: a > a,SV147: real,SV109: real > complex,SV53: complex > a] :
( ( ( ( SV53 @ ( SV109 @ SV147 ) )
!= ( SV184 @ ( SV212 @ SV147 ) ) )
= $true )
| ( ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV224 @ SV53 ) @ SV109 @ SV147 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SV224 @ SV184 ) @ SV212 @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[836]) ).
thf(872,plain,
! [SV225: real,SV213: real > a,SV185: a > complex,SV148: real,SV110: real > a,SV54: a > complex] :
( ( ( ( SV54 @ ( SV110 @ SV148 ) )
!= ( SV185 @ ( SV213 @ SV225 ) ) )
= $true )
| ( ( ( comp_a_complex_real @ SV54 @ SV110 @ SV148 )
= ( comp_a_complex_real @ SV185 @ SV213 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(873,plain,
! [SV186: real,SV149: real > complex,SV111: real > a,SV55: a > complex] :
( ( ( ! [SV238: real] :
( ( comp_a_complex_real @ SV55 @ SV111 @ SV238 )
= ( comp_c595887981x_real @ id_complex @ SV149 @ SV238 ) ) )
= $false )
| ( ( ( SV55 @ ( SV111 @ SV186 ) )
= ( SV149 @ SV186 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[838]) ).
thf(874,plain,
! [SV186: real,SV149: real > complex,SV111: real > a,SV55: a > complex] :
( ( ( ( comp_a_complex_real @ SV55 @ SV111 )
= ( comp_c595887981x_real @ id_complex @ SV149 ) )
= $false )
| ( ( ( SV55 @ ( SV111 @ SV186 ) )
= ( SV149 @ SV186 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[838]) ).
thf(875,plain,
! [SV226: complex > a,SV214: complex > real,SV187: real > a,SV150: a > complex,SV112: real > a,SV56: a > complex] :
( ( ( ( comp_a_complex_real @ SV56 @ SV112 )
!= ( comp_a_complex_real @ SV150 @ SV187 ) )
= $true )
| ( ( ( ( comp_real_a_complex @ SV187 @ SV214 )
!= SV226 )
| ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(876,plain,
! [SV227: a > complex,SV215: real > a,SV188: a > a,SV151: real,SV113: real > real,SV57: real > a] :
( ( ( ( SV57 @ ( SV113 @ SV151 ) )
!= ( SV188 @ ( SV215 @ SV151 ) ) )
= $true )
| ( ( ( comp_r701421291x_real @ ( comp_a_complex_real @ SV227 @ SV57 ) @ SV113 @ SV151 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SV227 @ SV188 ) @ SV215 @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(877,plain,
! [SV228: real,SV216: real > a,SV189: a > complex,SV152: complex,SV114: complex > a,SV58: a > complex] :
( ( ( ( SV58 @ ( SV114 @ SV152 ) )
!= ( SV189 @ ( SV216 @ SV228 ) ) )
= $true )
| ( ( ( comp_a1063143865omplex @ SV58 @ SV114 @ SV152 )
= ( comp_a_complex_real @ SV189 @ SV216 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[841]) ).
thf(878,plain,
! [SV190: real > real,SV153: real > complex,SV115: real > a,SV59: a > complex] :
( ( ( ! [SV239: real] :
( ( comp_a_complex_real @ SV59 @ SV115 @ SV239 )
= ( SV153 @ SV239 ) ) )
= $false )
| ( ( ( comp_a_complex_real @ SV59 @ ( comp_real_a_real @ SV115 @ SV190 ) )
= ( comp_r701421291x_real @ SV153 @ SV190 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[842]) ).
thf(879,plain,
! [SV190: real > real,SV153: real > complex,SV115: real > a,SV59: a > complex] :
( ( ( ( comp_a_complex_real @ SV59 @ SV115 )
= SV153 )
= $false )
| ( ( ( comp_a_complex_real @ SV59 @ ( comp_real_a_real @ SV115 @ SV190 ) )
= ( comp_r701421291x_real @ SV153 @ SV190 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[842]) ).
thf(880,plain,
! [SV217: set_complex,SV191: a > complex,SV154: set_a,SV116: set_real,SV60: real > a] :
( ( ( bij_betw_real_a @ SV60 @ SV116 @ SV154 )
= $false )
| ( ( ~ ( bij_betw_a_complex @ SV191 @ SV154 @ SV217 )
| ( bij_be122140626omplex @ ( comp_a_complex_real @ SV191 @ SV60 ) @ SV116 @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(881,plain,
! [SV220: a > complex,SV206: a > a,SV169: a > a,SV132: a,SV87: a > real,SV27: real > a] :
( ( ( ( SV27 @ ( SV87 @ SV132 ) )
= ( SV169 @ ( SV206 @ SV132 ) ) )
= $false )
| ( ( ( comp_real_complex_a @ ( comp_a_complex_real @ SV220 @ SV27 ) @ SV87 @ SV132 )
= ( comp_a_complex_a @ ( comp_a_complex_a @ SV220 @ SV169 ) @ SV206 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(882,plain,
! [SV133: a > a,SV170: a > complex,SV89: a > real,SV29: real > a] :
( ( ( ( comp_real_a_a @ SV29 @ SV89 @ ( sK1_SV229 @ SV170 @ SV133 @ SV89 @ SV29 ) )
= ( SV133 @ ( sK1_SV229 @ SV170 @ SV133 @ SV89 @ SV29 ) ) )
= $false )
| ( ( ( comp_real_complex_a @ ( comp_a_complex_real @ SV170 @ SV29 ) @ SV89 )
= ( comp_a_complex_a @ SV170 @ SV133 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[845]) ).
thf(883,plain,
! [SV133: a > a,SV89: a > real,SV29: real > a,SV170: a > complex] :
( ( ( ! [SV240: a] :
( ( comp_real_complex_a @ ( comp_a_complex_real @ SV170 @ SV29 ) @ SV89 @ SV240 )
= ( comp_a_complex_a @ SV170 @ SV133 @ SV240 ) ) )
= $true )
| ( ( ( comp_real_a_a @ SV29 @ SV89 )
= SV133 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[846]) ).
thf(884,plain,
! [SV133: a > a,SV89: a > real,SV29: real > a,SV170: a > complex] :
( ( ( ( comp_real_complex_a @ ( comp_a_complex_real @ SV170 @ SV29 ) @ SV89 )
= ( comp_a_complex_a @ SV170 @ SV133 ) )
= $true )
| ( ( ( comp_real_a_a @ SV29 @ SV89 )
= SV133 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[846]) ).
thf(885,plain,
! [SV134: complex > complex,SV171: real > complex,SV90: complex > a,SV30: a > complex] :
( ( ( ( comp_a1063143865omplex @ SV30 @ SV90 @ ( sK2_SV230 @ SV171 @ SV134 @ SV90 @ SV30 ) )
= ( SV134 @ ( sK2_SV230 @ SV171 @ SV134 @ SV90 @ SV30 ) ) )
= $false )
| ( ( ( comp_a_complex_real @ SV30 @ ( comp_complex_a_real @ SV90 @ SV171 ) )
= ( comp_c595887981x_real @ SV134 @ SV171 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[847]) ).
thf(886,plain,
! [SV134: complex > complex,SV171: real > complex,SV90: complex > a,SV30: a > complex] :
( ( ( ! [SV241: real] :
( ( comp_a_complex_real @ SV30 @ ( comp_complex_a_real @ SV90 @ SV171 ) @ SV241 )
= ( comp_c595887981x_real @ SV134 @ SV171 @ SV241 ) ) )
= $true )
| ( ( ( comp_a1063143865omplex @ SV30 @ SV90 )
= SV134 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[848]) ).
thf(887,plain,
! [SV134: complex > complex,SV171: real > complex,SV90: complex > a,SV30: a > complex] :
( ( ( ( comp_a_complex_real @ SV30 @ ( comp_complex_a_real @ SV90 @ SV171 ) )
= ( comp_c595887981x_real @ SV134 @ SV171 ) )
= $true )
| ( ( ( comp_a1063143865omplex @ SV30 @ SV90 )
= SV134 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[848]) ).
thf(888,plain,
! [SV32: real > complex] :
( ( ( path_s36253918omplex @ SV32 )
= $false )
| ( ( ~ ( ~ ( path_s36253918omplex @ SV32 )
| ~ ( path_arc_complex @ SV32 ) ) )
= $true )
| ( ( ( path_p769714271omplex @ SV32 )
= ( path_p797330068omplex @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(889,plain,
! [SV32: real > complex] :
( ( ( path_arc_complex @ SV32 )
= $false )
| ( ( ~ ( ~ ( path_s36253918omplex @ SV32 )
| ~ ( path_arc_complex @ SV32 ) ) )
= $true )
| ( ( ( path_p769714271omplex @ SV32 )
= ( path_p797330068omplex @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(890,plain,
! [SV135: real > complex,SV172: a > real,SV91: real > a,SV33: a > complex] :
( ( ( ( comp_a_complex_real @ SV33 @ SV91 @ ( sK3_SV231 @ SV172 @ SV135 @ SV91 @ SV33 ) )
= ( SV135 @ ( sK3_SV231 @ SV172 @ SV135 @ SV91 @ SV33 ) ) )
= $false )
| ( ( ( comp_a_complex_a @ SV33 @ ( comp_real_a_a @ SV91 @ SV172 ) )
= ( comp_real_complex_a @ SV135 @ SV172 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[850]) ).
thf(891,plain,
! [SV135: real > complex,SV172: a > real,SV91: real > a,SV33: a > complex] :
( ( ( ! [SV242: a] :
( ( comp_a_complex_a @ SV33 @ ( comp_real_a_a @ SV91 @ SV172 ) @ SV242 )
= ( comp_real_complex_a @ SV135 @ SV172 @ SV242 ) ) )
= $true )
| ( ( ( comp_a_complex_real @ SV33 @ SV91 )
= SV135 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[851]) ).
thf(892,plain,
! [SV135: real > complex,SV172: a > real,SV91: real > a,SV33: a > complex] :
( ( ( ( comp_a_complex_a @ SV33 @ ( comp_real_a_a @ SV91 @ SV172 ) )
= ( comp_real_complex_a @ SV135 @ SV172 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV33 @ SV91 )
= SV135 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[851]) ).
thf(893,plain,
! [SV136: real > complex,SV173: complex > real,SV92: real > a,SV34: a > complex] :
( ( ( ( comp_a_complex_real @ SV34 @ SV92 @ ( sK4_SV232 @ SV173 @ SV136 @ SV92 @ SV34 ) )
= ( SV136 @ ( sK4_SV232 @ SV173 @ SV136 @ SV92 @ SV34 ) ) )
= $false )
| ( ( ( comp_a1063143865omplex @ SV34 @ ( comp_real_a_complex @ SV92 @ SV173 ) )
= ( comp_r667767405omplex @ SV136 @ SV173 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[852]) ).
thf(894,plain,
! [SV136: real > complex,SV173: complex > real,SV92: real > a,SV34: a > complex] :
( ( ( ! [SV243: complex] :
( ( comp_a1063143865omplex @ SV34 @ ( comp_real_a_complex @ SV92 @ SV173 ) @ SV243 )
= ( comp_r667767405omplex @ SV136 @ SV173 @ SV243 ) ) )
= $true )
| ( ( ( comp_a_complex_real @ SV34 @ SV92 )
= SV136 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[853]) ).
thf(895,plain,
! [SV136: real > complex,SV173: complex > real,SV92: real > a,SV34: a > complex] :
( ( ( ( comp_a1063143865omplex @ SV34 @ ( comp_real_a_complex @ SV92 @ SV173 ) )
= ( comp_r667767405omplex @ SV136 @ SV173 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV34 @ SV92 )
= SV136 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[853]) ).
thf(896,plain,
! [SV137: a > complex,SV174: real > a,SV93: real > a,SV35: a > complex] :
( ( ( ( comp_a_complex_real @ SV35 @ SV93 @ ( sK5_SV233 @ SV174 @ SV137 @ SV93 @ SV35 ) )
= ( comp_a_complex_real @ SV137 @ SV174 @ ( sK5_SV233 @ SV174 @ SV137 @ SV93 @ SV35 ) ) )
= $false )
| ( ( ! [SY466: real] :
( ( SV35 @ ( SV93 @ SY466 ) )
= ( SV137 @ ( SV174 @ SY466 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[854]) ).
thf(897,plain,
! [SV174: real > a,SV137: a > complex,SV244: real,SV93: real > a,SV35: a > complex] :
( ( ( ( SV35 @ ( SV93 @ SV244 ) )
= ( SV137 @ ( SV174 @ SV244 ) ) )
= $true )
| ( ( ( comp_a_complex_real @ SV35 @ SV93 )
= ( comp_a_complex_real @ SV137 @ SV174 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(898,plain,
! [SV138: real > complex,SV175: real,SV94: real > a,SV37: a > complex] :
( ( ( ( comp_a_complex_real @ SV37 @ SV94 @ ( sK6_SV234 @ SV175 @ SV138 @ SV94 @ SV37 ) )
= ( SV138 @ ( sK6_SV234 @ SV175 @ SV138 @ SV94 @ SV37 ) ) )
= $false )
| ( ( ( SV37 @ ( SV94 @ SV175 ) )
= ( SV138 @ SV175 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[856]) ).
thf(899,plain,
! [SV139: real > a,SV176: a > complex,SV97: real > complex,SV40: complex > a] :
( ( ( ( comp_complex_a_real @ SV40 @ SV97 @ ( sK7_SV235 @ SV176 @ SV139 @ SV97 @ SV40 ) )
= ( SV139 @ ( sK7_SV235 @ SV176 @ SV139 @ SV97 @ SV40 ) ) )
= $false )
| ( ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV176 @ SV40 ) @ SV97 )
= ( comp_a_complex_real @ SV176 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[858]) ).
thf(900,plain,
! [SV139: real > a,SV97: real > complex,SV40: complex > a,SV176: a > complex] :
( ( ( ! [SV245: real] :
( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV176 @ SV40 ) @ SV97 @ SV245 )
= ( comp_a_complex_real @ SV176 @ SV139 @ SV245 ) ) )
= $true )
| ( ( ( comp_complex_a_real @ SV40 @ SV97 )
= SV139 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[859]) ).
thf(901,plain,
! [SV139: real > a,SV97: real > complex,SV40: complex > a,SV176: a > complex] :
( ( ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV176 @ SV40 ) @ SV97 )
= ( comp_a_complex_real @ SV176 @ SV139 ) )
= $true )
| ( ( ( comp_complex_a_real @ SV40 @ SV97 )
= SV139 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[859]) ).
thf(902,plain,
! [SV221: a,SV207: a > a,SV177: a > complex,SV140: real,SV98: real > a,SV41: a > complex] :
( ( ( ( SV41 @ ( SV98 @ SV140 ) )
= ( SV177 @ ( SV207 @ SV221 ) ) )
= $false )
| ( ( ( comp_a_complex_real @ SV41 @ SV98 @ SV140 )
= ( comp_a_complex_a @ SV177 @ SV207 @ SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(903,plain,
! [SV99: real > complex] :
( ( ( ~ ( path_arc_complex @ SV99 ) )
= $false )
| ( ( path_arc_complex @ SV99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[861]) ).
thf(904,plain,
! [SV99: real > complex] :
( ( ( ~ ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) )
= $false )
| ( ( path_arc_complex @ SV99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[861]) ).
thf(905,plain,
! [SV99: real > complex] :
( ( ( ~ ( path_s36253918omplex @ SV99 ) )
= $true )
| ( ( ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) )
= $true )
| ( ( ~ ( ~ ( path_arc_complex @ SV99 )
| ~ ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(906,plain,
! [SV100: set_real,SV43: real > a,SV208: set_complex,SV141: set_a,SV178: a > complex] :
( ( ( ~ ( ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
| ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 ) )
| ~ ( ~ ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
| ~ ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 ) ) )
= $true )
| ( ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[863]) ).
thf(907,plain,
! [SV100: set_real,SV43: real > a,SV208: set_complex,SV141: set_a,SV178: a > complex] :
( ( ( ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
= ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 ) )
= $true )
| ( ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[863]) ).
thf(908,plain,
! [SV209: real,SV179: real > a,SV142: a > complex,SV101: real > a,SV44: a > complex] :
( ( ( ! [SV246: real] :
( ( comp_a_complex_real @ SV44 @ SV101 @ SV246 )
= ( comp_a_complex_real @ SV142 @ SV179 @ SV246 ) ) )
= $false )
| ( ( ( SV44 @ ( SV101 @ SV209 ) )
= ( SV142 @ ( SV179 @ SV209 ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[864]) ).
thf(909,plain,
! [SV209: real,SV179: real > a,SV142: a > complex,SV101: real > a,SV44: a > complex] :
( ( ( ( comp_a_complex_real @ SV44 @ SV101 )
= ( comp_a_complex_real @ SV142 @ SV179 ) )
= $false )
| ( ( ( SV44 @ ( SV101 @ SV209 ) )
= ( SV142 @ ( SV179 @ SV209 ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[864]) ).
thf(910,plain,
! [SV143: a > complex,SV180: real > a,SV104: a > complex,SV47: complex > complex] :
( ( ( ( comp_c124850173plex_a @ SV47 @ SV104 @ ( sK8_SV236 @ SV180 @ SV143 @ SV104 @ SV47 ) )
= ( SV143 @ ( sK8_SV236 @ SV180 @ SV143 @ SV104 @ SV47 ) ) )
= $false )
| ( ( ( comp_c595887981x_real @ SV47 @ ( comp_a_complex_real @ SV104 @ SV180 ) )
= ( comp_a_complex_real @ SV143 @ SV180 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[865]) ).
thf(911,plain,
! [SV143: a > complex,SV180: real > a,SV104: a > complex,SV47: complex > complex] :
( ( ( ! [SV247: real] :
( ( comp_c595887981x_real @ SV47 @ ( comp_a_complex_real @ SV104 @ SV180 ) @ SV247 )
= ( comp_a_complex_real @ SV143 @ SV180 @ SV247 ) ) )
= $true )
| ( ( ( comp_c124850173plex_a @ SV47 @ SV104 )
= SV143 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[866]) ).
thf(912,plain,
! [SV143: a > complex,SV180: real > a,SV104: a > complex,SV47: complex > complex] :
( ( ( ( comp_c595887981x_real @ SV47 @ ( comp_a_complex_real @ SV104 @ SV180 ) )
= ( comp_a_complex_real @ SV143 @ SV180 ) )
= $true )
| ( ( ( comp_c124850173plex_a @ SV47 @ SV104 )
= SV143 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[866]) ).
thf(913,plain,
! [SV222: complex,SV210: complex > a,SV181: a > complex,SV144: real,SV105: real > a,SV48: a > complex] :
( ( ( ( SV48 @ ( SV105 @ SV144 ) )
= ( SV181 @ ( SV210 @ SV222 ) ) )
= $false )
| ( ( ( comp_a_complex_real @ SV48 @ SV105 @ SV144 )
= ( comp_a1063143865omplex @ SV181 @ SV210 @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(914,plain,
! [SV145: complex > a,SV182: a > complex,SV106: complex > real,SV49: real > a] :
( ( ( ( comp_real_a_complex @ SV49 @ SV106 @ ( sK9_SV237 @ SV182 @ SV145 @ SV106 @ SV49 ) )
= ( SV145 @ ( sK9_SV237 @ SV182 @ SV145 @ SV106 @ SV49 ) ) )
= $false )
| ( ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV182 @ SV49 ) @ SV106 )
= ( comp_a1063143865omplex @ SV182 @ SV145 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[868]) ).
thf(915,plain,
! [SV145: complex > a,SV106: complex > real,SV49: real > a,SV182: a > complex] :
( ( ( ! [SV248: complex] :
( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV182 @ SV49 ) @ SV106 @ SV248 )
= ( comp_a1063143865omplex @ SV182 @ SV145 @ SV248 ) ) )
= $true )
| ( ( ( comp_real_a_complex @ SV49 @ SV106 )
= SV145 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[869]) ).
thf(916,plain,
! [SV145: complex > a,SV106: complex > real,SV49: real > a,SV182: a > complex] :
( ( ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV182 @ SV49 ) @ SV106 )
= ( comp_a1063143865omplex @ SV182 @ SV145 ) )
= $true )
| ( ( ( comp_real_a_complex @ SV49 @ SV106 )
= SV145 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[869]) ).
thf(917,plain,
! [SV223: a > complex,SV211: complex > a,SV183: a > a,SV146: complex,SV108: complex > real,SV51: real > a] :
( ( ( ( SV51 @ ( SV108 @ SV146 ) )
= ( SV183 @ ( SV211 @ SV146 ) ) )
= $false )
| ( ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV223 @ SV51 ) @ SV108 @ SV146 )
= ( comp_a1063143865omplex @ ( comp_a_complex_a @ SV223 @ SV183 ) @ SV211 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(918,plain,
! [SV224: a > complex,SV212: real > a,SV184: a > a,SV147: real,SV109: real > complex,SV53: complex > a] :
( ( ( ( SV53 @ ( SV109 @ SV147 ) )
= ( SV184 @ ( SV212 @ SV147 ) ) )
= $false )
| ( ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV224 @ SV53 ) @ SV109 @ SV147 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SV224 @ SV184 ) @ SV212 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(919,plain,
! [SV225: real,SV213: real > a,SV185: a > complex,SV148: real,SV110: real > a,SV54: a > complex] :
( ( ( ( SV54 @ ( SV110 @ SV148 ) )
= ( SV185 @ ( SV213 @ SV225 ) ) )
= $false )
| ( ( ( comp_a_complex_real @ SV54 @ SV110 @ SV148 )
= ( comp_a_complex_real @ SV185 @ SV213 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(920,plain,
! [SV149: real > complex,SV186: real,SV111: real > a,SV55: a > complex] :
( ( ( ( comp_a_complex_real @ SV55 @ SV111 @ ( sK10_SV238 @ SV186 @ SV149 @ SV111 @ SV55 ) )
= ( comp_c595887981x_real @ id_complex @ SV149 @ ( sK10_SV238 @ SV186 @ SV149 @ SV111 @ SV55 ) ) )
= $false )
| ( ( ( SV55 @ ( SV111 @ SV186 ) )
= ( SV149 @ SV186 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[873]) ).
thf(921,plain,
! [SV226: complex > a,SV214: complex > real,SV187: real > a,SV150: a > complex,SV112: real > a,SV56: a > complex] :
( ( ( ( comp_a_complex_real @ SV56 @ SV112 )
= ( comp_a_complex_real @ SV150 @ SV187 ) )
= $false )
| ( ( ( ( comp_real_a_complex @ SV187 @ SV214 )
!= SV226 )
| ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[875]) ).
thf(922,plain,
! [SV227: a > complex,SV215: real > a,SV188: a > a,SV151: real,SV113: real > real,SV57: real > a] :
( ( ( ( SV57 @ ( SV113 @ SV151 ) )
= ( SV188 @ ( SV215 @ SV151 ) ) )
= $false )
| ( ( ( comp_r701421291x_real @ ( comp_a_complex_real @ SV227 @ SV57 ) @ SV113 @ SV151 )
= ( comp_a_complex_real @ ( comp_a_complex_a @ SV227 @ SV188 ) @ SV215 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(923,plain,
! [SV228: real,SV216: real > a,SV189: a > complex,SV152: complex,SV114: complex > a,SV58: a > complex] :
( ( ( ( SV58 @ ( SV114 @ SV152 ) )
= ( SV189 @ ( SV216 @ SV228 ) ) )
= $false )
| ( ( ( comp_a1063143865omplex @ SV58 @ SV114 @ SV152 )
= ( comp_a_complex_real @ SV189 @ SV216 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(924,plain,
! [SV153: real > complex,SV190: real > real,SV115: real > a,SV59: a > complex] :
( ( ( ( comp_a_complex_real @ SV59 @ SV115 @ ( sK11_SV239 @ SV190 @ SV153 @ SV115 @ SV59 ) )
= ( SV153 @ ( sK11_SV239 @ SV190 @ SV153 @ SV115 @ SV59 ) ) )
= $false )
| ( ( ( comp_a_complex_real @ SV59 @ ( comp_real_a_real @ SV115 @ SV190 ) )
= ( comp_r701421291x_real @ SV153 @ SV190 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[878]) ).
thf(925,plain,
! [SV153: real > complex,SV190: real > real,SV115: real > a,SV59: a > complex] :
( ( ( ! [SV249: real] :
( ( comp_a_complex_real @ SV59 @ ( comp_real_a_real @ SV115 @ SV190 ) @ SV249 )
= ( comp_r701421291x_real @ SV153 @ SV190 @ SV249 ) ) )
= $true )
| ( ( ( comp_a_complex_real @ SV59 @ SV115 )
= SV153 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[879]) ).
thf(926,plain,
! [SV153: real > complex,SV190: real > real,SV115: real > a,SV59: a > complex] :
( ( ( ( comp_a_complex_real @ SV59 @ ( comp_real_a_real @ SV115 @ SV190 ) )
= ( comp_r701421291x_real @ SV153 @ SV190 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV59 @ SV115 )
= SV153 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[879]) ).
thf(927,plain,
! [SV116: set_real,SV60: real > a,SV217: set_complex,SV154: set_a,SV191: a > complex] :
( ( ( ~ ( bij_betw_a_complex @ SV191 @ SV154 @ SV217 ) )
= $true )
| ( ( bij_be122140626omplex @ ( comp_a_complex_real @ SV191 @ SV60 ) @ SV116 @ SV217 )
= $true )
| ( ( bij_betw_real_a @ SV60 @ SV116 @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(928,plain,
! [SV133: a > a,SV89: a > real,SV29: real > a,SV170: a > complex] :
( ( ( ! [SV250: a] :
( ( comp_real_complex_a @ ( comp_a_complex_real @ SV170 @ SV29 ) @ SV89 @ SV250 )
= ( comp_a_complex_a @ SV170 @ SV133 @ SV250 ) ) )
= $true )
| ( ( ( comp_real_a_a @ SV29 @ SV89 @ ( sK1_SV229 @ SV170 @ SV133 @ SV89 @ SV29 ) )
= ( SV133 @ ( sK1_SV229 @ SV170 @ SV133 @ SV89 @ SV29 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[882]) ).
thf(929,plain,
! [SV133: a > a,SV89: a > real,SV29: real > a,SV170: a > complex] :
( ( ( ( comp_real_complex_a @ ( comp_a_complex_real @ SV170 @ SV29 ) @ SV89 )
= ( comp_a_complex_a @ SV170 @ SV133 ) )
= $true )
| ( ( ( comp_real_a_a @ SV29 @ SV89 @ ( sK1_SV229 @ SV170 @ SV133 @ SV89 @ SV29 ) )
= ( SV133 @ ( sK1_SV229 @ SV170 @ SV133 @ SV89 @ SV29 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[882]) ).
thf(930,plain,
! [SV133: a > a,SV251: a,SV89: a > real,SV29: real > a,SV170: a > complex] :
( ( ( ( comp_real_complex_a @ ( comp_a_complex_real @ SV170 @ SV29 ) @ SV89 @ SV251 )
= ( comp_a_complex_a @ SV170 @ SV133 @ SV251 ) )
= $true )
| ( ( ( comp_real_a_a @ SV29 @ SV89 )
= SV133 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(931,plain,
! [SV134: complex > complex,SV171: real > complex,SV90: complex > a,SV30: a > complex] :
( ( ( ! [SV252: real] :
( ( comp_a_complex_real @ SV30 @ ( comp_complex_a_real @ SV90 @ SV171 ) @ SV252 )
= ( comp_c595887981x_real @ SV134 @ SV171 @ SV252 ) ) )
= $true )
| ( ( ( comp_a1063143865omplex @ SV30 @ SV90 @ ( sK2_SV230 @ SV171 @ SV134 @ SV90 @ SV30 ) )
= ( SV134 @ ( sK2_SV230 @ SV171 @ SV134 @ SV90 @ SV30 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[885]) ).
thf(932,plain,
! [SV134: complex > complex,SV171: real > complex,SV90: complex > a,SV30: a > complex] :
( ( ( ( comp_a_complex_real @ SV30 @ ( comp_complex_a_real @ SV90 @ SV171 ) )
= ( comp_c595887981x_real @ SV134 @ SV171 ) )
= $true )
| ( ( ( comp_a1063143865omplex @ SV30 @ SV90 @ ( sK2_SV230 @ SV171 @ SV134 @ SV90 @ SV30 ) )
= ( SV134 @ ( sK2_SV230 @ SV171 @ SV134 @ SV90 @ SV30 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[885]) ).
thf(933,plain,
! [SV134: complex > complex,SV253: real,SV171: real > complex,SV90: complex > a,SV30: a > complex] :
( ( ( ( comp_a_complex_real @ SV30 @ ( comp_complex_a_real @ SV90 @ SV171 ) @ SV253 )
= ( comp_c595887981x_real @ SV134 @ SV171 @ SV253 ) )
= $true )
| ( ( ( comp_a1063143865omplex @ SV30 @ SV90 )
= SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(934,plain,
! [SV32: real > complex] :
( ( ( ~ ( path_s36253918omplex @ SV32 )
| ~ ( path_arc_complex @ SV32 ) )
= $false )
| ( ( path_s36253918omplex @ SV32 )
= $false )
| ( ( ( path_p769714271omplex @ SV32 )
= ( path_p797330068omplex @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(935,plain,
! [SV32: real > complex] :
( ( ( ~ ( path_s36253918omplex @ SV32 )
| ~ ( path_arc_complex @ SV32 ) )
= $false )
| ( ( path_arc_complex @ SV32 )
= $false )
| ( ( ( path_p769714271omplex @ SV32 )
= ( path_p797330068omplex @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(936,plain,
! [SV135: real > complex,SV172: a > real,SV91: real > a,SV33: a > complex] :
( ( ( ! [SV254: a] :
( ( comp_a_complex_a @ SV33 @ ( comp_real_a_a @ SV91 @ SV172 ) @ SV254 )
= ( comp_real_complex_a @ SV135 @ SV172 @ SV254 ) ) )
= $true )
| ( ( ( comp_a_complex_real @ SV33 @ SV91 @ ( sK3_SV231 @ SV172 @ SV135 @ SV91 @ SV33 ) )
= ( SV135 @ ( sK3_SV231 @ SV172 @ SV135 @ SV91 @ SV33 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[890]) ).
thf(937,plain,
! [SV135: real > complex,SV172: a > real,SV91: real > a,SV33: a > complex] :
( ( ( ( comp_a_complex_a @ SV33 @ ( comp_real_a_a @ SV91 @ SV172 ) )
= ( comp_real_complex_a @ SV135 @ SV172 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV33 @ SV91 @ ( sK3_SV231 @ SV172 @ SV135 @ SV91 @ SV33 ) )
= ( SV135 @ ( sK3_SV231 @ SV172 @ SV135 @ SV91 @ SV33 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[890]) ).
thf(938,plain,
! [SV135: real > complex,SV255: a,SV172: a > real,SV91: real > a,SV33: a > complex] :
( ( ( ( comp_a_complex_a @ SV33 @ ( comp_real_a_a @ SV91 @ SV172 ) @ SV255 )
= ( comp_real_complex_a @ SV135 @ SV172 @ SV255 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV33 @ SV91 )
= SV135 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(939,plain,
! [SV136: real > complex,SV173: complex > real,SV92: real > a,SV34: a > complex] :
( ( ( ! [SV256: complex] :
( ( comp_a1063143865omplex @ SV34 @ ( comp_real_a_complex @ SV92 @ SV173 ) @ SV256 )
= ( comp_r667767405omplex @ SV136 @ SV173 @ SV256 ) ) )
= $true )
| ( ( ( comp_a_complex_real @ SV34 @ SV92 @ ( sK4_SV232 @ SV173 @ SV136 @ SV92 @ SV34 ) )
= ( SV136 @ ( sK4_SV232 @ SV173 @ SV136 @ SV92 @ SV34 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[893]) ).
thf(940,plain,
! [SV136: real > complex,SV173: complex > real,SV92: real > a,SV34: a > complex] :
( ( ( ( comp_a1063143865omplex @ SV34 @ ( comp_real_a_complex @ SV92 @ SV173 ) )
= ( comp_r667767405omplex @ SV136 @ SV173 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV34 @ SV92 @ ( sK4_SV232 @ SV173 @ SV136 @ SV92 @ SV34 ) )
= ( SV136 @ ( sK4_SV232 @ SV173 @ SV136 @ SV92 @ SV34 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[893]) ).
thf(941,plain,
! [SV136: real > complex,SV257: complex,SV173: complex > real,SV92: real > a,SV34: a > complex] :
( ( ( ( comp_a1063143865omplex @ SV34 @ ( comp_real_a_complex @ SV92 @ SV173 ) @ SV257 )
= ( comp_r667767405omplex @ SV136 @ SV173 @ SV257 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV34 @ SV92 )
= SV136 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(942,plain,
! [SV174: real > a,SV137: a > complex,SV258: real,SV93: real > a,SV35: a > complex] :
( ( ( ( SV35 @ ( SV93 @ SV258 ) )
= ( SV137 @ ( SV174 @ SV258 ) ) )
= $true )
| ( ( ( comp_a_complex_real @ SV35 @ SV93 @ ( sK5_SV233 @ SV174 @ SV137 @ SV93 @ SV35 ) )
= ( comp_a_complex_real @ SV137 @ SV174 @ ( sK5_SV233 @ SV174 @ SV137 @ SV93 @ SV35 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(943,plain,
! [SV139: real > a,SV97: real > complex,SV40: complex > a,SV176: a > complex] :
( ( ( ! [SV259: real] :
( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV176 @ SV40 ) @ SV97 @ SV259 )
= ( comp_a_complex_real @ SV176 @ SV139 @ SV259 ) ) )
= $true )
| ( ( ( comp_complex_a_real @ SV40 @ SV97 @ ( sK7_SV235 @ SV176 @ SV139 @ SV97 @ SV40 ) )
= ( SV139 @ ( sK7_SV235 @ SV176 @ SV139 @ SV97 @ SV40 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[899]) ).
thf(944,plain,
! [SV139: real > a,SV97: real > complex,SV40: complex > a,SV176: a > complex] :
( ( ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV176 @ SV40 ) @ SV97 )
= ( comp_a_complex_real @ SV176 @ SV139 ) )
= $true )
| ( ( ( comp_complex_a_real @ SV40 @ SV97 @ ( sK7_SV235 @ SV176 @ SV139 @ SV97 @ SV40 ) )
= ( SV139 @ ( sK7_SV235 @ SV176 @ SV139 @ SV97 @ SV40 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[899]) ).
thf(945,plain,
! [SV139: real > a,SV260: real,SV97: real > complex,SV40: complex > a,SV176: a > complex] :
( ( ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV176 @ SV40 ) @ SV97 @ SV260 )
= ( comp_a_complex_real @ SV176 @ SV139 @ SV260 ) )
= $true )
| ( ( ( comp_complex_a_real @ SV40 @ SV97 )
= SV139 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(946,plain,
! [SV99: real > complex] :
( ( ( path_arc_complex @ SV99 )
= $true )
| ( ( path_arc_complex @ SV99 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[903]) ).
thf(947,plain,
! [SV99: real > complex] :
( ( ( ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) )
= $true )
| ( ( path_arc_complex @ SV99 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[904]) ).
thf(948,plain,
! [SV99: real > complex] :
( ( ( path_s36253918omplex @ SV99 )
= $false )
| ( ( ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) )
= $true )
| ( ( ~ ( ~ ( path_arc_complex @ SV99 )
| ~ ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(949,plain,
! [SV100: set_real,SV43: real > a,SV208: set_complex,SV141: set_a,SV178: a > complex] :
( ( ( ~ ( ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
| ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 ) ) )
= $true )
| ( ( ~ ( ~ ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
| ~ ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 ) ) )
= $true )
| ( ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(950,plain,
! [SV142: a > complex,SV179: real > a,SV209: real,SV101: real > a,SV44: a > complex] :
( ( ( ( comp_a_complex_real @ SV44 @ SV101 @ ( sK12_SV246 @ SV209 @ SV179 @ SV142 @ SV101 @ SV44 ) )
= ( comp_a_complex_real @ SV142 @ SV179 @ ( sK12_SV246 @ SV209 @ SV179 @ SV142 @ SV101 @ SV44 ) ) )
= $false )
| ( ( ( SV44 @ ( SV101 @ SV209 ) )
= ( SV142 @ ( SV179 @ SV209 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[908]) ).
thf(951,plain,
! [SV143: a > complex,SV180: real > a,SV104: a > complex,SV47: complex > complex] :
( ( ( ! [SV261: real] :
( ( comp_c595887981x_real @ SV47 @ ( comp_a_complex_real @ SV104 @ SV180 ) @ SV261 )
= ( comp_a_complex_real @ SV143 @ SV180 @ SV261 ) ) )
= $true )
| ( ( ( comp_c124850173plex_a @ SV47 @ SV104 @ ( sK8_SV236 @ SV180 @ SV143 @ SV104 @ SV47 ) )
= ( SV143 @ ( sK8_SV236 @ SV180 @ SV143 @ SV104 @ SV47 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[910]) ).
thf(952,plain,
! [SV143: a > complex,SV180: real > a,SV104: a > complex,SV47: complex > complex] :
( ( ( ( comp_c595887981x_real @ SV47 @ ( comp_a_complex_real @ SV104 @ SV180 ) )
= ( comp_a_complex_real @ SV143 @ SV180 ) )
= $true )
| ( ( ( comp_c124850173plex_a @ SV47 @ SV104 @ ( sK8_SV236 @ SV180 @ SV143 @ SV104 @ SV47 ) )
= ( SV143 @ ( sK8_SV236 @ SV180 @ SV143 @ SV104 @ SV47 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[910]) ).
thf(953,plain,
! [SV143: a > complex,SV262: real,SV180: real > a,SV104: a > complex,SV47: complex > complex] :
( ( ( ( comp_c595887981x_real @ SV47 @ ( comp_a_complex_real @ SV104 @ SV180 ) @ SV262 )
= ( comp_a_complex_real @ SV143 @ SV180 @ SV262 ) )
= $true )
| ( ( ( comp_c124850173plex_a @ SV47 @ SV104 )
= SV143 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(954,plain,
! [SV145: complex > a,SV106: complex > real,SV49: real > a,SV182: a > complex] :
( ( ( ! [SV263: complex] :
( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV182 @ SV49 ) @ SV106 @ SV263 )
= ( comp_a1063143865omplex @ SV182 @ SV145 @ SV263 ) ) )
= $true )
| ( ( ( comp_real_a_complex @ SV49 @ SV106 @ ( sK9_SV237 @ SV182 @ SV145 @ SV106 @ SV49 ) )
= ( SV145 @ ( sK9_SV237 @ SV182 @ SV145 @ SV106 @ SV49 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[914]) ).
thf(955,plain,
! [SV145: complex > a,SV106: complex > real,SV49: real > a,SV182: a > complex] :
( ( ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV182 @ SV49 ) @ SV106 )
= ( comp_a1063143865omplex @ SV182 @ SV145 ) )
= $true )
| ( ( ( comp_real_a_complex @ SV49 @ SV106 @ ( sK9_SV237 @ SV182 @ SV145 @ SV106 @ SV49 ) )
= ( SV145 @ ( sK9_SV237 @ SV182 @ SV145 @ SV106 @ SV49 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[914]) ).
thf(956,plain,
! [SV145: complex > a,SV264: complex,SV106: complex > real,SV49: real > a,SV182: a > complex] :
( ( ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV182 @ SV49 ) @ SV106 @ SV264 )
= ( comp_a1063143865omplex @ SV182 @ SV145 @ SV264 ) )
= $true )
| ( ( ( comp_real_a_complex @ SV49 @ SV106 )
= SV145 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(957,plain,
! [SV226: complex > a,SV214: complex > real,SV187: real > a,SV150: a > complex,SV112: real > a,SV56: a > complex] :
( ( ( ! [SV265: real] :
( ( comp_a_complex_real @ SV56 @ SV112 @ SV265 )
= ( comp_a_complex_real @ SV150 @ SV187 @ SV265 ) ) )
= $false )
| ( ( ( ( comp_real_a_complex @ SV187 @ SV214 )
!= SV226 )
| ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[921]) ).
thf(958,plain,
! [SV226: complex > a,SV214: complex > real,SV187: real > a,SV150: a > complex,SV112: real > a,SV56: a > complex] :
( ( ( ( comp_a_complex_real @ SV56 @ SV112 )
= ( comp_a_complex_real @ SV150 @ SV187 ) )
= $false )
| ( ( ( ( comp_real_a_complex @ SV187 @ SV214 )
!= SV226 )
| ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[921]) ).
thf(959,plain,
! [SV153: real > complex,SV190: real > real,SV115: real > a,SV59: a > complex] :
( ( ( ! [SV266: real] :
( ( comp_a_complex_real @ SV59 @ ( comp_real_a_real @ SV115 @ SV190 ) @ SV266 )
= ( comp_r701421291x_real @ SV153 @ SV190 @ SV266 ) ) )
= $true )
| ( ( ( comp_a_complex_real @ SV59 @ SV115 @ ( sK11_SV239 @ SV190 @ SV153 @ SV115 @ SV59 ) )
= ( SV153 @ ( sK11_SV239 @ SV190 @ SV153 @ SV115 @ SV59 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[924]) ).
thf(960,plain,
! [SV153: real > complex,SV190: real > real,SV115: real > a,SV59: a > complex] :
( ( ( ( comp_a_complex_real @ SV59 @ ( comp_real_a_real @ SV115 @ SV190 ) )
= ( comp_r701421291x_real @ SV153 @ SV190 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV59 @ SV115 @ ( sK11_SV239 @ SV190 @ SV153 @ SV115 @ SV59 ) )
= ( SV153 @ ( sK11_SV239 @ SV190 @ SV153 @ SV115 @ SV59 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[924]) ).
thf(961,plain,
! [SV153: real > complex,SV267: real,SV190: real > real,SV115: real > a,SV59: a > complex] :
( ( ( ( comp_a_complex_real @ SV59 @ ( comp_real_a_real @ SV115 @ SV190 ) @ SV267 )
= ( comp_r701421291x_real @ SV153 @ SV190 @ SV267 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV59 @ SV115 )
= SV153 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(962,plain,
! [SV116: set_real,SV60: real > a,SV217: set_complex,SV154: set_a,SV191: a > complex] :
( ( ( bij_betw_a_complex @ SV191 @ SV154 @ SV217 )
= $false )
| ( ( bij_be122140626omplex @ ( comp_a_complex_real @ SV191 @ SV60 ) @ SV116 @ SV217 )
= $true )
| ( ( bij_betw_real_a @ SV60 @ SV116 @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(963,plain,
! [SV133: a > a,SV268: a,SV89: a > real,SV29: real > a,SV170: a > complex] :
( ( ( ( comp_real_complex_a @ ( comp_a_complex_real @ SV170 @ SV29 ) @ SV89 @ SV268 )
= ( comp_a_complex_a @ SV170 @ SV133 @ SV268 ) )
= $true )
| ( ( ( comp_real_a_a @ SV29 @ SV89 @ ( sK1_SV229 @ SV170 @ SV133 @ SV89 @ SV29 ) )
= ( SV133 @ ( sK1_SV229 @ SV170 @ SV133 @ SV89 @ SV29 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(964,plain,
! [SV134: complex > complex,SV269: real,SV171: real > complex,SV90: complex > a,SV30: a > complex] :
( ( ( ( comp_a_complex_real @ SV30 @ ( comp_complex_a_real @ SV90 @ SV171 ) @ SV269 )
= ( comp_c595887981x_real @ SV134 @ SV171 @ SV269 ) )
= $true )
| ( ( ( comp_a1063143865omplex @ SV30 @ SV90 @ ( sK2_SV230 @ SV171 @ SV134 @ SV90 @ SV30 ) )
= ( SV134 @ ( sK2_SV230 @ SV171 @ SV134 @ SV90 @ SV30 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(965,plain,
! [SV32: real > complex] :
( ( ( ~ ( path_s36253918omplex @ SV32 ) )
= $false )
| ( ( path_s36253918omplex @ SV32 )
= $false )
| ( ( ( path_p769714271omplex @ SV32 )
= ( path_p797330068omplex @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[934]) ).
thf(966,plain,
! [SV32: real > complex] :
( ( ( ~ ( path_arc_complex @ SV32 ) )
= $false )
| ( ( path_s36253918omplex @ SV32 )
= $false )
| ( ( ( path_p769714271omplex @ SV32 )
= ( path_p797330068omplex @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[934]) ).
thf(967,plain,
! [SV32: real > complex] :
( ( ( ~ ( path_s36253918omplex @ SV32 ) )
= $false )
| ( ( path_arc_complex @ SV32 )
= $false )
| ( ( ( path_p769714271omplex @ SV32 )
= ( path_p797330068omplex @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[935]) ).
thf(968,plain,
! [SV32: real > complex] :
( ( ( ~ ( path_arc_complex @ SV32 ) )
= $false )
| ( ( path_arc_complex @ SV32 )
= $false )
| ( ( ( path_p769714271omplex @ SV32 )
= ( path_p797330068omplex @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[935]) ).
thf(969,plain,
! [SV135: real > complex,SV270: a,SV172: a > real,SV91: real > a,SV33: a > complex] :
( ( ( ( comp_a_complex_a @ SV33 @ ( comp_real_a_a @ SV91 @ SV172 ) @ SV270 )
= ( comp_real_complex_a @ SV135 @ SV172 @ SV270 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV33 @ SV91 @ ( sK3_SV231 @ SV172 @ SV135 @ SV91 @ SV33 ) )
= ( SV135 @ ( sK3_SV231 @ SV172 @ SV135 @ SV91 @ SV33 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(970,plain,
! [SV136: real > complex,SV271: complex,SV173: complex > real,SV92: real > a,SV34: a > complex] :
( ( ( ( comp_a1063143865omplex @ SV34 @ ( comp_real_a_complex @ SV92 @ SV173 ) @ SV271 )
= ( comp_r667767405omplex @ SV136 @ SV173 @ SV271 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV34 @ SV92 @ ( sK4_SV232 @ SV173 @ SV136 @ SV92 @ SV34 ) )
= ( SV136 @ ( sK4_SV232 @ SV173 @ SV136 @ SV92 @ SV34 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(971,plain,
! [SV139: real > a,SV272: real,SV97: real > complex,SV40: complex > a,SV176: a > complex] :
( ( ( ( comp_c595887981x_real @ ( comp_a1063143865omplex @ SV176 @ SV40 ) @ SV97 @ SV272 )
= ( comp_a_complex_real @ SV176 @ SV139 @ SV272 ) )
= $true )
| ( ( ( comp_complex_a_real @ SV40 @ SV97 @ ( sK7_SV235 @ SV176 @ SV139 @ SV97 @ SV40 ) )
= ( SV139 @ ( sK7_SV235 @ SV176 @ SV139 @ SV97 @ SV40 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(972,plain,
! [SV99: real > complex] :
( ( ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) )
= $false )
| ( ( path_arc_complex @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(973,plain,
! [SV99: real > complex] :
( ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) )
= $false )
| ( ( path_s36253918omplex @ SV99 )
= $false )
| ( ( ~ ( ~ ( path_arc_complex @ SV99 )
| ~ ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[948]) ).
thf(974,plain,
! [SV100: set_real,SV43: real > a,SV208: set_complex,SV141: set_a,SV178: a > complex] :
( ( ( ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
| ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 ) )
= $false )
| ( ( ~ ( ~ ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
| ~ ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 ) ) )
= $true )
| ( ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(975,plain,
! [SV143: a > complex,SV273: real,SV180: real > a,SV104: a > complex,SV47: complex > complex] :
( ( ( ( comp_c595887981x_real @ SV47 @ ( comp_a_complex_real @ SV104 @ SV180 ) @ SV273 )
= ( comp_a_complex_real @ SV143 @ SV180 @ SV273 ) )
= $true )
| ( ( ( comp_c124850173plex_a @ SV47 @ SV104 @ ( sK8_SV236 @ SV180 @ SV143 @ SV104 @ SV47 ) )
= ( SV143 @ ( sK8_SV236 @ SV180 @ SV143 @ SV104 @ SV47 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(976,plain,
! [SV145: complex > a,SV274: complex,SV106: complex > real,SV49: real > a,SV182: a > complex] :
( ( ( ( comp_r667767405omplex @ ( comp_a_complex_real @ SV182 @ SV49 ) @ SV106 @ SV274 )
= ( comp_a1063143865omplex @ SV182 @ SV145 @ SV274 ) )
= $true )
| ( ( ( comp_real_a_complex @ SV49 @ SV106 @ ( sK9_SV237 @ SV182 @ SV145 @ SV106 @ SV49 ) )
= ( SV145 @ ( sK9_SV237 @ SV182 @ SV145 @ SV106 @ SV49 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(977,plain,
! [SV150: a > complex,SV187: real > a,SV214: complex > real,SV226: complex > a,SV112: real > a,SV56: a > complex] :
( ( ( ( comp_a_complex_real @ SV56 @ SV112 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) )
= ( comp_a_complex_real @ SV150 @ SV187 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) ) )
= $false )
| ( ( ( ( comp_real_a_complex @ SV187 @ SV214 )
!= SV226 )
| ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[957]) ).
thf(978,plain,
! [SV150: a > complex,SV112: real > a,SV56: a > complex,SV226: complex > a,SV214: complex > real,SV187: real > a] :
( ( ( ( comp_real_a_complex @ SV187 @ SV214 )
!= SV226 )
= $true )
| ( ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 )
= ( comp_a_complex_real @ SV150 @ SV187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[958]) ).
thf(979,plain,
! [SV153: real > complex,SV275: real,SV190: real > real,SV115: real > a,SV59: a > complex] :
( ( ( ( comp_a_complex_real @ SV59 @ ( comp_real_a_real @ SV115 @ SV190 ) @ SV275 )
= ( comp_r701421291x_real @ SV153 @ SV190 @ SV275 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV59 @ SV115 @ ( sK11_SV239 @ SV190 @ SV153 @ SV115 @ SV59 ) )
= ( SV153 @ ( sK11_SV239 @ SV190 @ SV153 @ SV115 @ SV59 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(980,plain,
! [SV32: real > complex] :
( ( ( path_s36253918omplex @ SV32 )
= $true )
| ( ( path_s36253918omplex @ SV32 )
= $false )
| ( ( ( path_p769714271omplex @ SV32 )
= ( path_p797330068omplex @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[965]) ).
thf(981,plain,
! [SV32: real > complex] :
( ( ( path_arc_complex @ SV32 )
= $true )
| ( ( path_s36253918omplex @ SV32 )
= $false )
| ( ( ( path_p769714271omplex @ SV32 )
= ( path_p797330068omplex @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[966]) ).
thf(982,plain,
! [SV32: real > complex] :
( ( ( path_s36253918omplex @ SV32 )
= $true )
| ( ( path_arc_complex @ SV32 )
= $false )
| ( ( ( path_p769714271omplex @ SV32 )
= ( path_p797330068omplex @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[967]) ).
thf(983,plain,
! [SV32: real > complex] :
( ( ( path_arc_complex @ SV32 )
= $true )
| ( ( path_arc_complex @ SV32 )
= $false )
| ( ( ( path_p769714271omplex @ SV32 )
= ( path_p797330068omplex @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[968]) ).
thf(984,plain,
! [SV99: real > complex] :
( ( ( ~ ( path_s36253918omplex @ SV99 ) )
= $false )
| ( ( path_arc_complex @ SV99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[972]) ).
thf(985,plain,
! [SV99: real > complex] :
( ( ( ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) )
= $false )
| ( ( path_arc_complex @ SV99 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[972]) ).
thf(986,plain,
! [SV99: real > complex] :
( ( ( ( path_p769714271omplex @ SV99 )
= ( path_p797330068omplex @ SV99 ) )
= $true )
| ( ( path_s36253918omplex @ SV99 )
= $false )
| ( ( ~ ( ~ ( path_arc_complex @ SV99 )
| ~ ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(987,plain,
! [SV100: set_real,SV43: real > a,SV208: set_complex,SV141: set_a,SV178: a > complex] :
( ( ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
= $false )
| ( ( ~ ( ~ ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
| ~ ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 ) ) )
= $true )
| ( ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[974]) ).
thf(988,plain,
! [SV141: set_a,SV208: set_complex,SV100: set_real,SV43: real > a,SV178: a > complex] :
( ( ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 )
= $false )
| ( ( ~ ( ~ ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
| ~ ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 ) ) )
= $true )
| ( ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[974]) ).
thf(989,plain,
! [SV150: a > complex,SV112: real > a,SV56: a > complex,SV226: complex > a,SV214: complex > real,SV187: real > a] :
( ( ( ( comp_real_a_complex @ SV187 @ SV214 )
!= SV226 )
= $true )
| ( ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) )
= ( comp_a_complex_real @ SV150 @ SV187 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[977]) ).
thf(990,plain,
! [SV150: a > complex,SV112: real > a,SV56: a > complex,SV226: complex > a,SV214: complex > real,SV187: real > a] :
( ( ( ( comp_real_a_complex @ SV187 @ SV214 )
= SV226 )
= $false )
| ( ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 )
= ( comp_a_complex_real @ SV150 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(991,plain,
! [SV99: real > complex] :
( ( ( path_s36253918omplex @ SV99 )
= $true )
| ( ( path_arc_complex @ SV99 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(992,plain,
! [SV99: real > complex] :
( ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) )
= $true )
| ( ( path_arc_complex @ SV99 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(993,plain,
! [SV99: real > complex] :
( ( ( ~ ( path_arc_complex @ SV99 )
| ~ ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) )
= $false )
| ( ( path_s36253918omplex @ SV99 )
= $false )
| ( ( ( path_p769714271omplex @ SV99 )
= ( path_p797330068omplex @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(994,plain,
! [SV100: set_real,SV43: real > a,SV208: set_complex,SV141: set_a,SV178: a > complex] :
( ( ( ~ ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
| ~ ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 ) )
= $false )
| ( ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
= $false )
| ( ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(995,plain,
! [SV100: set_real,SV43: real > a,SV208: set_complex,SV141: set_a,SV178: a > complex] :
( ( ( ~ ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
| ~ ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 ) )
= $false )
| ( ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 )
= $false )
| ( ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(996,plain,
! [SV150: a > complex,SV112: real > a,SV56: a > complex,SV226: complex > a,SV214: complex > real,SV187: real > a] :
( ( ( ( comp_real_a_complex @ SV187 @ SV214 )
= SV226 )
= $false )
| ( ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) )
= ( comp_a_complex_real @ SV150 @ SV187 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(997,plain,
! [SV150: a > complex,SV112: real > a,SV56: a > complex,SV226: complex > a,SV214: complex > real,SV187: real > a] :
( ( ( ! [SV276: complex] :
( ( comp_real_a_complex @ SV187 @ SV214 @ SV276 )
= ( SV226 @ SV276 ) ) )
= $false )
| ( ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 )
= ( comp_a_complex_real @ SV150 @ SV187 ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[990]) ).
thf(998,plain,
! [SV150: a > complex,SV112: real > a,SV56: a > complex,SV226: complex > a,SV214: complex > real,SV187: real > a] :
( ( ( ( comp_real_a_complex @ SV187 @ SV214 )
= SV226 )
= $false )
| ( ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 )
= ( comp_a_complex_real @ SV150 @ SV187 ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[990]) ).
thf(999,plain,
! [SV99: real > complex] :
( ( ( ( path_p769714271omplex @ SV99 )
= ( path_p797330068omplex @ SV99 ) )
= $false )
| ( ( path_arc_complex @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1000,plain,
! [SV99: real > complex] :
( ( ( ~ ( path_arc_complex @ SV99 ) )
= $false )
| ( ( path_s36253918omplex @ SV99 )
= $false )
| ( ( ( path_p769714271omplex @ SV99 )
= ( path_p797330068omplex @ SV99 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[993]) ).
thf(1001,plain,
! [SV99: real > complex] :
( ( ( ~ ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) )
= $false )
| ( ( path_s36253918omplex @ SV99 )
= $false )
| ( ( ( path_p769714271omplex @ SV99 )
= ( path_p797330068omplex @ SV99 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[993]) ).
thf(1002,plain,
! [SV100: set_real,SV43: real > a,SV208: set_complex,SV141: set_a,SV178: a > complex] :
( ( ( ~ ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 ) )
= $false )
| ( ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
= $false )
| ( ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[994]) ).
thf(1003,plain,
! [SV141: set_a,SV208: set_complex,SV100: set_real,SV43: real > a,SV178: a > complex] :
( ( ( ~ ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 ) )
= $false )
| ( ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
= $false )
| ( ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[994]) ).
thf(1004,plain,
! [SV100: set_real,SV43: real > a,SV208: set_complex,SV141: set_a,SV178: a > complex] :
( ( ( ~ ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 ) )
= $false )
| ( ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 )
= $false )
| ( ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[995]) ).
thf(1005,plain,
! [SV141: set_a,SV208: set_complex,SV100: set_real,SV43: real > a,SV178: a > complex] :
( ( ( ~ ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 ) )
= $false )
| ( ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 )
= $false )
| ( ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[995]) ).
thf(1006,plain,
! [SV150: a > complex,SV112: real > a,SV56: a > complex,SV226: complex > a,SV214: complex > real,SV187: real > a] :
( ( ( ! [SV277: complex] :
( ( comp_real_a_complex @ SV187 @ SV214 @ SV277 )
= ( SV226 @ SV277 ) ) )
= $false )
| ( ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) )
= ( comp_a_complex_real @ SV150 @ SV187 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[996]) ).
thf(1007,plain,
! [SV150: a > complex,SV112: real > a,SV56: a > complex,SV226: complex > a,SV214: complex > real,SV187: real > a] :
( ( ( ( comp_real_a_complex @ SV187 @ SV214 )
= SV226 )
= $false )
| ( ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) )
= ( comp_a_complex_real @ SV150 @ SV187 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[996]) ).
thf(1008,plain,
! [SV226: complex > a,SV56: a > complex,SV112: real > a,SV150: a > complex,SV214: complex > real,SV187: real > a] :
( ( ( ( comp_real_a_complex @ SV187 @ SV214 @ ( sK14_SV276 @ SV150 @ SV112 @ SV56 @ SV226 @ SV214 @ SV187 ) )
= ( SV226 @ ( sK14_SV276 @ SV150 @ SV112 @ SV56 @ SV226 @ SV214 @ SV187 ) ) )
= $false )
| ( ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 )
= ( comp_a_complex_real @ SV150 @ SV187 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[997]) ).
thf(1009,plain,
! [SV187: real > a,SV226: complex > a,SV150: a > complex,SV214: complex > real,SV112: real > a,SV56: a > complex] :
( ( ( ! [SV278: complex] :
( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) @ SV278 )
= ( comp_a1063143865omplex @ SV150 @ SV226 @ SV278 ) ) )
= $true )
| ( ( ( comp_real_a_complex @ SV187 @ SV214 )
= SV226 )
= $false )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 )
= ( comp_a_complex_real @ SV150 @ SV187 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[998]) ).
thf(1010,plain,
! [SV187: real > a,SV226: complex > a,SV150: a > complex,SV214: complex > real,SV112: real > a,SV56: a > complex] :
( ( ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) )
= $true )
| ( ( ( comp_real_a_complex @ SV187 @ SV214 )
= SV226 )
= $false )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 )
= ( comp_a_complex_real @ SV150 @ SV187 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[998]) ).
thf(1011,plain,
! [SV99: real > complex] :
( ( ( path_arc_complex @ SV99 )
= $true )
| ( ( path_s36253918omplex @ SV99 )
= $false )
| ( ( ( path_p769714271omplex @ SV99 )
= ( path_p797330068omplex @ SV99 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1012,plain,
! [SV99: real > complex] :
( ( ( ~ ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) ) )
= $true )
| ( ( path_s36253918omplex @ SV99 )
= $false )
| ( ( ( path_p769714271omplex @ SV99 )
= ( path_p797330068omplex @ SV99 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1001]) ).
thf(1013,plain,
! [SV100: set_real,SV43: real > a,SV208: set_complex,SV141: set_a,SV178: a > complex] :
( ( ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
= $true )
| ( ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
= $false )
| ( ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1002]) ).
thf(1014,plain,
! [SV141: set_a,SV208: set_complex,SV100: set_real,SV43: real > a,SV178: a > complex] :
( ( ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 )
= $true )
| ( ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
= $false )
| ( ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1003]) ).
thf(1015,plain,
! [SV100: set_real,SV43: real > a,SV208: set_complex,SV141: set_a,SV178: a > complex] :
( ( ( bij_betw_a_complex @ SV178 @ SV141 @ SV208 )
= $true )
| ( ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 )
= $false )
| ( ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1004]) ).
thf(1016,plain,
! [SV141: set_a,SV208: set_complex,SV100: set_real,SV43: real > a,SV178: a > complex] :
( ( ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 )
= $true )
| ( ( bij_be122140626omplex @ ( comp_a_complex_real @ SV178 @ SV43 ) @ SV100 @ SV208 )
= $false )
| ( ( bij_betw_real_a @ SV43 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1005]) ).
thf(1017,plain,
! [SV226: complex > a,SV56: a > complex,SV112: real > a,SV150: a > complex,SV214: complex > real,SV187: real > a] :
( ( ( ( comp_real_a_complex @ SV187 @ SV214 @ ( sK15_SV277 @ SV150 @ SV112 @ SV56 @ SV226 @ SV214 @ SV187 ) )
= ( SV226 @ ( sK15_SV277 @ SV150 @ SV112 @ SV56 @ SV226 @ SV214 @ SV187 ) ) )
= $false )
| ( ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) )
= $true )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) )
= ( comp_a_complex_real @ SV150 @ SV187 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1006]) ).
thf(1018,plain,
! [SV187: real > a,SV226: complex > a,SV150: a > complex,SV214: complex > real,SV112: real > a,SV56: a > complex] :
( ( ( ! [SV279: complex] :
( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) @ SV279 )
= ( comp_a1063143865omplex @ SV150 @ SV226 @ SV279 ) ) )
= $true )
| ( ( ( comp_real_a_complex @ SV187 @ SV214 )
= SV226 )
= $false )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) )
= ( comp_a_complex_real @ SV150 @ SV187 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1007]) ).
thf(1019,plain,
! [SV187: real > a,SV226: complex > a,SV150: a > complex,SV214: complex > real,SV112: real > a,SV56: a > complex] :
( ( ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) )
= $true )
| ( ( ( comp_real_a_complex @ SV187 @ SV214 )
= SV226 )
= $false )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) )
= ( comp_a_complex_real @ SV150 @ SV187 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1007]) ).
thf(1020,plain,
! [SV187: real > a,SV226: complex > a,SV150: a > complex,SV214: complex > real,SV112: real > a,SV56: a > complex] :
( ( ( ! [SV280: complex] :
( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) @ SV280 )
= ( comp_a1063143865omplex @ SV150 @ SV226 @ SV280 ) ) )
= $true )
| ( ( ( comp_real_a_complex @ SV187 @ SV214 @ ( sK14_SV276 @ SV150 @ SV112 @ SV56 @ SV226 @ SV214 @ SV187 ) )
= ( SV226 @ ( sK14_SV276 @ SV150 @ SV112 @ SV56 @ SV226 @ SV214 @ SV187 ) ) )
= $false )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 )
= ( comp_a_complex_real @ SV150 @ SV187 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1008]) ).
thf(1021,plain,
! [SV187: real > a,SV226: complex > a,SV150: a > complex,SV214: complex > real,SV112: real > a,SV56: a > complex] :
( ( ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) )
= $true )
| ( ( ( comp_real_a_complex @ SV187 @ SV214 @ ( sK14_SV276 @ SV150 @ SV112 @ SV56 @ SV226 @ SV214 @ SV187 ) )
= ( SV226 @ ( sK14_SV276 @ SV150 @ SV112 @ SV56 @ SV226 @ SV214 @ SV187 ) ) )
= $false )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 )
= ( comp_a_complex_real @ SV150 @ SV187 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1008]) ).
thf(1022,plain,
! [SV187: real > a,SV226: complex > a,SV150: a > complex,SV281: complex,SV214: complex > real,SV112: real > a,SV56: a > complex] :
( ( ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) @ SV281 )
= ( comp_a1063143865omplex @ SV150 @ SV226 @ SV281 ) )
= $true )
| ( ( ( comp_real_a_complex @ SV187 @ SV214 )
= SV226 )
= $false )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 )
= ( comp_a_complex_real @ SV150 @ SV187 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1023,plain,
! [SV99: real > complex] :
( ( ( ~ ( path_s36253918omplex @ SV99 )
| ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) )
= $false )
| ( ( path_s36253918omplex @ SV99 )
= $false )
| ( ( ( path_p769714271omplex @ SV99 )
= ( path_p797330068omplex @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1024,plain,
! [SV187: real > a,SV226: complex > a,SV150: a > complex,SV214: complex > real,SV112: real > a,SV56: a > complex] :
( ( ( ! [SV282: complex] :
( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) @ SV282 )
= ( comp_a1063143865omplex @ SV150 @ SV226 @ SV282 ) ) )
= $true )
| ( ( ( comp_real_a_complex @ SV187 @ SV214 @ ( sK15_SV277 @ SV150 @ SV112 @ SV56 @ SV226 @ SV214 @ SV187 ) )
= ( SV226 @ ( sK15_SV277 @ SV150 @ SV112 @ SV56 @ SV226 @ SV214 @ SV187 ) ) )
= $false )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) )
= ( comp_a_complex_real @ SV150 @ SV187 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1017]) ).
thf(1025,plain,
! [SV187: real > a,SV226: complex > a,SV150: a > complex,SV214: complex > real,SV112: real > a,SV56: a > complex] :
( ( ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) )
= ( comp_a1063143865omplex @ SV150 @ SV226 ) )
= $true )
| ( ( ( comp_real_a_complex @ SV187 @ SV214 @ ( sK15_SV277 @ SV150 @ SV112 @ SV56 @ SV226 @ SV214 @ SV187 ) )
= ( SV226 @ ( sK15_SV277 @ SV150 @ SV112 @ SV56 @ SV226 @ SV214 @ SV187 ) ) )
= $false )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) )
= ( comp_a_complex_real @ SV150 @ SV187 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1017]) ).
thf(1026,plain,
! [SV187: real > a,SV226: complex > a,SV150: a > complex,SV283: complex,SV214: complex > real,SV112: real > a,SV56: a > complex] :
( ( ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) @ SV283 )
= ( comp_a1063143865omplex @ SV150 @ SV226 @ SV283 ) )
= $true )
| ( ( ( comp_real_a_complex @ SV187 @ SV214 )
= SV226 )
= $false )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) )
= ( comp_a_complex_real @ SV150 @ SV187 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1027,plain,
! [SV187: real > a,SV226: complex > a,SV150: a > complex,SV284: complex,SV214: complex > real,SV112: real > a,SV56: a > complex] :
( ( ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) @ SV284 )
= ( comp_a1063143865omplex @ SV150 @ SV226 @ SV284 ) )
= $true )
| ( ( ( comp_real_a_complex @ SV187 @ SV214 @ ( sK14_SV276 @ SV150 @ SV112 @ SV56 @ SV226 @ SV214 @ SV187 ) )
= ( SV226 @ ( sK14_SV276 @ SV150 @ SV112 @ SV56 @ SV226 @ SV214 @ SV187 ) ) )
= $false )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 )
= ( comp_a_complex_real @ SV150 @ SV187 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1028,plain,
! [SV99: real > complex] :
( ( ( ~ ( path_s36253918omplex @ SV99 ) )
= $false )
| ( ( path_s36253918omplex @ SV99 )
= $false )
| ( ( ( path_p769714271omplex @ SV99 )
= ( path_p797330068omplex @ SV99 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1023]) ).
thf(1029,plain,
! [SV99: real > complex] :
( ( ( ~ ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) ) ) )
= $false )
| ( ( path_s36253918omplex @ SV99 )
= $false )
| ( ( ( path_p769714271omplex @ SV99 )
= ( path_p797330068omplex @ SV99 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1023]) ).
thf(1030,plain,
! [SV187: real > a,SV226: complex > a,SV150: a > complex,SV285: complex,SV214: complex > real,SV112: real > a,SV56: a > complex] :
( ( ( ( comp_a1063143865omplex @ SV56 @ ( comp_real_a_complex @ SV112 @ SV214 ) @ SV285 )
= ( comp_a1063143865omplex @ SV150 @ SV226 @ SV285 ) )
= $true )
| ( ( ( comp_real_a_complex @ SV187 @ SV214 @ ( sK15_SV277 @ SV150 @ SV112 @ SV56 @ SV226 @ SV214 @ SV187 ) )
= ( SV226 @ ( sK15_SV277 @ SV150 @ SV112 @ SV56 @ SV226 @ SV214 @ SV187 ) ) )
= $false )
| ( ( ( comp_a_complex_real @ SV56 @ SV112 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) )
= ( comp_a_complex_real @ SV150 @ SV187 @ ( sK13_SV265 @ SV226 @ SV214 @ SV187 @ SV150 @ SV112 @ SV56 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1031,plain,
! [SV99: real > complex] :
( ( ( path_s36253918omplex @ SV99 )
= $true )
| ( ( path_s36253918omplex @ SV99 )
= $false )
| ( ( ( path_p769714271omplex @ SV99 )
= ( path_p797330068omplex @ SV99 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1028]) ).
thf(1032,plain,
! [SV99: real > complex] :
( ( ( ( path_p769714271omplex @ SV99 )
!= ( path_p797330068omplex @ SV99 ) )
= $true )
| ( ( path_s36253918omplex @ SV99 )
= $false )
| ( ( ( path_p769714271omplex @ SV99 )
= ( path_p797330068omplex @ SV99 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1029]) ).
thf(1033,plain,
! [SV99: real > complex] :
( ( ( ( path_p769714271omplex @ SV99 )
= ( path_p797330068omplex @ SV99 ) )
= $false )
| ( ( path_s36253918omplex @ SV99 )
= $false )
| ( ( ( path_p769714271omplex @ SV99 )
= ( path_p797330068omplex @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1034,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[425,1033,1031,1030,1027,1026,1025,1022,1021,1019,1016,1015,1014,1013,1011,1010,999,991,983,982,981,980,979,976,975,971,970,969,964,963,962,961,960,956,955,953,952,950,946,945,944,942,941,940,938,937,933,932,930,929,926,923,922,920,919,918,917,916,913,912,909,907,902,901,898,897,895,892,887,884,881,874,857,834,819,815,814,791,785,784,783,782,781,780,779,778,777,776,775,774,773,772,770,760,754,753,747,746,744,736,733,732,730,728,726,724,722,720,718,716,714,712,710,688,657,655,617,616,609,608,600,599,598,597,596,595,575,556,555,553,537,529,483,436,435,427,426]) ).
thf(1035,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1034]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP148^1 : 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
% 0.11/0.18 % Computer : n026.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Oct 6 11:21:16 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.27/1.64 ..
% 8.27/1.64
% 8.27/1.64 No.of.Axioms: 66
% 8.27/1.64
% 8.27/1.64 Length.of.Defs: 0
% 8.27/1.64
% 8.27/1.64 Contains.Choice.Funs: false
% 8.27/1.64 ............................
% 8.27/1.64
% 8.27/1.64 ********************************
% 8.27/1.64 * All subproblems solved! *
% 8.27/1.64 ********************************
% 8.27/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:66,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1034,loop_count:0,foatp_calls:1,translation:fof_full)
% 8.27/1.64
% 8.27/1.64 %**** Beginning of derivation protocol ****
% 8.27/1.64 % SZS output start CNFRefutation
% See solution above
% 8.27/1.65
% 8.27/1.65 %**** End of derivation protocol ****
% 8.27/1.65 %**** no. of clauses in derivation: 747 ****
% 8.27/1.65 %**** clause counter: 1034 ****
% 8.27/1.65
% 8.27/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:66,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1034,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------