%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP035^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:30 AM UTC 2026
% Result : Theorem 17.78s 5.21s
% Output : Refutation 18.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 254
% Syntax : Number of formulae : 510 ( 307 unt; 0 typ; 0 def)
% Number of atoms : 1245 ( 779 equ; 6 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 3121 ( 68 ~; 45 |; 78 &;2496 @)
% ( 0 <=>; 434 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 416 ( 416 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 48 usr; 10 con; 0-4 aty)
% Number of variables : 1157 ( 56 ^;1091 !; 10 ?;1157 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_complex_complex_type,type,
set_complex_complex: $tType ).
thf(set_complex_type,type,
set_complex: $tType ).
thf(set_real_type,type,
set_real: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(complex_type,type,
complex: $tType ).
thf(real_type,type,
real: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(comple372758642hic_on_decl,type,
comple372758642hic_on: ( complex > complex ) > set_complex > $o ).
thf(deriv_complex_decl,type,
deriv_complex: ( complex > complex ) > complex > complex ).
thf(comp_c1610621014omplex_decl,type,
comp_c1610621014omplex: ( ( complex > complex ) > complex > complex ) > ( ( complex > complex ) > complex > complex ) > ( complex > complex ) > complex > complex ).
thf(comp_c881053372omplex_decl,type,
comp_c881053372omplex: ( ( complex > complex ) > complex ) > ( complex > complex > complex ) > complex > complex ).
thf(comp_c1884694328l_real_decl,type,
comp_c1884694328l_real: ( ( complex > complex ) > real ) > ( real > complex > complex ) > real > real ).
thf(comp_c606622857omplex_decl,type,
comp_c606622857omplex: ( complex > complex > complex ) > ( ( complex > complex ) > complex ) > ( complex > complex ) > complex > complex ).
thf(comp_c130555887omplex_decl,type,
comp_c130555887omplex: ( complex > complex ) > ( complex > complex ) > complex > complex ).
thf(comp_c819638635l_real_decl,type,
comp_c819638635l_real: ( complex > real ) > ( real > complex ) > real > real ).
thf(comp_r2009261319omplex_decl,type,
comp_r2009261319omplex: ( real > complex > complex ) > ( ( complex > complex ) > real ) > ( complex > complex ) > complex > complex ).
thf(comp_r667767405omplex_decl,type,
comp_r667767405omplex: ( real > complex ) > ( complex > real ) > complex > complex ).
thf(comp_real_real_real_decl,type,
comp_real_real_real: ( real > real ) > ( real > real ) > real > real ).
thf(id_complex_complex_decl,type,
id_complex_complex: ( complex > complex ) > complex > complex ).
thf(id_complex_decl,type,
id_complex: complex > complex ).
thf(id_real_decl,type,
id_real: real > real ).
thf(id_set1618538368omplex_decl,type,
id_set1618538368omplex: set_complex_complex > set_complex_complex ).
thf(id_set_complex_decl,type,
id_set_complex: set_complex > set_complex ).
thf(id_set_real_decl,type,
id_set_real: set_real > set_real ).
thf(one_one_complex_decl,type,
one_one_complex: complex ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(times_times_complex_decl,type,
times_times_complex: complex > complex > complex ).
thf(times_times_nat_decl,type,
times_times_nat: nat > nat > nat ).
thf(times_1316095593omplex_decl,type,
times_1316095593omplex: set_complex > set_complex > set_complex ).
thf(zero_zero_complex_decl,type,
zero_zero_complex: complex ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(if_complex_decl,type,
if_complex: $o > complex > complex > complex ).
thf(compow1098280738omplex_decl,type,
compow1098280738omplex: nat > ( ( complex > complex ) > complex > complex ) > ( complex > complex ) > complex > complex ).
thf(compow1667379464omplex_decl,type,
compow1667379464omplex: nat > ( complex > complex ) > complex > complex ).
thf(compow_real_real_decl,type,
compow_real_real: nat > ( real > real ) > real > real ).
thf(funpow1854104714omplex_decl,type,
funpow1854104714omplex: nat > ( ( complex > complex ) > complex > complex ) > ( complex > complex ) > complex > complex ).
thf(funpow_complex_decl,type,
funpow_complex: nat > ( complex > complex ) > complex > complex ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ord_le701908932omplex_decl,type,
ord_le701908932omplex: set_complex > set_complex > $o ).
thf(collect_complex_decl,type,
collect_complex: ( complex > $o ) > set_complex ).
thf(image_944012797omplex_decl,type,
image_944012797omplex: ( ( complex > complex ) > complex > complex ) > set_complex_complex > set_complex_complex ).
thf(image_58037603omplex_decl,type,
image_58037603omplex: ( complex > complex ) > set_complex > set_complex ).
thf(image_real_real_decl,type,
image_real_real: ( real > real ) > set_real > set_real ).
thf(topolo935673511omplex_decl,type,
topolo935673511omplex: set_complex > $o ).
thf(topolo2127351575omplex_decl,type,
topolo2127351575omplex: set_complex > $o ).
thf(arcosh_complex_decl,type,
arcosh_complex: complex > complex ).
thf(arsinh_complex_decl,type,
arsinh_complex: complex > complex ).
thf(artanh_complex_decl,type,
artanh_complex: complex > complex ).
thf(ln_ln_complex_decl,type,
ln_ln_complex: complex > complex ).
thf(member_complex_decl,type,
member_complex: complex > set_complex > $o ).
thf(s_decl,type,
s: set_complex ).
thf(t_decl,type,
t: set_complex ).
thf(f_decl,type,
f: complex > complex ).
thf(g_decl,type,
g: complex > complex ).
thf(w_decl,type,
w: complex ).
thf(237,axiom,
! [A: real > complex,B: complex > real,C: real > complex] :
( ( ( comp_r667767405omplex @ A @ B )
= id_complex )
=> ( ( ( comp_c819638635l_real @ B @ C )
= id_real )
=> ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_left__right__inverse__eq) ).
thf(1024,plain,
! [A: real > complex,B: complex > real,C: real > complex] :
( ( ( comp_r667767405omplex @ A @ B )
= id_complex )
=> ( ( ( comp_c819638635l_real @ B @ C )
= id_real )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(201,axiom,
! [A: set_complex,B: set_complex] :
( ! [C: complex] :
( ( member_complex @ C @ A )
=> ( member_complex @ C @ B ) )
=> ( ord_le701908932omplex @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_subsetI) ).
thf(909,plain,
! [A: set_complex,B: set_complex] :
( ! [C: complex] :
( ( member_complex @ C @ A )
=> ( member_complex @ C @ B ) )
=> ( ord_le701908932omplex @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(72,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ one_one_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_mult__left__le) ).
thf(481,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ one_one_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(127,axiom,
! [A: complex > complex,B: complex > complex,C: complex > complex,D: complex] :
( ( ( comp_c130555887omplex @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_comp__eq__dest__lhs) ).
thf(645,plain,
! [A: complex > complex,B: complex > complex,C: complex > complex,D: complex] :
( ( ( comp_c130555887omplex @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(195,axiom,
! [A: set_complex,B: set_complex,C: set_complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( ord_le701908932omplex @ B @ C )
=> ( ord_le701908932omplex @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_order__trans) ).
thf(892,plain,
! [A: set_complex,B: set_complex,C: set_complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( ord_le701908932omplex @ B @ C )
=> ( ord_le701908932omplex @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(249,axiom,
! [A: complex > real,B: real > complex] :
( ( ( ( comp_c819638635l_real @ A @ B )
= id_real )
& ( ( comp_r667767405omplex @ B @ A )
= id_complex ) )
= ( ! [C: real] :
( ( A @ ( B @ C ) )
= C )
& ! [C: complex] :
( ( B @ ( A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_isomorphism__expand) ).
thf(1083,plain,
! [A: complex > real,B: real > complex] :
( ( ( ( comp_c819638635l_real @ A @ B )
= id_real )
& ( ( comp_r667767405omplex @ B @ A )
= id_complex ) )
= ( ! [C: real] :
( ( A @ ( B @ C ) )
= C )
& ! [C: complex] :
( ( B @ ( A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(69,axiom,
! [A: nat,B: nat] :
( ( one_one_nat
= ( times_times_nat @ A @ B ) )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_nat__1__eq__mult__iff) ).
thf(468,plain,
! [A: nat,B: nat] :
( ( one_one_nat
= ( times_times_nat @ A @ B ) )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(230,axiom,
! [A: complex,B: complex] :
( ( A
= ( times_times_complex @ A @ B ) )
= ( ( A = zero_zero_complex )
| ( B = one_one_complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_mult__cancel__left1) ).
thf(1005,plain,
! [A: complex,B: complex] :
( ( A
= ( times_times_complex @ A @ B ) )
= ( ( A = zero_zero_complex )
| ( B = one_one_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(9,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_mult_Oassoc) ).
thf(276,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(246,axiom,
! [A: complex > complex,B: complex > complex,C: complex > complex,D: complex] :
( ( ( comp_c130555887omplex @ A @ B )
= ( comp_c130555887omplex @ id_complex @ C ) )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_comp__eq__id__dest) ).
thf(1068,plain,
! [A: complex > complex,B: complex > complex,C: complex > complex,D: complex] :
( ( ( comp_c130555887omplex @ A @ B )
= ( comp_c130555887omplex @ id_complex @ C ) )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(152,axiom,
( id_complex_complex
= ( ^ [A: complex > complex] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_id__apply) ).
thf(741,plain,
( id_complex_complex
= ( ^ [A: complex > complex] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(188,axiom,
! [A: complex,B: complex,C: complex] :
( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
= ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_mult_Oassoc) ).
thf(873,plain,
! [A: complex,B: complex,C: complex] :
( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
= ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(40,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_mult__left__mono) ).
thf(384,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(94,axiom,
! [A: ( complex > complex ) > real,B: real > complex > complex,C: ( complex > complex ) > real] :
( ( ( comp_c1884694328l_real @ A @ B )
= id_real )
=> ( ( ( comp_r2009261319omplex @ B @ C )
= id_complex_complex )
=> ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_left__right__inverse__eq) ).
thf(550,plain,
! [A: ( complex > complex ) > real,B: real > complex > complex,C: ( complex > complex ) > real] :
( ( ( comp_c1884694328l_real @ A @ B )
= id_real )
=> ( ( ( comp_r2009261319omplex @ B @ C )
= id_complex_complex )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(202,axiom,
! [A: complex,B: set_complex,C: set_complex] :
( ( member_complex @ A @ ( times_1316095593omplex @ B @ C ) )
=> ~ ! [D: complex,E: complex] :
( ( A
= ( times_times_complex @ D @ E ) )
=> ( ( member_complex @ D @ B )
=> ~ ( member_complex @ E @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_set__times__elim) ).
thf(913,plain,
! [A: complex,B: set_complex,C: set_complex] :
( ( member_complex @ A @ ( times_1316095593omplex @ B @ C ) )
=> ~ ! [D: complex,E: complex] :
( ( A
= ( times_times_complex @ D @ E ) )
=> ( ( member_complex @ D @ B )
=> ~ ( member_complex @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(212,axiom,
! [A: complex > complex,B: complex > complex,C: complex > complex] :
( ( ( comp_c130555887omplex @ A @ B )
= id_complex )
=> ( ( ( comp_c130555887omplex @ B @ C )
= id_complex )
=> ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_left__right__inverse__eq) ).
thf(945,plain,
! [A: complex > complex,B: complex > complex,C: complex > complex] :
( ( ( comp_c130555887omplex @ A @ B )
= id_complex )
=> ( ( ( comp_c130555887omplex @ B @ C )
= id_complex )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(25,axiom,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_mult__0__right) ).
thf(340,plain,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(91,axiom,
! [A: complex > complex,B: set_complex,C: complex > $o] :
( ! [D: complex] :
( ( member_complex @ D @ ( image_58037603omplex @ A @ B ) )
=> ( C @ D ) )
=> ! [D: complex] :
( ( member_complex @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_ball__imageD) ).
thf(538,plain,
! [A: complex > complex,B: set_complex,C: complex > $o] :
( ! [D: complex] :
( ( member_complex @ D @ ( image_58037603omplex @ A @ B ) )
=> ( C @ D ) )
=> ! [D: complex] :
( ( member_complex @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(135,axiom,
! [A: complex > complex,B: complex > complex,C: complex > complex,D: complex > complex] :
( ( ( comp_c130555887omplex @ A @ B )
= ( comp_c130555887omplex @ C @ D ) )
=> ! [E: complex] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_comp__eq__elim) ).
thf(670,plain,
! [A: complex > complex,B: complex > complex,C: complex > complex,D: complex > complex] :
( ( ( comp_c130555887omplex @ A @ B )
= ( comp_c130555887omplex @ C @ D ) )
=> ! [E: complex] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(197,axiom,
! [A: complex] :
( ( times_times_complex @ zero_zero_complex @ A )
= zero_zero_complex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_vector__space__over__itself_Oscale__zero__left) ).
thf(898,plain,
! [A: complex] :
( ( times_times_complex @ zero_zero_complex @ A )
= zero_zero_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(229,axiom,
! [A: complex > complex > complex,B: ( complex > complex ) > complex,C: complex > complex > complex] :
( ( ( comp_c606622857omplex @ A @ B )
= id_complex_complex )
=> ( ( ( comp_c881053372omplex @ B @ C )
= id_complex )
=> ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_left__right__inverse__eq) ).
thf(1001,plain,
! [A: complex > complex > complex,B: ( complex > complex ) > complex,C: complex > complex > complex] :
( ( ( comp_c606622857omplex @ A @ B )
= id_complex_complex )
=> ( ( ( comp_c881053372omplex @ B @ C )
= id_complex )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(146,axiom,
! [A: $o,B: complex,C: complex] :
( ( A
=> ( ( times_times_complex @ ( if_complex @ A @ B @ zero_zero_complex ) @ C )
= ( times_times_complex @ B @ C ) ) )
& ( ~ A
=> ( ( times_times_complex @ ( if_complex @ A @ B @ zero_zero_complex ) @ C )
= zero_zero_complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_mult__delta__left) ).
thf(709,plain,
! [A: $o,B: complex,C: complex] :
( ( A
=> ( ( times_times_complex @ ( if_complex @ A @ B @ zero_zero_complex ) @ C )
= ( times_times_complex @ B @ C ) ) )
& ( ~ A
=> ( ( times_times_complex @ ( if_complex @ A @ B @ zero_zero_complex ) @ C )
= zero_zero_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(220,axiom,
! [A: nat] :
( ( compow1667379464omplex @ A @ id_complex )
= id_complex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_id__funpow) ).
thf(973,plain,
! [A: nat] :
( ( compow1667379464omplex @ A @ id_complex )
= id_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(129,axiom,
! [A: nat,B: complex > complex] :
( ( compow1098280738omplex @ A @ ( comp_c130555887omplex @ B ) )
= ( comp_c130555887omplex @ ( compow1667379464omplex @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_comp__funpow) ).
thf(651,plain,
! [A: nat,B: complex > complex] :
( ( compow1098280738omplex @ A @ ( comp_c130555887omplex @ B ) )
= ( comp_c130555887omplex @ ( compow1667379464omplex @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(36,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_nat__le__linear) ).
thf(372,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(155,axiom,
! [A: complex > $o,B: complex > $o] :
( ! [C: complex] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le701908932omplex @ ( collect_complex @ A ) @ ( collect_complex @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_Collect__mono) ).
thf(751,plain,
! [A: complex > $o,B: complex > $o] :
( ! [C: complex] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le701908932omplex @ ( collect_complex @ A ) @ ( collect_complex @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(169,axiom,
! [A: complex] :
( ( times_times_complex @ zero_zero_complex @ A )
= zero_zero_complex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_mult__zero__left) ).
thf(802,plain,
! [A: complex] :
( ( times_times_complex @ zero_zero_complex @ A )
= zero_zero_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(213,axiom,
! [A: set_complex > complex,B: set_complex] :
( ( A @ ( image_58037603omplex @ id_complex @ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_Sup_OSUP__id__eq) ).
thf(949,plain,
! [A: set_complex > complex,B: set_complex] :
( ( A @ ( image_58037603omplex @ id_complex @ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(209,axiom,
( ( times_times_complex @ ( deriv_complex @ f @ w ) @ ( deriv_complex @ g @ ( f @ w ) ) )
= ( deriv_complex @ id_complex @ w ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_calculation) ).
thf(934,plain,
( ( times_times_complex @ ( deriv_complex @ f @ w ) @ ( deriv_complex @ g @ ( f @ w ) ) )
= ( deriv_complex @ id_complex @ w ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(31,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_le__0__eq) ).
thf(357,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(125,axiom,
! [A: set_complex,B: complex > complex,C: set_complex] :
( ! [D: complex] :
( ( member_complex @ D @ A )
=> ( member_complex @ ( B @ D ) @ C ) )
=> ( ord_le701908932omplex @ ( image_58037603omplex @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_image__subsetI) ).
thf(638,plain,
! [A: set_complex,B: complex > complex,C: set_complex] :
( ! [D: complex] :
( ( member_complex @ D @ A )
=> ( member_complex @ ( B @ D ) @ C ) )
=> ( ord_le701908932omplex @ ( image_58037603omplex @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(187,axiom,
! [A: set_real > real,B: set_real] :
( ( A @ ( image_real_real @ id_real @ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_Sup_OSUP__id__eq) ).
thf(870,plain,
! [A: set_real > real,B: set_real] :
( ( A @ ( image_real_real @ id_real @ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(113,axiom,
! [A: real > real] :
( ( ! [B: real] :
( ( A @ B )
= B ) )
= ( A = id_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_eq__id__iff) ).
thf(606,plain,
! [A: real > real] :
( ( ! [B: real] :
( ( A @ B )
= B ) )
= ( A = id_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(13,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ ( times_times_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_le__square) ).
thf(289,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ ( times_times_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(62,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_mult__eq__0__iff) ).
thf(448,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(255,axiom,
! [A: complex,B: complex] :
( ( ( times_times_complex @ A @ B )
= B )
= ( ( B = zero_zero_complex )
| ( A = one_one_complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_mult__cancel__right2) ).
thf(1100,plain,
! [A: complex,B: complex] :
( ( ( times_times_complex @ A @ B )
= B )
= ( ( B = zero_zero_complex )
| ( A = one_one_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(4,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ A @ one_one_nat )
=> ( ( ord_less_eq_nat @ B @ one_one_nat )
=> ( ( ( times_times_nat @ A @ B )
= one_one_nat )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_mult__eq__1) ).
thf(261,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ A @ one_one_nat )
=> ( ( ord_less_eq_nat @ B @ one_one_nat )
=> ( ( ( times_times_nat @ A @ B )
= one_one_nat )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(76,axiom,
! [A: complex] :
( ( zero_zero_complex = A )
= ( A = zero_zero_complex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_zero__reorient) ).
thf(492,plain,
! [A: complex] :
( ( zero_zero_complex = A )
= ( A = zero_zero_complex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(109,axiom,
! [A: set_complex,B: complex > complex,C: set_complex] :
( ( ord_le701908932omplex @ A @ ( image_58037603omplex @ B @ C ) )
=> ~ ! [D: set_complex] :
( ( ord_le701908932omplex @ D @ C )
=> ( A
!= ( image_58037603omplex @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_subset__imageE) ).
thf(591,plain,
! [A: set_complex,B: complex > complex,C: set_complex] :
( ( ord_le701908932omplex @ A @ ( image_58037603omplex @ B @ C ) )
=> ~ ! [D: set_complex] :
( ( ord_le701908932omplex @ D @ C )
=> ( A
!= ( image_58037603omplex @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(20,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_less__eq__nat_Osimps_I1_J) ).
thf(321,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(102,axiom,
! [A: complex > complex,B: complex > complex,C: complex > complex] :
( ( comp_c130555887omplex @ ( comp_c130555887omplex @ A @ B ) @ C )
= ( comp_c130555887omplex @ A @ ( comp_c130555887omplex @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_comp__assoc) ).
thf(574,plain,
! [A: complex > complex,B: complex > complex,C: complex > complex] :
( ( comp_c130555887omplex @ ( comp_c130555887omplex @ A @ B ) @ C )
= ( comp_c130555887omplex @ A @ ( comp_c130555887omplex @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(241,axiom,
! [A: complex > complex] :
( ( ! [B: complex] :
( ( A @ B )
= B ) )
= ( A = id_complex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_eq__id__iff) ).
thf(1051,plain,
! [A: complex > complex] :
( ( ! [B: complex] :
( ( A @ B )
= B ) )
= ( A = id_complex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(15,axiom,
! [A: nat,B: nat,C: ( complex > complex ) > complex > complex] :
( ( compow1098280738omplex @ A @ ( compow1098280738omplex @ B @ C ) )
= ( compow1098280738omplex @ ( times_times_nat @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_funpow__mult) ).
thf(293,plain,
! [A: nat,B: nat,C: ( complex > complex ) > complex > complex] :
( ( compow1098280738omplex @ A @ ( compow1098280738omplex @ B @ C ) )
= ( compow1098280738omplex @ ( times_times_nat @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(247,axiom,
! [A: complex > complex > complex,B: ( complex > complex ) > complex] :
( ( ( ( comp_c606622857omplex @ A @ B )
= id_complex_complex )
& ( ( comp_c881053372omplex @ B @ A )
= id_complex ) )
= ( ! [C: complex > complex] :
( ( A @ ( B @ C ) )
= C )
& ! [C: complex] :
( ( B @ ( A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_isomorphism__expand) ).
thf(1072,plain,
! [A: complex > complex > complex,B: ( complex > complex ) > complex] :
( ( ( ( comp_c606622857omplex @ A @ B )
= id_complex_complex )
& ( ( comp_c881053372omplex @ B @ A )
= id_complex ) )
= ( ! [C: complex > complex] :
( ( A @ ( B @ C ) )
= C )
& ! [C: complex] :
( ( B @ ( A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(163,axiom,
! [A: $o,B: complex,C: complex] :
( ( A
=> ( ( times_times_complex @ B @ ( if_complex @ A @ C @ zero_zero_complex ) )
= ( times_times_complex @ B @ C ) ) )
& ( ~ A
=> ( ( times_times_complex @ B @ ( if_complex @ A @ C @ zero_zero_complex ) )
= zero_zero_complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_mult__delta__right) ).
thf(774,plain,
! [A: $o,B: complex,C: complex] :
( ( A
=> ( ( times_times_complex @ B @ ( if_complex @ A @ C @ zero_zero_complex ) )
= ( times_times_complex @ B @ C ) ) )
& ( ~ A
=> ( ( times_times_complex @ B @ ( if_complex @ A @ C @ zero_zero_complex ) )
= zero_zero_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(55,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001t__Complex__Ocomplex_T) ).
thf(428,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(5,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_comm__monoid__mult__class_Omult__1) ).
thf(265,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(87,axiom,
! [A: nat] :
( ( compow_real_real @ A @ id_real )
= id_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_id__funpow) ).
thf(527,plain,
! [A: nat] :
( ( compow_real_real @ A @ id_real )
= id_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(17,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
= ( ( A = C )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_mult__cancel2) ).
thf(312,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
= ( ( A = C )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_mult__le__mono) ).
thf(270,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(132,axiom,
! [A: set_complex,B: set_complex,C: complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( member_complex @ C @ A )
=> ( member_complex @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_subsetD) ).
thf(661,plain,
! [A: set_complex,B: set_complex,C: complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( member_complex @ C @ A )
=> ( member_complex @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(205,axiom,
( ( deriv_complex @ ( comp_c130555887omplex @ g @ f ) @ w )
= ( deriv_complex @ id_complex @ w ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24__092_060open_062deriv_A_Ig_A_092_060circ_062_Af_J_Aw_A_061_Aderiv_Aid_Aw_092_060close_062) ).
thf(925,plain,
( ( deriv_complex @ ( comp_c130555887omplex @ g @ f ) @ w )
= ( deriv_complex @ id_complex @ w ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(158,axiom,
! [A: set_complex,B: set_complex,C: set_complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( ord_le701908932omplex @ C @ A )
=> ( ord_le701908932omplex @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_dual__order_Otrans) ).
thf(761,plain,
! [A: set_complex,B: set_complex,C: set_complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( ord_le701908932omplex @ C @ A )
=> ( ord_le701908932omplex @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(39,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_mult__nonpos__nonneg) ).
thf(381,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(34,axiom,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_mult__0) ).
thf(366,plain,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(243,axiom,
! [A: complex] :
( ( times_times_complex @ one_one_complex @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_vector__space__over__itself_Oscale__one) ).
thf(1057,plain,
! [A: complex] :
( ( times_times_complex @ one_one_complex @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(236,axiom,
! [A: complex > complex,B: complex > complex] :
( ( ( ( comp_c130555887omplex @ A @ B )
= id_complex )
& ( ( comp_c130555887omplex @ B @ A )
= id_complex ) )
= ( ! [C: complex] :
( ( A @ ( B @ C ) )
= C )
& ! [C: complex] :
( ( B @ ( A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_isomorphism__expand) ).
thf(1021,plain,
! [A: complex > complex,B: complex > complex] :
( ( ( ( comp_c130555887omplex @ A @ B )
= id_complex )
& ( ( comp_c130555887omplex @ B @ A )
= id_complex ) )
= ( ! [C: complex] :
( ( A @ ( B @ C ) )
= C )
& ! [C: complex] :
( ( B @ ( A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(173,axiom,
! [A: set_complex,B: complex > complex,C: set_complex] :
( ( ord_le701908932omplex @ A @ ( image_58037603omplex @ B @ C ) )
= ( ? [D: set_complex] :
( ( ord_le701908932omplex @ D @ C )
& ( A
= ( image_58037603omplex @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_subset__image__iff) ).
thf(820,plain,
! [A: set_complex,B: complex > complex,C: set_complex] :
( ( ord_le701908932omplex @ A @ ( image_58037603omplex @ B @ C ) )
= ( ? [D: set_complex] :
( ( ord_le701908932omplex @ D @ C )
& ( A
= ( image_58037603omplex @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(43,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_le__antisym) ).
thf(392,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(121,axiom,
( ( image_real_real @ id_real )
= id_set_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_image__id) ).
thf(630,plain,
( ( image_real_real @ id_real )
= id_set_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(56,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_order__class_Oorder_Oantisym) ).
thf(429,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(154,axiom,
! [A: complex > complex,B: complex > complex,C: complex > complex,D: complex > complex] :
( ( ( comp_c130555887omplex @ A @ B )
= C )
=> ( ( comp_c130555887omplex @ ( comp_c130555887omplex @ D @ A ) @ B )
= ( comp_c130555887omplex @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_rewriteR__comp__comp) ).
thf(746,plain,
! [A: complex > complex,B: complex > complex,C: complex > complex,D: complex > complex] :
( ( ( comp_c130555887omplex @ A @ B )
= C )
=> ( ( comp_c130555887omplex @ ( comp_c130555887omplex @ D @ A ) @ B )
= ( comp_c130555887omplex @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(252,axiom,
! [A: complex] :
( ( times_times_complex @ one_one_complex @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_comm__monoid__mult__class_Omult__1) ).
thf(1091,plain,
! [A: complex] :
( ( times_times_complex @ one_one_complex @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(240,axiom,
! [A: $o,B: complex] :
( ( A
=> ( ( times_times_complex @ ( if_complex @ A @ one_one_complex @ zero_zero_complex ) @ B )
= B ) )
& ( ~ A
=> ( ( times_times_complex @ ( if_complex @ A @ one_one_complex @ zero_zero_complex ) @ B )
= zero_zero_complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_mult__if__delta) ).
thf(1042,plain,
! [A: $o,B: complex] :
( ( A
=> ( ( times_times_complex @ ( if_complex @ A @ one_one_complex @ zero_zero_complex ) @ B )
= B ) )
& ( ~ A
=> ( ( times_times_complex @ ( if_complex @ A @ one_one_complex @ zero_zero_complex ) @ B )
= zero_zero_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(214,axiom,
! [A: complex > complex] :
( ( compow1667379464omplex @ zero_zero_nat @ A )
= id_complex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_funpow__simps__right_I1_J) ).
thf(952,plain,
! [A: complex > complex] :
( ( compow1667379464omplex @ zero_zero_nat @ A )
= id_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(185,axiom,
! [A: set_complex,B: set_complex,C: set_complex,D: set_complex,E: complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( ord_le701908932omplex @ C @ D )
=> ( ( member_complex @ E @ ( times_1316095593omplex @ A @ C ) )
=> ( member_complex @ E @ ( times_1316095593omplex @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_set__times__mono2__b) ).
thf(862,plain,
! [A: set_complex,B: set_complex,C: set_complex,D: set_complex,E: complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( ord_le701908932omplex @ C @ D )
=> ( ( member_complex @ E @ ( times_1316095593omplex @ A @ C ) )
=> ( member_complex @ E @ ( times_1316095593omplex @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(28,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_bot__nat__0_Oextremum) ).
thf(349,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(190,axiom,
! [A: complex,B: complex,C: complex] :
( ( times_times_complex @ A @ ( times_times_complex @ B @ C ) )
= ( times_times_complex @ B @ ( times_times_complex @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_mult_Oleft__commute) ).
thf(879,plain,
! [A: complex,B: complex,C: complex] :
( ( times_times_complex @ A @ ( times_times_complex @ B @ C ) )
= ( times_times_complex @ B @ ( times_times_complex @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(58,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_order__trans) ).
thf(435,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(106,axiom,
! [A: complex,B: complex,C: complex] :
( ( ( times_times_complex @ A @ B )
= ( times_times_complex @ A @ C ) )
= ( ( A = zero_zero_complex )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_mult__cancel__left) ).
thf(583,plain,
! [A: complex,B: complex,C: complex] :
( ( ( times_times_complex @ A @ B )
= ( times_times_complex @ A @ C ) )
= ( ( A = zero_zero_complex )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(194,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_zero__neq__one) ).
thf(889,plain,
zero_zero_nat != one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(67,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( times_times_nat @ B @ A )
= ( times_times_nat @ C @ A ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_mult__right__cancel) ).
thf(461,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( times_times_nat @ B @ A )
= ( times_times_nat @ C @ A ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(138,axiom,
( id_complex_complex
= ( ^ [A: complex > complex] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_id__def) ).
thf(682,plain,
( id_complex_complex
= ( ^ [A: complex > complex] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(65,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_dual__order_Otrans) ).
thf(456,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(12,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_mult__left__cancel) ).
thf(285,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(179,axiom,
! [A: set_complex,B: set_complex,C: complex > complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ord_le701908932omplex @ ( image_58037603omplex @ C @ A ) @ ( image_58037603omplex @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_image__mono) ).
thf(847,plain,
! [A: set_complex,B: set_complex,C: complex > complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ord_le701908932omplex @ ( image_58037603omplex @ C @ A ) @ ( image_58037603omplex @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(99,axiom,
! [A: complex,B: set_complex,C: complex > complex] :
( ( member_complex @ A @ B )
=> ( member_complex @ ( C @ A ) @ ( image_58037603omplex @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_imageI) ).
thf(566,plain,
! [A: complex,B: set_complex,C: complex > complex] :
( ( member_complex @ A @ B )
=> ( member_complex @ ( C @ A ) @ ( image_58037603omplex @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(73,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_mult_Oright__neutral) ).
thf(484,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(142,axiom,
! [A: complex,B: complex,C: complex] :
( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
= ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(697,plain,
! [A: complex,B: complex,C: complex] :
( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
= ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(128,axiom,
topolo935673511omplex @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_assms_I4_J) ).
thf(650,plain,
topolo935673511omplex @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(116,axiom,
( comp_c130555887omplex
= ( ^ [A: complex > complex,B: complex > complex,C: complex] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_comp__def) ).
thf(615,plain,
( comp_c130555887omplex
= ( ^ [A: complex > complex,B: complex > complex,C: complex] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(245,axiom,
! [A: ( complex > complex ) > complex,B: complex > complex > complex,C: ( complex > complex ) > complex] :
( ( ( comp_c881053372omplex @ A @ B )
= id_complex )
=> ( ( ( comp_c606622857omplex @ B @ C )
= id_complex_complex )
=> ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_left__right__inverse__eq) ).
thf(1064,plain,
! [A: ( complex > complex ) > complex,B: complex > complex > complex,C: ( complex > complex ) > complex] :
( ( ( comp_c881053372omplex @ A @ B )
= id_complex )
=> ( ( ( comp_c606622857omplex @ B @ C )
= id_complex_complex )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(47,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_mult__le__mono2) ).
thf(403,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(254,axiom,
! [A: complex > complex,B: complex > complex,C: complex] :
( ( ( comp_c130555887omplex @ A @ B )
= id_complex )
=> ( ( A @ ( B @ C ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_pointfree__idE) ).
thf(1096,plain,
! [A: complex > complex,B: complex > complex,C: complex] :
( ( ( comp_c130555887omplex @ A @ B )
= id_complex )
=> ( ( A @ ( B @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(79,axiom,
! [A: complex > complex,B: complex] :
( ( compow1667379464omplex @ zero_zero_nat @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_funpow__0) ).
thf(499,plain,
! [A: complex > complex,B: complex] :
( ( compow1667379464omplex @ zero_zero_nat @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(85,axiom,
! [A: complex > complex,B: complex > complex,C: complex > complex,D: complex > complex,E: complex > complex,F: complex > complex] :
( ( ( comp_c130555887omplex @ A @ B )
= ( comp_c130555887omplex @ C @ D ) )
=> ( ( ( comp_c130555887omplex @ E @ C )
= F )
=> ( ( comp_c130555887omplex @ ( comp_c130555887omplex @ E @ A ) @ B )
= ( comp_c130555887omplex @ F @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_rewriteR__comp__comp2) ).
thf(519,plain,
! [A: complex > complex,B: complex > complex,C: complex > complex,D: complex > complex,E: complex > complex,F: complex > complex] :
( ( ( comp_c130555887omplex @ A @ B )
= ( comp_c130555887omplex @ C @ D ) )
=> ( ( ( comp_c130555887omplex @ E @ C )
= F )
=> ( ( comp_c130555887omplex @ ( comp_c130555887omplex @ E @ A ) @ B )
= ( comp_c130555887omplex @ F @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(104,axiom,
! [A: set_complex] : ( ord_le701908932omplex @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_order__refl) ).
thf(578,plain,
! [A: set_complex] : ( ord_le701908932omplex @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(164,axiom,
! [A: complex,B: complex] :
( ( A != zero_zero_complex )
=> ( ( B != zero_zero_complex )
=> ( ( times_times_complex @ A @ B )
!= zero_zero_complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_no__zero__divisors) ).
thf(783,plain,
! [A: complex,B: complex] :
( ( A != zero_zero_complex )
=> ( ( B != zero_zero_complex )
=> ( ( times_times_complex @ A @ B )
!= zero_zero_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(53,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_ord__le__eq__trans) ).
thf(420,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(192,axiom,
! [A: set_complex,B: set_complex,C: set_complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( ord_le701908932omplex @ B @ C )
=> ( ord_le701908932omplex @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_subset__trans) ).
thf(884,plain,
! [A: set_complex,B: set_complex,C: set_complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( ord_le701908932omplex @ B @ C )
=> ( ord_le701908932omplex @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(238,axiom,
! [A: set_complex] : ( comple372758642hic_on @ id_complex @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_holomorphic__on__id) ).
thf(1028,plain,
! [A: set_complex] : ( comple372758642hic_on @ id_complex @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(95,axiom,
! [A: complex] :
( ( times_times_complex @ A @ zero_zero_complex )
= zero_zero_complex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_vector__space__over__itself_Oscale__zero__right) ).
thf(554,plain,
! [A: complex] :
( ( times_times_complex @ A @ zero_zero_complex )
= zero_zero_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(126,axiom,
! [A: complex > complex,B: set_complex,C: set_complex] :
( ( comple372758642hic_on @ A @ B )
=> ( ( ord_le701908932omplex @ C @ B )
=> ( comple372758642hic_on @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_holomorphic__on__subset) ).
thf(642,plain,
! [A: complex > complex,B: set_complex,C: set_complex] :
( ( comple372758642hic_on @ A @ B )
=> ( ( ord_le701908932omplex @ C @ B )
=> ( comple372758642hic_on @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(234,axiom,
! [A: complex] :
( ( times_times_complex @ one_one_complex @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_mult_Oleft__neutral) ).
thf(1016,plain,
! [A: complex] :
( ( times_times_complex @ one_one_complex @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(93,axiom,
! [A: complex > complex,B: set_complex,C: complex > complex] :
( ( comple372758642hic_on @ A @ B )
=> ( ( comple372758642hic_on @ C @ ( image_58037603omplex @ A @ B ) )
=> ( comple372758642hic_on @ ( comp_c130555887omplex @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_holomorphic__on__compose) ).
thf(547,plain,
! [A: complex > complex,B: set_complex,C: complex > complex] :
( ( comple372758642hic_on @ A @ B )
=> ( ( comple372758642hic_on @ C @ ( image_58037603omplex @ A @ B ) )
=> ( comple372758642hic_on @ ( comp_c130555887omplex @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(70,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_mult__nonneg__nonneg) ).
thf(471,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(1,conjecture,
( ( deriv_complex @ id_complex @ w )
= one_one_complex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( deriv_complex @ id_complex @ w )
!= one_one_complex ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(256,plain,
( ( deriv_complex @ id_complex @ w )
!= one_one_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(198,axiom,
( ( arsinh_complex @ zero_zero_complex )
= zero_zero_complex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_arsinh__0) ).
thf(901,plain,
( ( arsinh_complex @ zero_zero_complex )
= zero_zero_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(248,axiom,
! [A: complex] :
( ( ( one_one_nat = zero_zero_nat )
=> ( ( compow1098280738omplex @ one_one_nat @ deriv_complex @ id_complex @ A )
= A ) )
& ( ( one_one_nat != zero_zero_nat )
=> ( ( compow1098280738omplex @ one_one_nat @ deriv_complex @ id_complex @ A )
= one_one_complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062_092_060And_062z_O_A_Ideriv_A_094_094_A1_J_Aid_Az_A_061_A_Iif_A1_A_061_A0_Athen_Az_Aelse_Aif_A1_A_061_A1_Athen_A1_058_058_063_Ha_Aelse_A_I0_058_058_063_Ha_J_J_092_060close_062) ).
thf(1075,plain,
! [A: complex] :
( ( ( one_one_nat = zero_zero_nat )
=> ( ( compow1098280738omplex @ one_one_nat @ deriv_complex @ id_complex @ A )
= A ) )
& ( ( one_one_nat != zero_zero_nat )
=> ( ( compow1098280738omplex @ one_one_nat @ deriv_complex @ id_complex @ A )
= one_one_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(151,axiom,
! [A: set_complex_complex > complex > complex,B: set_complex_complex] :
( ( A @ ( image_944012797omplex @ id_complex_complex @ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_Sup_OSUP__id__eq) ).
thf(738,plain,
! [A: set_complex_complex > complex > complex,B: set_complex_complex] :
( ( A @ ( image_944012797omplex @ id_complex_complex @ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(130,axiom,
! [A: nat] :
( ( compow1098280738omplex @ A @ id_complex_complex )
= id_complex_complex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_id__funpow) ).
thf(654,plain,
! [A: nat] :
( ( compow1098280738omplex @ A @ id_complex_complex )
= id_complex_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(244,axiom,
! [A: complex > real,B: real > complex,C: complex > real] :
( ( ( comp_c819638635l_real @ A @ B )
= id_real )
=> ( ( ( comp_r667767405omplex @ B @ C )
= id_complex )
=> ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_left__right__inverse__eq) ).
thf(1060,plain,
! [A: complex > real,B: real > complex,C: complex > real] :
( ( ( comp_c819638635l_real @ A @ B )
= id_real )
=> ( ( ( comp_r667767405omplex @ B @ C )
= id_complex )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(100,axiom,
funpow_complex = compow1667379464omplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_funpow__code__def) ).
thf(569,plain,
funpow_complex = compow1667379464omplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(26,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_mult__mono_H) ).
thf(343,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(32,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_mult_Oleft__commute) ).
thf(360,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(170,axiom,
! [A: complex,B: complex] :
( ( ( times_times_complex @ A @ B )
!= zero_zero_complex )
=> ( ( A != zero_zero_complex )
& ( B != zero_zero_complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_mult__not__zero) ).
thf(805,plain,
! [A: complex,B: complex] :
( ( ( times_times_complex @ A @ B )
!= zero_zero_complex )
=> ( ( A != zero_zero_complex )
& ( B != zero_zero_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(131,axiom,
! [A: complex,B: complex,C: complex] :
( ( A != zero_zero_complex )
=> ( ( ( times_times_complex @ B @ A )
= ( times_times_complex @ C @ A ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_vector__space__over__itself_Oscale__right__imp__eq) ).
thf(657,plain,
! [A: complex,B: complex,C: complex] :
( ( A != zero_zero_complex )
=> ( ( ( times_times_complex @ B @ A )
= ( times_times_complex @ C @ A ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(242,axiom,
! [A: real > complex,B: complex > real] :
( ( ( ( comp_r667767405omplex @ A @ B )
= id_complex )
& ( ( comp_c819638635l_real @ B @ A )
= id_real ) )
= ( ! [C: complex] :
( ( A @ ( B @ C ) )
= C )
& ! [C: real] :
( ( B @ ( A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_isomorphism__expand) ).
thf(1054,plain,
! [A: real > complex,B: complex > real] :
( ( ( ( comp_r667767405omplex @ A @ B )
= id_complex )
& ( ( comp_c819638635l_real @ B @ A )
= id_real ) )
= ( ! [C: complex] :
( ( A @ ( B @ C ) )
= C )
& ! [C: real] :
( ( B @ ( A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(45,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_mult__right__mono) ).
thf(398,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(88,axiom,
( id_real
= ( ^ [A: real] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_id__def) ).
thf(530,plain,
( id_real
= ( ^ [A: real] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(107,axiom,
! [A: complex > $o,B: complex > $o] :
( ( ord_le701908932omplex @ ( collect_complex @ A ) @ ( collect_complex @ B ) )
= ( ! [C: complex] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_Collect__mono__iff) ).
thf(586,plain,
! [A: complex > $o,B: complex > $o] :
( ( ord_le701908932omplex @ ( collect_complex @ A ) @ ( collect_complex @ B ) )
= ( ! [C: complex] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(147,axiom,
! [A: complex > complex,B: set_complex,C: complex > complex,D: set_complex,E: complex > complex] :
( ( ( image_58037603omplex @ A @ B )
= ( image_58037603omplex @ C @ D ) )
=> ( ( image_58037603omplex @ ( comp_c130555887omplex @ E @ A ) @ B )
= ( image_58037603omplex @ ( comp_c130555887omplex @ E @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_image__eq__imp__comp) ).
thf(718,plain,
! [A: complex > complex,B: set_complex,C: complex > complex,D: set_complex,E: complex > complex] :
( ( ( image_58037603omplex @ A @ B )
= ( image_58037603omplex @ C @ D ) )
=> ( ( image_58037603omplex @ ( comp_c130555887omplex @ E @ A ) @ B )
= ( image_58037603omplex @ ( comp_c130555887omplex @ E @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(250,axiom,
( ( arcosh_complex @ one_one_complex )
= zero_zero_complex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_arcosh__1) ).
thf(1086,plain,
( ( arcosh_complex @ one_one_complex )
= zero_zero_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(211,axiom,
! [A: complex > complex,B: set_complex,C: complex > complex,D: complex] :
( ( comple372758642hic_on @ A @ B )
=> ( ( comple372758642hic_on @ C @ B )
=> ( ( topolo935673511omplex @ B )
=> ( ( member_complex @ D @ B )
=> ( ! [E: complex] :
( ( member_complex @ E @ B )
=> ( ( A @ E )
= ( C @ E ) ) )
=> ( ( deriv_complex @ A @ D )
= ( deriv_complex @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_complex__derivative__transform__within__open) ).
thf(938,plain,
! [A: complex > complex,B: set_complex,C: complex > complex,D: complex] :
( ( comple372758642hic_on @ A @ B )
=> ( ( comple372758642hic_on @ C @ B )
=> ( ( topolo935673511omplex @ B )
=> ( ( member_complex @ D @ B )
=> ( ! [E: complex] :
( ( member_complex @ E @ B )
=> ( ( A @ E )
= ( C @ E ) ) )
=> ( ( deriv_complex @ A @ D )
= ( deriv_complex @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(200,axiom,
! [A: complex > complex,B: set_complex,C: complex > complex,D: set_complex] :
( ( comple372758642hic_on @ A @ B )
=> ( ( comple372758642hic_on @ C @ D )
=> ( ( ord_le701908932omplex @ ( image_58037603omplex @ A @ B ) @ D )
=> ( comple372758642hic_on @ ( comp_c130555887omplex @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_holomorphic__on__compose__gen) ).
thf(906,plain,
! [A: complex > complex,B: set_complex,C: complex > complex,D: set_complex] :
( ( comple372758642hic_on @ A @ B )
=> ( ( comple372758642hic_on @ C @ D )
=> ( ( ord_le701908932omplex @ ( image_58037603omplex @ A @ B ) @ D )
=> ( comple372758642hic_on @ ( comp_c130555887omplex @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(50,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_bot__nat__0_Oextremum__unique) ).
thf(412,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(217,axiom,
! [A: complex] :
( ( times_times_complex @ A @ one_one_complex )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mult_Oright__neutral) ).
thf(965,plain,
! [A: complex] :
( ( times_times_complex @ A @ one_one_complex )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(54,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( A = zero_zero_nat )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_nat__mult__eq__cancel__disj) ).
thf(425,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( A = zero_zero_nat )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(83,axiom,
! [A: complex > complex,B: complex > complex,C: complex > complex] :
( ( comp_c130555887omplex @ A @ ( comp_c130555887omplex @ B @ C ) )
= ( comp_c130555887omplex @ ( comp_c130555887omplex @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_fun_Omap__comp) ).
thf(513,plain,
! [A: complex > complex,B: complex > complex,C: complex > complex] :
( ( comp_c130555887omplex @ A @ ( comp_c130555887omplex @ B @ C ) )
= ( comp_c130555887omplex @ ( comp_c130555887omplex @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(10,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_mult_Ocomm__neutral) ).
thf(279,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(61,axiom,
! [A: nat,B: nat] :
( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
& ( ord_less_eq_nat @ B @ zero_zero_nat ) )
| ( ( ord_less_eq_nat @ A @ zero_zero_nat )
& ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_split__mult__neg__le) ).
thf(444,plain,
! [A: nat,B: nat] :
( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
& ( ord_less_eq_nat @ B @ zero_zero_nat ) )
| ( ( ord_less_eq_nat @ A @ zero_zero_nat )
& ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(140,axiom,
! [A: complex,B: complex > complex,C: complex,D: set_complex] :
( ( A
= ( B @ C ) )
=> ( ( member_complex @ C @ D )
=> ( member_complex @ A @ ( image_58037603omplex @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_image__eqI) ).
thf(689,plain,
! [A: complex,B: complex > complex,C: complex,D: set_complex] :
( ( A
= ( B @ C ) )
=> ( ( member_complex @ C @ D )
=> ( member_complex @ A @ ( image_58037603omplex @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(16,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_Nat_Oex__has__greatest__nat) ).
thf(296,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(98,axiom,
! [A: ( complex > complex ) > complex > complex,B: ( complex > complex ) > complex > complex,C: ( complex > complex ) > complex > complex] :
( ( ( comp_c1610621014omplex @ A @ B )
= id_complex_complex )
=> ( ( ( comp_c1610621014omplex @ B @ C )
= id_complex_complex )
=> ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_left__right__inverse__eq) ).
thf(562,plain,
! [A: ( complex > complex ) > complex > complex,B: ( complex > complex ) > complex > complex,C: ( complex > complex ) > complex > complex] :
( ( ( comp_c1610621014omplex @ A @ B )
= id_complex_complex )
=> ( ( ( comp_c1610621014omplex @ B @ C )
= id_complex_complex )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(141,axiom,
! [A: complex,B: complex] :
( ( if_complex @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Complex__Ocomplex_T) ).
thf(694,plain,
! [A: complex,B: complex] :
( ( if_complex @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(177,axiom,
~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_not__one__le__zero) ).
thf(843,plain,
~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(162,axiom,
( ( image_944012797omplex @ id_complex_complex )
= id_set1618538368omplex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_image__id) ).
thf(772,plain,
( ( image_944012797omplex @ id_complex_complex )
= id_set1618538368omplex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(153,axiom,
! [A: ( complex > complex ) > real,B: real > complex > complex] :
( ( ( ( comp_c1884694328l_real @ A @ B )
= id_real )
& ( ( comp_r2009261319omplex @ B @ A )
= id_complex_complex ) )
= ( ! [C: real] :
( ( A @ ( B @ C ) )
= C )
& ! [C: complex > complex] :
( ( B @ ( A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_isomorphism__expand) ).
thf(743,plain,
! [A: ( complex > complex ) > real,B: real > complex > complex] :
( ( ( ( comp_c1884694328l_real @ A @ B )
= id_real )
& ( ( comp_r2009261319omplex @ B @ A )
= id_complex_complex ) )
= ( ! [C: real] :
( ( A @ ( B @ C ) )
= C )
& ! [C: complex > complex] :
( ( B @ ( A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(14,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_le__refl) ).
thf(291,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(216,axiom,
! [A: complex > complex,B: set_complex,C: complex > complex,D: complex,E: nat] :
( ( comple372758642hic_on @ A @ B )
=> ( ( comple372758642hic_on @ C @ B )
=> ( ( topolo935673511omplex @ B )
=> ( ( member_complex @ D @ B )
=> ( ! [F: complex] :
( ( member_complex @ F @ B )
=> ( ( A @ F )
= ( C @ F ) ) )
=> ( ( compow1098280738omplex @ E @ deriv_complex @ A @ D )
= ( compow1098280738omplex @ E @ deriv_complex @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_higher__deriv__transform__within__open) ).
thf(958,plain,
! [A: complex > complex,B: set_complex,C: complex > complex,D: complex,E: nat] :
( ( comple372758642hic_on @ A @ B )
=> ( ( comple372758642hic_on @ C @ B )
=> ( ( topolo935673511omplex @ B )
=> ( ( member_complex @ D @ B )
=> ( ! [F: complex] :
( ( member_complex @ F @ B )
=> ( ( A @ F )
= ( C @ F ) ) )
=> ( ( compow1098280738omplex @ E @ deriv_complex @ A @ D )
= ( compow1098280738omplex @ E @ deriv_complex @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(175,axiom,
! [A: set_complex,B: set_complex,C: complex > complex,D: complex > complex] :
( ( A = B )
=> ( ! [E: complex] :
( ( member_complex @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_58037603omplex @ C @ A )
= ( image_58037603omplex @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_image__cong) ).
thf(826,plain,
! [A: set_complex,B: set_complex,C: complex > complex,D: complex > complex] :
( ( A = B )
=> ( ! [E: complex] :
( ( member_complex @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_58037603omplex @ C @ A )
= ( image_58037603omplex @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(103,axiom,
topolo935673511omplex @ s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_assms_I3_J) ).
thf(577,plain,
topolo935673511omplex @ s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(210,axiom,
( id_complex
= ( ^ [A: complex] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_id__apply) ).
thf(936,plain,
( id_complex
= ( ^ [A: complex] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(165,axiom,
! [A: ( complex > complex ) > complex > complex,B: ( complex > complex ) > complex > complex] :
( ( ( ( comp_c1610621014omplex @ A @ B )
= id_complex_complex )
& ( ( comp_c1610621014omplex @ B @ A )
= id_complex_complex ) )
= ( ! [C: complex > complex] :
( ( A @ ( B @ C ) )
= C )
& ! [C: complex > complex] :
( ( B @ ( A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_isomorphism__expand) ).
thf(787,plain,
! [A: ( complex > complex ) > complex > complex,B: ( complex > complex ) > complex > complex] :
( ( ( ( comp_c1610621014omplex @ A @ B )
= id_complex_complex )
& ( ( comp_c1610621014omplex @ B @ A )
= id_complex_complex ) )
= ( ! [C: complex > complex] :
( ( A @ ( B @ C ) )
= C )
& ! [C: complex > complex] :
( ( B @ ( A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(203,axiom,
! [A: set_complex] :
( ( collect_complex
@ ^ [B: complex] : ( member_complex @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_Collect__mem__eq) ).
thf(919,plain,
! [A: set_complex] :
( ( collect_complex
@ ^ [B: complex] : ( member_complex @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(159,axiom,
! [A: complex,B: complex,C: complex] :
( ( A != zero_zero_complex )
=> ( ( ( times_times_complex @ B @ A )
= ( times_times_complex @ C @ A ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_mult__right__cancel) ).
thf(764,plain,
! [A: complex,B: complex,C: complex] :
( ( A != zero_zero_complex )
=> ( ( ( times_times_complex @ B @ A )
= ( times_times_complex @ C @ A ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(48,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_bot__nat__0_Oextremum__uniqueI) ).
thf(406,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(232,axiom,
! [A: complex] :
( ( one_one_complex = A )
= ( A = one_one_complex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_one__reorient) ).
thf(1011,plain,
! [A: complex] :
( ( one_one_complex = A )
= ( A = one_one_complex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(150,axiom,
! [A: complex,B: set_complex] : ( comple372758642hic_on @ ( times_times_complex @ A ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_holomorphic__on__linear) ).
thf(736,plain,
! [A: complex,B: set_complex] : ( comple372758642hic_on @ ( times_times_complex @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(63,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_nat__mult__1) ).
thf(451,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(19,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
= ( ( B = zero_zero_nat )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_mult__cancel__right) ).
thf(318,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
= ( ( B = zero_zero_nat )
| ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(82,axiom,
! [A: real > real,B: real > real,C: real > real] :
( ( ( comp_real_real_real @ A @ B )
= id_real )
=> ( ( ( comp_real_real_real @ B @ C )
= id_real )
=> ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_left__right__inverse__eq) ).
thf(509,plain,
! [A: real > real,B: real > real,C: real > real] :
( ( ( comp_real_real_real @ A @ B )
= id_real )
=> ( ( ( comp_real_real_real @ B @ C )
= id_real )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(38,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ A @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_no__zero__divisors) ).
thf(377,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ A @ B )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(225,axiom,
( ( comp_c130555887omplex @ id_complex )
= id_complex_complex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_fun_Omap__id0) ).
thf(990,plain,
( ( comp_c130555887omplex @ id_complex )
= id_complex_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(41,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_divisors__zero) ).
thf(387,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(157,axiom,
! [A: nat,B: nat] :
( ( A
= ( times_times_nat @ A @ B ) )
=> ( ( B = one_one_nat )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_mult__eq__self__implies__10) ).
thf(758,plain,
! [A: nat,B: nat] :
( ( A
= ( times_times_nat @ A @ B ) )
=> ( ( B = one_one_nat )
| ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(90,axiom,
! [A: complex,B: complex] :
( ( if_complex @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Complex__Ocomplex_T) ).
thf(535,plain,
! [A: complex,B: complex] :
( ( if_complex @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(172,axiom,
! [A: complex > complex,B: complex > complex,C: complex > complex,D: complex > complex,E: complex] :
( ( ( comp_c130555887omplex @ A @ B )
= ( comp_c130555887omplex @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_comp__eq__dest) ).
thf(816,plain,
! [A: complex > complex,B: complex > complex,C: complex > complex,D: complex > complex,E: complex] :
( ( ( comp_c130555887omplex @ A @ B )
= ( comp_c130555887omplex @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(114,axiom,
! [A: complex,B: complex] :
( ( ( times_times_complex @ A @ B )
= zero_zero_complex )
= ( ( A = zero_zero_complex )
| ( B = zero_zero_complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_vector__space__over__itself_Oscale__eq__0__iff) ).
thf(609,plain,
! [A: complex,B: complex] :
( ( ( times_times_complex @ A @ B )
= zero_zero_complex )
= ( ( A = zero_zero_complex )
| ( B = zero_zero_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(21,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_mult__mono) ).
thf(323,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(168,axiom,
! [A: real > real,B: real > real] :
( ( ( ( comp_real_real_real @ A @ B )
= id_real )
& ( ( comp_real_real_real @ B @ A )
= id_real ) )
= ( ! [C: real] :
( ( A @ ( B @ C ) )
= C )
& ! [C: real] :
( ( B @ ( A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_isomorphism__expand) ).
thf(799,plain,
! [A: real > real,B: real > real] :
( ( ( ( comp_real_real_real @ A @ B )
= id_real )
& ( ( comp_real_real_real @ B @ A )
= id_real ) )
= ( ! [C: real] :
( ( A @ ( B @ C ) )
= C )
& ! [C: real] :
( ( B @ ( A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(143,axiom,
! [A: set_complex,B: set_complex,C: set_complex,D: set_complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( ord_le701908932omplex @ C @ D )
=> ( ord_le701908932omplex @ ( times_1316095593omplex @ A @ C ) @ ( times_1316095593omplex @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_set__times__mono2) ).
thf(700,plain,
! [A: set_complex,B: set_complex,C: set_complex,D: set_complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( ord_le701908932omplex @ C @ D )
=> ( ord_le701908932omplex @ ( times_1316095593omplex @ A @ C ) @ ( times_1316095593omplex @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(196,axiom,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_one__reorient) ).
thf(895,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(23,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_le0) ).
thf(330,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(208,axiom,
( ( image_58037603omplex @ id_complex )
= id_set_complex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_image__id) ).
thf(932,plain,
( ( image_58037603omplex @ id_complex )
= id_set_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(222,axiom,
! [A: complex,B: complex] :
( ( A
= ( times_times_complex @ B @ A ) )
= ( ( A = zero_zero_complex )
| ( B = one_one_complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_mult__cancel__right1) ).
thf(983,plain,
! [A: complex,B: complex] :
( ( A
= ( times_times_complex @ B @ A ) )
= ( ( A = zero_zero_complex )
| ( B = one_one_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(160,axiom,
! [A: real > real] :
( ( compow_real_real @ zero_zero_nat @ A )
= id_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_funpow__simps__right_I1_J) ).
thf(768,plain,
! [A: real > real] :
( ( compow_real_real @ zero_zero_nat @ A )
= id_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(124,axiom,
! [A: set_complex] : ( ord_le701908932omplex @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_subset__refl) ).
thf(636,plain,
! [A: set_complex] : ( ord_le701908932omplex @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(223,axiom,
member_complex @ w @ s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_assms_I7_J) ).
thf(986,plain,
member_complex @ w @ s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(181,axiom,
! [A: set_complex,B: set_complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( ord_le701908932omplex @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_subset__antisym) ).
thf(851,plain,
! [A: set_complex,B: set_complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( ord_le701908932omplex @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(59,axiom,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_mult__zero__left) ).
thf(438,plain,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(204,axiom,
! [A: ( complex > complex ) > complex,B: complex > complex > complex] :
( ( ( ( comp_c881053372omplex @ A @ B )
= id_complex )
& ( ( comp_c606622857omplex @ B @ A )
= id_complex_complex ) )
= ( ! [C: complex] :
( ( A @ ( B @ C ) )
= C )
& ! [C: complex > complex] :
( ( B @ ( A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_isomorphism__expand) ).
thf(922,plain,
! [A: ( complex > complex ) > complex,B: complex > complex > complex] :
( ( ( ( comp_c881053372omplex @ A @ B )
= id_complex )
& ( ( comp_c606622857omplex @ B @ A )
= id_complex_complex ) )
= ( ! [C: complex] :
( ( A @ ( B @ C ) )
= C )
& ! [C: complex > complex] :
( ( B @ ( A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(148,axiom,
! [A: set_complex,B: set_complex,C: complex > complex,D: complex > complex] :
( ( A = B )
=> ( ! [E: complex] :
( ( member_complex @ E @ A )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( comple372758642hic_on @ C @ A )
= ( comple372758642hic_on @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_holomorphic__cong) ).
thf(722,plain,
! [A: set_complex,B: set_complex,C: complex > complex,D: complex > complex] :
( ( A = B )
=> ( ! [E: complex] :
( ( member_complex @ E @ A )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( comple372758642hic_on @ C @ A )
= ( comple372758642hic_on @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(75,axiom,
( ( artanh_complex @ zero_zero_complex )
= zero_zero_complex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_artanh__0) ).
thf(490,plain,
( ( artanh_complex @ zero_zero_complex )
= zero_zero_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(108,axiom,
funpow1854104714omplex = compow1098280738omplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_funpow__code__def) ).
thf(589,plain,
funpow1854104714omplex = compow1098280738omplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(137,axiom,
! [A: set_complex] : ( ord_le701908932omplex @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_dual__order_Orefl) ).
thf(680,plain,
! [A: set_complex] : ( ord_le701908932omplex @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(74,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_mult__nonneg__nonpos2) ).
thf(487,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(206,axiom,
( ( times_times_complex @ ( deriv_complex @ g @ ( f @ w ) ) @ ( deriv_complex @ f @ w ) )
= ( deriv_complex @ ( comp_c130555887omplex @ g @ f ) @ w ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57__092_060open_062deriv_Ag_A_If_Aw_J_A_K_Aderiv_Af_Aw_A_061_Aderiv_A_Ig_A_092_060circ_062_Af_J_Aw_092_060close_062) ).
thf(927,plain,
( ( times_times_complex @ ( deriv_complex @ g @ ( f @ w ) ) @ ( deriv_complex @ f @ w ) )
= ( deriv_complex @ ( comp_c130555887omplex @ g @ f ) @ w ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(37,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_le__zero__eq) ).
thf(374,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(117,axiom,
! [A: set_complex,B: set_complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( ord_le701908932omplex @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_order__class_Oorder_Oantisym) ).
thf(617,plain,
! [A: set_complex,B: set_complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( ord_le701908932omplex @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(84,axiom,
! [A: complex,B: complex] :
( ( ( times_times_complex @ A @ B )
= zero_zero_complex )
=> ( ( A = zero_zero_complex )
| ( B = zero_zero_complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_divisors__zero) ).
thf(516,plain,
! [A: complex,B: complex] :
( ( ( times_times_complex @ A @ B )
= zero_zero_complex )
=> ( ( A = zero_zero_complex )
| ( B = zero_zero_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(218,axiom,
! [A: complex > complex] :
( ( comp_c130555887omplex @ id_complex @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_fun_Omap__id) ).
thf(968,plain,
! [A: complex > complex] :
( ( comp_c130555887omplex @ id_complex @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(174,axiom,
! [A: ( complex > complex ) > complex > complex] :
( ( compow1098280738omplex @ zero_zero_nat @ A )
= id_complex_complex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_funpow__simps__right_I1_J) ).
thf(823,plain,
! [A: ( complex > complex ) > complex > complex] :
( ( compow1098280738omplex @ zero_zero_nat @ A )
= id_complex_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(96,axiom,
! [A: ( complex > complex ) > complex > complex,B: nat,C: complex > complex] :
( ( A @ ( compow1098280738omplex @ B @ A @ C ) )
= ( compow1098280738omplex @ B @ A @ ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_funpow__swap1) ).
thf(557,plain,
! [A: ( complex > complex ) > complex > complex,B: nat,C: complex > complex] :
( ( A @ ( compow1098280738omplex @ B @ A @ C ) )
= ( compow1098280738omplex @ B @ A @ ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(11,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( B = C )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_mult__cancel1) ).
thf(282,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( B = C )
| ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(145,axiom,
( times_times_complex
= ( ^ [A: complex,B: complex] : ( times_times_complex @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_mult_Ocommute) ).
thf(707,plain,
( times_times_complex
= ( ^ [A: complex,B: complex] : ( times_times_complex @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(193,axiom,
( ord_le701908932omplex
= ( ^ [A: set_complex,B: set_complex] :
! [C: complex] :
( ( member_complex @ C @ A )
=> ( member_complex @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_subset__iff) ).
thf(887,plain,
( ord_le701908932omplex
= ( ^ [A: set_complex,B: set_complex] :
! [C: complex] :
( ( member_complex @ C @ A )
=> ( member_complex @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(219,axiom,
( ( ln_ln_complex @ one_one_complex )
= zero_zero_complex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_Ln__1) ).
thf(971,plain,
( ( ln_ln_complex @ one_one_complex )
= zero_zero_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(49,axiom,
! [A: nat,B: nat,C: complex > complex] :
( ( compow1667379464omplex @ A @ ( compow1667379464omplex @ B @ C ) )
= ( compow1667379464omplex @ ( times_times_nat @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_funpow__mult) ).
thf(409,plain,
! [A: nat,B: nat,C: complex > complex] :
( ( compow1667379464omplex @ A @ ( compow1667379464omplex @ B @ C ) )
= ( compow1667379464omplex @ ( times_times_nat @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(105,axiom,
! [A: complex > complex,B: complex > complex,C: set_complex] :
( ( image_58037603omplex @ A @ ( image_58037603omplex @ B @ C ) )
= ( image_58037603omplex @ ( comp_c130555887omplex @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_image__comp) ).
thf(580,plain,
! [A: complex > complex,B: complex > complex,C: set_complex] :
( ( image_58037603omplex @ A @ ( image_58037603omplex @ B @ C ) )
= ( image_58037603omplex @ ( comp_c130555887omplex @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(183,axiom,
! [A: complex,B: complex,C: complex] :
( ( A != zero_zero_complex )
=> ( ( ( times_times_complex @ A @ B )
= ( times_times_complex @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_mult__left__cancel) ).
thf(855,plain,
! [A: complex,B: complex,C: complex] :
( ( A != zero_zero_complex )
=> ( ( ( times_times_complex @ A @ B )
= ( times_times_complex @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(136,axiom,
! [A: complex > complex,B: set_complex,C: complex > $o] :
( ? [D: complex] :
( ( member_complex @ D @ ( image_58037603omplex @ A @ B ) )
& ( C @ D ) )
=> ? [D: complex] :
( ( member_complex @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_bex__imageD) ).
thf(673,plain,
! [A: complex > complex,B: set_complex,C: complex > $o] :
( ? [D: complex] :
( ( member_complex @ D @ ( image_58037603omplex @ A @ B ) )
& ( C @ D ) )
=> ? [D: complex] :
( ( member_complex @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(60,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_ordered__comm__semiring__class_Ocomm__mult__left__mono) ).
thf(441,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(80,axiom,
! [A: set_complex,B: set_complex] :
( ( A = B )
=> ( ord_le701908932omplex @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_equalityD1) ).
thf(502,plain,
! [A: set_complex,B: set_complex] :
( ( A = B )
=> ( ord_le701908932omplex @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(92,axiom,
! [A: complex,B: complex,C: complex] :
( ( ( times_times_complex @ A @ B )
= ( times_times_complex @ C @ B ) )
= ( ( B = zero_zero_complex )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_mult__cancel__right) ).
thf(544,plain,
! [A: complex,B: complex,C: complex] :
( ( ( times_times_complex @ A @ B )
= ( times_times_complex @ C @ B ) )
= ( ( B = zero_zero_complex )
| ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(144,axiom,
! [A: set_complex,B: set_complex] :
( ( A = B )
=> ( ord_le701908932omplex @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_equalityD2) ).
thf(703,plain,
! [A: set_complex,B: set_complex] :
( ( A = B )
=> ( ord_le701908932omplex @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(111,axiom,
! [A: set_complex,B: set_complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( ord_le701908932omplex @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_dual__order_Oantisym) ).
thf(600,plain,
! [A: set_complex,B: set_complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( ord_le701908932omplex @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(253,axiom,
( id_complex
= ( ^ [A: complex] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_id__def) ).
thf(1094,plain,
( id_complex
= ( ^ [A: complex] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(231,axiom,
! [A: complex,B: complex] :
( ( ( times_times_complex @ A @ B )
= A )
= ( ( A = zero_zero_complex )
| ( B = one_one_complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_mult__cancel__left2) ).
thf(1008,plain,
! [A: complex,B: complex] :
( ( ( times_times_complex @ A @ B )
= A )
= ( ( A = zero_zero_complex )
| ( B = one_one_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(101,axiom,
! [A: ( complex > complex ) > complex > complex] :
( ( ! [B: complex > complex] :
( ( A @ B )
= B ) )
= ( A = id_complex_complex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_eq__id__iff) ).
thf(571,plain,
! [A: ( complex > complex ) > complex > complex] :
( ( ! [B: complex > complex] :
( ( A @ B )
= B ) )
= ( A = id_complex_complex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(115,axiom,
! [A: ( complex > complex ) > complex > complex,B: complex > complex] :
( ( compow1098280738omplex @ zero_zero_nat @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_funpow__0) ).
thf(612,plain,
! [A: ( complex > complex ) > complex > complex,B: complex > complex] :
( ( compow1098280738omplex @ zero_zero_nat @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(184,axiom,
! [A: complex,B: complex,C: complex] :
( ( times_times_complex @ A @ ( times_times_complex @ B @ C ) )
= ( times_times_complex @ B @ ( times_times_complex @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_vector__space__over__itself_Oscale__left__commute) ).
thf(859,plain,
! [A: complex,B: complex,C: complex] :
( ( times_times_complex @ A @ ( times_times_complex @ B @ C ) )
= ( times_times_complex @ B @ ( times_times_complex @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(78,axiom,
( comp_c130555887omplex
= ( ^ [A: complex > complex,B: complex > complex,C: complex] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_comp__apply) ).
thf(497,plain,
( comp_c130555887omplex
= ( ^ [A: complex > complex,B: complex > complex,C: complex] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(189,axiom,
! [A: complex > complex,B: nat,C: complex] :
( ( A @ ( compow1667379464omplex @ B @ A @ C ) )
= ( compow1667379464omplex @ B @ A @ ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_funpow__swap1) ).
thf(876,plain,
! [A: complex > complex,B: nat,C: complex] :
( ( A @ ( compow1667379464omplex @ B @ A @ C ) )
= ( compow1667379464omplex @ B @ A @ ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(178,axiom,
( ( (=) @ set_complex )
= ( ^ [A: set_complex,B: set_complex] :
( ( ord_le701908932omplex @ A @ B )
& ( ord_le701908932omplex @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_set__eq__subset) ).
thf(845,plain,
( ( (=) @ set_complex )
= ( ^ [A: set_complex,B: set_complex] :
( ( ord_le701908932omplex @ A @ B )
& ( ord_le701908932omplex @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(68,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(465,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(120,axiom,
! [A: complex,B: complex,C: complex] :
( ( ( times_times_complex @ A @ B )
= ( times_times_complex @ C @ B ) )
= ( ( A = C )
| ( B = zero_zero_complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_vector__space__over__itself_Oscale__cancel__right) ).
thf(627,plain,
! [A: complex,B: complex,C: complex] :
( ( ( times_times_complex @ A @ B )
= ( times_times_complex @ C @ B ) )
= ( ( A = C )
| ( B = zero_zero_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(33,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ one_one_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ B @ one_one_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_mult__le__one) ).
thf(363,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ one_one_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ B @ one_one_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(86,axiom,
! [A: complex > complex,B: set_complex,C: set_complex] :
( ( ord_le701908932omplex @ ( image_58037603omplex @ A @ B ) @ C )
= ( ! [D: complex] :
( ( member_complex @ D @ B )
=> ( member_complex @ ( A @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_image__subset__iff) ).
thf(524,plain,
! [A: complex > complex,B: set_complex,C: set_complex] :
( ( ord_le701908932omplex @ ( image_58037603omplex @ A @ B ) @ C )
= ( ! [D: complex] :
( ( member_complex @ D @ B )
=> ( member_complex @ ( A @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(77,axiom,
( ord_le701908932omplex
= ( ^ [A: set_complex,B: set_complex] :
! [C: complex] :
( ( member_complex @ C @ A )
=> ( member_complex @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_subset__eq) ).
thf(495,plain,
( ord_le701908932omplex
= ( ^ [A: set_complex,B: set_complex] :
! [C: complex] :
( ( member_complex @ C @ A )
=> ( member_complex @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(161,axiom,
ord_le701908932omplex @ ( image_58037603omplex @ f @ s ) @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_assms_I5_J) ).
thf(771,plain,
ord_le701908932omplex @ ( image_58037603omplex @ f @ s ) @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(221,axiom,
! [A: complex > complex,B: set_complex,C: complex > complex,D: set_complex,E: complex] :
( ( comple372758642hic_on @ A @ B )
=> ( ( comple372758642hic_on @ C @ D )
=> ( ( topolo935673511omplex @ B )
=> ( ( topolo935673511omplex @ D )
=> ( ( ord_le701908932omplex @ ( image_58037603omplex @ A @ B ) @ D )
=> ( ! [F: complex] :
( ( member_complex @ F @ B )
=> ( ( C @ ( A @ F ) )
= F ) )
=> ( ( member_complex @ E @ B )
=> ( ( times_times_complex @ ( deriv_complex @ A @ E ) @ ( deriv_complex @ C @ ( A @ E ) ) )
= one_one_complex ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_deriv__left__inverse) ).
thf(976,plain,
! [A: complex > complex,B: set_complex,C: complex > complex,D: set_complex,E: complex] :
( ( comple372758642hic_on @ A @ B )
=> ( ( comple372758642hic_on @ C @ D )
=> ( ( topolo935673511omplex @ B )
=> ( ( topolo935673511omplex @ D )
=> ( ( ord_le701908932omplex @ ( image_58037603omplex @ A @ B ) @ D )
=> ( ! [F: complex] :
( ( member_complex @ F @ B )
=> ( ( C @ ( A @ F ) )
= F ) )
=> ( ( member_complex @ E @ B )
=> ( ( times_times_complex @ ( deriv_complex @ A @ E ) @ ( deriv_complex @ C @ ( A @ E ) ) )
= one_one_complex ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(199,axiom,
! [A: complex,B: complex,C: complex] :
( ( times_times_complex @ A @ ( times_times_complex @ B @ C ) )
= ( times_times_complex @ ( times_times_complex @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_vector__space__over__itself_Oscale__scale) ).
thf(903,plain,
! [A: complex,B: complex,C: complex] :
( ( times_times_complex @ A @ ( times_times_complex @ B @ C ) )
= ( times_times_complex @ ( times_times_complex @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(171,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_zero__reorient) ).
thf(813,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(3,axiom,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_mult__zero__right) ).
thf(258,plain,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(29,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( A = zero_zero_nat )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_mult__cancel__left) ).
thf(351,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( A = zero_zero_nat )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(42,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ B @ A )
& ( ord_less_eq_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_dual__order_Oeq__iff) ).
thf(390,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ B @ A )
& ( ord_less_eq_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(122,axiom,
! [A: complex,B: complex > $o] :
( ( member_complex @ A @ ( collect_complex @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_mem__Collect__eq) ).
thf(632,plain,
! [A: complex,B: complex > $o] :
( ( member_complex @ A @ ( collect_complex @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(46,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_zero__le) ).
thf(401,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(227,axiom,
! [A: complex > complex,B: set_complex,C: complex,D: complex] :
( ( comple372758642hic_on @ A @ B )
=> ( ( topolo935673511omplex @ B )
=> ( ( topolo2127351575omplex @ B )
=> ( ! [E: nat] :
( ( compow1098280738omplex @ E @ deriv_complex @ A @ C )
= zero_zero_complex )
=> ( ( member_complex @ C @ B )
=> ( ( member_complex @ D @ B )
=> ( ( A @ D )
= zero_zero_complex ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_holomorphic__fun__eq__0__on__connected) ).
thf(995,plain,
! [A: complex > complex,B: set_complex,C: complex,D: complex] :
( ( comple372758642hic_on @ A @ B )
=> ( ( topolo935673511omplex @ B )
=> ( ( topolo2127351575omplex @ B )
=> ( ! [E: nat] :
( ( compow1098280738omplex @ E @ deriv_complex @ A @ C )
= zero_zero_complex )
=> ( ( member_complex @ C @ B )
=> ( ( member_complex @ D @ B )
=> ( ( A @ D )
= zero_zero_complex ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(149,axiom,
! [A: complex > complex,B: complex > complex,C: complex > complex,D: complex > complex,E: complex > complex,F: complex > complex] :
( ( ( comp_c130555887omplex @ A @ B )
= ( comp_c130555887omplex @ C @ D ) )
=> ( ( ( comp_c130555887omplex @ D @ E )
= F )
=> ( ( comp_c130555887omplex @ A @ ( comp_c130555887omplex @ B @ E ) )
= ( comp_c130555887omplex @ C @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_rewriteL__comp__comp2) ).
thf(731,plain,
! [A: complex > complex,B: complex > complex,C: complex > complex,D: complex > complex,E: complex > complex,F: complex > complex] :
( ( ( comp_c130555887omplex @ A @ B )
= ( comp_c130555887omplex @ C @ D ) )
=> ( ( ( comp_c130555887omplex @ D @ E )
= F )
=> ( ( comp_c130555887omplex @ A @ ( comp_c130555887omplex @ B @ E ) )
= ( comp_c130555887omplex @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(52,axiom,
( times_times_nat
= ( ^ [A: nat,B: nat] : ( times_times_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_mult_Ocommute) ).
thf(418,plain,
( times_times_nat
= ( ^ [A: nat,B: nat] : ( times_times_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(239,axiom,
! [A: nat,B: complex] :
( ( ( A = zero_zero_nat )
=> ( ( compow1098280738omplex @ A @ deriv_complex @ id_complex @ B )
= B ) )
& ( ( A != zero_zero_nat )
=> ( ( ( A = one_one_nat )
=> ( ( compow1098280738omplex @ A @ deriv_complex @ id_complex @ B )
= one_one_complex ) )
& ( ( A != one_one_nat )
=> ( ( compow1098280738omplex @ A @ deriv_complex @ id_complex @ B )
= zero_zero_complex ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_higher__deriv__id) ).
thf(1030,plain,
! [A: nat,B: complex] :
( ( ( A = zero_zero_nat )
=> ( ( compow1098280738omplex @ A @ deriv_complex @ id_complex @ B )
= B ) )
& ( ( A != zero_zero_nat )
=> ( ( ( A = one_one_nat )
=> ( ( compow1098280738omplex @ A @ deriv_complex @ id_complex @ B )
= one_one_complex ) )
& ( ( A != one_one_nat )
=> ( ( compow1098280738omplex @ A @ deriv_complex @ id_complex @ B )
= zero_zero_complex ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(134,axiom,
! [A: complex,B: complex,C: complex] :
( ( ( times_times_complex @ A @ B )
= ( times_times_complex @ A @ C ) )
= ( ( B = C )
| ( A = zero_zero_complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_vector__space__over__itself_Oscale__cancel__left) ).
thf(667,plain,
! [A: complex,B: complex,C: complex] :
( ( ( times_times_complex @ A @ B )
= ( times_times_complex @ A @ C ) )
= ( ( B = C )
| ( A = zero_zero_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(207,axiom,
! [A: complex] :
( ( times_times_complex @ A @ one_one_complex )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_mult_Ocomm__neutral) ).
thf(929,plain,
! [A: complex] :
( ( times_times_complex @ A @ one_one_complex )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(139,axiom,
! [A: complex,B: set_complex,C: complex,D: complex > complex] :
( ( member_complex @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_complex @ C @ ( image_58037603omplex @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_rev__image__eqI) ).
thf(684,plain,
! [A: complex,B: set_complex,C: complex,D: complex > complex] :
( ( member_complex @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_complex @ C @ ( image_58037603omplex @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(27,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_le__trans) ).
thf(346,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(18,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_dual__order_Oantisym) ).
thf(315,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= one_one_nat )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_nat__mult__eq__1__iff) ).
thf(432,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= one_one_nat )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(176,axiom,
! [A: set_complex,B: set_complex] :
( ( A = B )
=> ~ ( ( ord_le701908932omplex @ A @ B )
=> ~ ( ord_le701908932omplex @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_equalityE) ).
thf(835,plain,
! [A: set_complex,B: set_complex] :
( ( A = B )
=> ~ ( ( ord_le701908932omplex @ A @ B )
=> ~ ( ord_le701908932omplex @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(182,axiom,
ord_less_eq_nat @ zero_zero_nat @ one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_zero__le__one) ).
thf(854,plain,
ord_less_eq_nat @ zero_zero_nat @ one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(166,axiom,
! [A: complex > complex,B: set_complex,C: complex > complex] :
( ( comple372758642hic_on @ A @ B )
=> ( ! [D: complex] :
( ( member_complex @ D @ B )
=> ( ( A @ D )
= ( C @ D ) ) )
=> ( comple372758642hic_on @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_holomorphic__transform) ).
thf(790,plain,
! [A: complex > complex,B: set_complex,C: complex > complex] :
( ( comple372758642hic_on @ A @ B )
=> ( ! [D: complex] :
( ( member_complex @ D @ B )
=> ( ( A @ D )
= ( C @ D ) ) )
=> ( comple372758642hic_on @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(8,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_mult_Oleft__neutral) ).
thf(273,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(186,axiom,
! [A: complex > complex,B: complex > complex,C: complex > complex,D: complex > complex] :
( ( ( comp_c130555887omplex @ A @ B )
= C )
=> ( ( comp_c130555887omplex @ A @ ( comp_c130555887omplex @ B @ D ) )
= ( comp_c130555887omplex @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_rewriteL__comp__comp) ).
thf(865,plain,
! [A: complex > complex,B: complex > complex,C: complex > complex,D: complex > complex] :
( ( ( comp_c130555887omplex @ A @ B )
= C )
=> ( ( comp_c130555887omplex @ A @ ( comp_c130555887omplex @ B @ D ) )
= ( comp_c130555887omplex @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(112,axiom,
! [A: real > complex > complex,B: ( complex > complex ) > real] :
( ( ( ( comp_r2009261319omplex @ A @ B )
= id_complex_complex )
& ( ( comp_c1884694328l_real @ B @ A )
= id_real ) )
= ( ! [C: complex > complex] :
( ( A @ ( B @ C ) )
= C )
& ! [C: real] :
( ( B @ ( A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_isomorphism__expand) ).
thf(603,plain,
! [A: real > complex > complex,B: ( complex > complex ) > real] :
( ( ( ( comp_r2009261319omplex @ A @ B )
= id_complex_complex )
& ( ( comp_c1884694328l_real @ B @ A )
= id_real ) )
= ( ! [C: complex > complex] :
( ( A @ ( B @ C ) )
= C )
& ! [C: real] :
( ( B @ ( A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(228,axiom,
( ( times_times_complex @ ( deriv_complex @ f @ w ) @ ( deriv_complex @ g @ ( f @ w ) ) )
= ( times_times_complex @ ( deriv_complex @ g @ ( f @ w ) ) @ ( deriv_complex @ f @ w ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28__092_060open_062deriv_Af_Aw_A_K_Aderiv_Ag_A_If_Aw_J_A_061_Aderiv_Ag_A_If_Aw_J_A_K_Aderiv_Af_Aw_092_060close_062) ).
thf(999,plain,
( ( times_times_complex @ ( deriv_complex @ f @ w ) @ ( deriv_complex @ g @ ( f @ w ) ) )
= ( times_times_complex @ ( deriv_complex @ g @ ( f @ w ) ) @ ( deriv_complex @ f @ w ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(118,axiom,
! [A: complex,B: complex,C: complex] :
( ( A != zero_zero_complex )
=> ( ( ( times_times_complex @ A @ B )
= ( times_times_complex @ A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_vector__space__over__itself_Oscale__left__imp__eq) ).
thf(620,plain,
! [A: complex,B: complex,C: complex] :
( ( A != zero_zero_complex )
=> ( ( ( times_times_complex @ A @ B )
= ( times_times_complex @ A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(22,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_eq__imp__le) ).
thf(326,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(71,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: nat,E: nat] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_linorder__wlog) ).
thf(474,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: nat,E: nat] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(133,axiom,
! [A: complex,B: complex > complex,C: set_complex] :
( ( member_complex @ A @ ( image_58037603omplex @ B @ C ) )
= ( ? [D: complex] :
( ( member_complex @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_image__iff) ).
thf(664,plain,
! [A: complex,B: complex > complex,C: set_complex] :
( ( member_complex @ A @ ( image_58037603omplex @ B @ C ) )
= ( ? [D: complex] :
( ( member_complex @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(123,axiom,
comple372758642hic_on @ f @ s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_assms_I1_J) ).
thf(635,plain,
comple372758642hic_on @ f @ s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(89,axiom,
! [A: complex] :
( ( member_complex @ A @ s )
=> ( ( g @ ( f @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_assms_I6_J) ).
thf(532,plain,
! [A: complex] :
( ( member_complex @ A @ s )
=> ( ( g @ ( f @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(215,axiom,
zero_zero_complex != one_one_complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_zero__neq__one) ).
thf(955,plain,
zero_zero_complex != one_one_complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(167,axiom,
! [A: complex,B: complex] :
( ( ( times_times_complex @ A @ B )
= zero_zero_complex )
= ( ( A = zero_zero_complex )
| ( B = zero_zero_complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_mult__eq__0__iff) ).
thf(796,plain,
! [A: complex,B: complex] :
( ( ( times_times_complex @ A @ B )
= zero_zero_complex )
= ( ( A = zero_zero_complex )
| ( B = zero_zero_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(51,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_nat__mult__1__right) ).
thf(415,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(81,axiom,
! [A: set_complex,B: set_complex,C: complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( member_complex @ C @ A )
=> ( member_complex @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_in__mono) ).
thf(506,plain,
! [A: set_complex,B: set_complex,C: complex] :
( ( ord_le701908932omplex @ A @ B )
=> ( ( member_complex @ C @ A )
=> ( member_complex @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(6,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_order__refl) ).
thf(268,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(224,axiom,
! [A: complex > complex] :
( ( comp_c130555887omplex @ A @ id_complex )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_comp__id) ).
thf(987,plain,
! [A: complex > complex] :
( ( comp_c130555887omplex @ A @ id_complex )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(24,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
!= zero_zero_nat )
=> ( ( A != zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_mult__not__zero) ).
thf(332,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
!= zero_zero_nat )
=> ( ( A != zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(110,axiom,
! [A: real > complex > complex,B: ( complex > complex ) > real,C: real > complex > complex] :
( ( ( comp_r2009261319omplex @ A @ B )
= id_complex_complex )
=> ( ( ( comp_c1884694328l_real @ B @ C )
= id_real )
=> ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_left__right__inverse__eq) ).
thf(596,plain,
! [A: real > complex > complex,B: ( complex > complex ) > real,C: real > complex > complex] :
( ( ( comp_r2009261319omplex @ A @ B )
= id_complex_complex )
=> ( ( ( comp_c1884694328l_real @ B @ C )
= id_real )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(235,axiom,
! [A: complex > complex,B: set_complex] :
( ( comple372758642hic_on @ A @ B )
=> ( ( topolo935673511omplex @ B )
=> ( comple372758642hic_on @ ( deriv_complex @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_holomorphic__deriv) ).
thf(1019,plain,
! [A: complex > complex,B: set_complex] :
( ( comple372758642hic_on @ A @ B )
=> ( ( topolo935673511omplex @ B )
=> ( comple372758642hic_on @ ( deriv_complex @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(66,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ ( times_times_nat @ A @ ( times_times_nat @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_le__cube) ).
thf(459,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ ( times_times_nat @ A @ ( times_times_nat @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(226,axiom,
! [A: complex > complex,B: set_complex,C: nat] :
( ( comple372758642hic_on @ A @ B )
=> ( ( topolo935673511omplex @ B )
=> ( comple372758642hic_on @ ( compow1098280738omplex @ C @ deriv_complex @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_holomorphic__higher__deriv) ).
thf(992,plain,
! [A: complex > complex,B: set_complex,C: nat] :
( ( comple372758642hic_on @ A @ B )
=> ( ( topolo935673511omplex @ B )
=> ( comple372758642hic_on @ ( compow1098280738omplex @ C @ deriv_complex @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(180,axiom,
comple372758642hic_on @ g @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_assms_I2_J) ).
thf(850,plain,
comple372758642hic_on @ g @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(35,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_mult__nonneg__nonpos) ).
thf(369,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(44,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_mult__le__mono1) ).
thf(395,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(119,axiom,
! [A: complex,B: set_complex,C: complex,D: set_complex] :
( ( member_complex @ A @ B )
=> ( ( member_complex @ C @ D )
=> ( member_complex @ ( times_times_complex @ A @ C ) @ ( times_1316095593omplex @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_set__times__intro) ).
thf(624,plain,
! [A: complex,B: set_complex,C: complex,D: set_complex] :
( ( member_complex @ A @ B )
=> ( ( member_complex @ C @ D )
=> ( member_complex @ ( times_times_complex @ A @ C ) @ ( times_1316095593omplex @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(30,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_mult__is__0) ).
thf(354,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(97,axiom,
( id_real
= ( ^ [A: real] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_id__apply) ).
thf(560,plain,
( id_real
= ( ^ [A: real] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(156,axiom,
! [A: complex] :
( ( times_times_complex @ A @ zero_zero_complex )
= zero_zero_complex ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_mult__zero__right) ).
thf(755,plain,
! [A: complex] :
( ( times_times_complex @ A @ zero_zero_complex )
= zero_zero_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(251,axiom,
! [A: complex > complex] :
( ( comp_c130555887omplex @ id_complex @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_id__comp) ).
thf(1088,plain,
! [A: complex > complex] :
( ( comp_c130555887omplex @ id_complex @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(64,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_dual__order_Orefl) ).
thf(454,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(191,axiom,
( ( (=) @ set_complex )
= ( ^ [A: set_complex,B: set_complex] :
( ( ord_le701908932omplex @ B @ A )
& ( ord_le701908932omplex @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_dual__order_Oeq__iff) ).
thf(882,plain,
( ( (=) @ set_complex )
= ( ^ [A: set_complex,B: set_complex] :
( ( ord_le701908932omplex @ B @ A )
& ( ord_le701908932omplex @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(233,axiom,
( ( deriv_complex @ id_complex )
= ( ^ [A: complex] : one_one_complex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_deriv__id) ).
thf(1014,plain,
( ( deriv_complex @ id_complex )
= ( ^ [A: complex] : one_one_complex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(1124,plain,
$false,
inference(e,[status(thm)],[1024,909,481,645,892,1083,468,1005,276,1068,741,873,384,550,913,945,340,538,670,898,1001,709,973,651,372,751,802,949,934,357,638,870,606,289,448,1100,261,492,591,321,574,1051,293,1072,774,428,265,527,312,270,661,925,761,381,366,1057,1021,820,392,630,429,746,1091,1042,952,862,349,879,435,583,889,461,682,456,285,847,566,484,697,650,615,1064,403,1096,499,519,578,783,420,884,1028,554,642,1016,547,471,256,901,1075,738,654,1060,569,343,360,805,657,1054,398,530,586,718,1086,938,906,412,965,425,513,279,444,689,296,562,694,843,772,743,291,958,826,577,936,787,919,764,406,1011,736,451,318,509,377,990,387,758,535,816,609,323,799,700,895,330,932,983,768,636,986,851,438,922,722,490,589,680,487,927,374,617,516,968,823,557,282,707,887,971,409,580,855,673,441,502,544,703,600,1094,1008,571,612,859,497,876,845,465,627,363,524,495,771,976,903,813,258,351,390,632,401,995,731,418,1030,667,929,684,346,315,432,835,854,790,273,865,603,999,620,326,474,664,635,532,955,796,415,506,268,987,332,596,1019,459,992,850,369,395,624,354,560,755,1088,454,882,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP035^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.22 % Computer : n018.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 19:42:12 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.03/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.37/1.22 % [INFO] Parsing done (402ms).
% 2.37/1.23 % [INFO] Running in sequential loop mode.
% 3.81/1.62 % [INFO] eprover registered as external prover.
% 3.81/1.63 % [INFO] Scanning for conjecture ...
% 4.03/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 359 axioms. Running axiom selection ...
% 4.54/1.90 % [INFO] Axiom selection finished. Selected 253 axioms (removed 106 axioms).
% 5.25/2.13 % [INFO] Problem is higher-order (TPTP THF).
% 5.25/2.16 % [INFO] Type checking passed.
% 5.25/2.16 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 17.78/5.20 % External prover 'e' found a proof!
% 17.78/5.20 % [INFO] Killing All external provers ...
% 17.78/5.20 % Time passed: 4816ms (effective reasoning time: 3960ms)
% 17.78/5.20 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 17.78/5.20 % Axioms used in derivation (253): fact_351_holomorphic__fun__eq__0__on__connected, fact_286_ball__imageD, fact_108_mult__right__cancel, fact_196_rewriteL__comp__comp, fact_215_image__id, fact_335_order__class_Oorder_Oantisym, fact_31_mult__zero__left, fact_271_le0, fact_185_isomorphism__expand, fact_252_not__one__le__zero, fact_96_mult_Oleft__commute, fact_39_mult__cancel__left, fact_140_funpow__code__def, fact_115_comm__monoid__mult__class_Omult__1, fact_137_set__times__intro, fact_203_nat__mult__eq__cancel__disj, fact_11_eq__id__iff, fact_317_Nat_Oex__has__greatest__nat, fact_321_dual__order_Oeq__iff, fact_276_bot__nat__0_Oextremum__uniqueI, fact_64_mult__cancel__left1, fact_49_mult_Oleft__neutral, fact_126_vector__space__over__itself_Oscale__zero__left, fact_120_funpow__simps__right_I1_J, fact_312_le__refl, fact_198_rewriteL__comp__comp2, fact_314_eq__imp__le, fact_142_funpow__code__def, fact_24__092_060open_062deriv_A_Ig_A_092_060circ_062_Af_J_Aw_A_061_Aderiv_Aid_Aw_092_060close_062, fact_36_mult__eq__0__iff, fact_33_mult__zero__right, fact_80_comp__eq__dest__lhs, fact_7_id__apply, fact_269_image__eqI, fact_22_id__funpow, fact_151_higher__deriv__transform__within__open, fact_118_funpow__simps__right_I1_J, fact_146_mult__cancel1, fact_2_assms_I7_J, fact_58_mult__cancel__right2, fact_157_funpow__mult, fact_145_mult__cancel2, fact_89_mult_Oassoc, fact_272_bot__nat__0_Oextremum, fact_99_divisors__zero, fact_122_vector__space__over__itself_Oscale__one, fact_51_id__comp, fact_214_image__id, fact_212_le__zero__eq, fact_232_mult__nonneg__nonneg, fact_71_comp__def, fact_60_mult__cancel__right1, fact_298_set__eq__subset, fact_302_subset__imageE, fact_85_mult__not__zero, fact_248_mult__mono, fact_295_subset__refl, fact_350_Ln__1, fact_169_vector__space__over__itself_Oscale__right__imp__eq, fact_327_linorder__wlog, fact_177_pointfree__idE, fact_79_funpow__swap1, fact_81_zero__reorient, fact_37_mult__eq__0__iff, fact_197_rewriteR__comp__comp, fact_152_holomorphic__higher__deriv, fact_305_order__refl, fact_182_isomorphism__expand, fact_102_no__zero__divisors, fact_42_mult__cancel__right, fact_262_mult__eq__1, fact_56_assms_I3_J, fact_306_order__refl, fact_310_Sup_OSUP__id__eq, fact_46_mult_Oright__neutral, fact_192_left__right__inverse__eq, fact_300_image__mono, fact_84_mult__not__zero, fact_218_image__comp, fact_83_zero__reorient, fact_282_imageI, fact_303_image__subset__iff, fact_57__092_060open_062deriv_Ag_A_If_Aw_J_A_K_Aderiv_Af_Aw_A_061_Aderiv_A_Ig_A_092_060circ_062_Af_J_Aw_092_060close_062, fact_279_mult__le__mono, fact_69_ab__semigroup__mult__class_Omult__ac_I1_J, fact_289_subsetD, fact_284_bex__imageD, fact_287_rev__image__eqI, fact_114_comm__monoid__mult__class_Omult__1, fact_189_left__right__inverse__eq, fact_258_mult__le__one, fact_240_mult__left__mono, fact_173_fun_Omap__id0, fact_223_ordered__comm__semiring__class_Ocomm__mult__left__mono, fact_183_isomorphism__expand, fact_296_Collect__mono, fact_194_left__right__inverse__eq, fact_132_vector__space__over__itself_Oscale__cancel__right, fact_101_no__zero__divisors, fact_333_order__trans, fact_230_mult__nonneg__nonpos, fact_277_mult__le__mono2, fact_171_vector__space__over__itself_Oscale__left__imp__eq, fact_5_id__apply, fact_184_isomorphism__expand, fact_27_zero__neq__one, fact_29_comp__apply, fact_304_subset__image__iff, fact_285_image__cong, fact_200_holomorphic__cong, fact_211_arcosh__1, fact_324_dual__order_Otrans, fact_270_subsetI, fact_178_isomorphism__expand, fact_294_subset__iff, fact_213_image__id, fact_318_dual__order_Oantisym, fact_153_holomorphic__deriv, fact_268_subset__antisym, fact_76_comp__eq__elim, fact_107_mult__right__cancel, fact_68_ab__semigroup__mult__class_Omult__ac_I1_J, fact_124_vector__space__over__itself_Oscale__eq__0__iff, fact_53_funpow__0, fact_121_fun_Omap__id, fact_283_image__iff, fact_55_funpow__0, help_If_1_1_If_001t__Complex__Ocomplex_T, fact_1__092_060open_062_092_060And_062z_O_A_Ideriv_A_094_094_A1_J_Aid_Az_A_061_A_Iif_A1_A_061_A0_Athen_Az_Aelse_Aif_A1_A_061_A1_Athen_A1_058_058_063_Ha_Aelse_A_I0_058_058_063_Ha_J_J_092_060close_062, fact_256_mult__left__le, fact_28__092_060open_062deriv_Af_Aw_A_K_Aderiv_Ag_A_If_Aw_J_A_061_Aderiv_Ag_A_If_Aw_J_A_K_Aderiv_Af_Aw_092_060close_062, fact_25_zero__neq__one, fact_62_mult__cancel__left2, fact_273_less__eq__nat_Osimps_I1_J, fact_330_dual__order_Orefl, fact_73_comp__funpow, fact_217_holomorphic__on__compose__gen, fact_159_funpow__mult, fact_163_vector__space__over__itself_Oscale__scale, fact_147_mult__0__right, fact_165_set__times__elim, fact_149_nat__mult__eq__1__iff, fact_130_vector__space__over__itself_Oscale__cancel__left, fact_186_isomorphism__expand, fact_161_vector__space__over__itself_Oscale__left__commute, fact_143_assms_I4_J, fact_325_dual__order_Otrans, fact_72_comp__assoc, fact_274_le__0__eq, fact_13_eq__id__iff, fact_280_le__square, fact_3_deriv__id, fact_93_mult_Ocommute, fact_154_mult__0, fact_66_assms_I6_J, fact_67_assms_I1_J, fact_105_mult__left__cancel, fact_319_dual__order_Oantisym, fact_267_arsinh__0, fact_299_Collect__mono__iff, fact_87_mem__Collect__eq, fact_219_image__eq__imp__comp, fact_15_higher__deriv__id, fact_207_mult__delta__right, fact_168_fun_Omap__comp, fact_134_mult__if__delta, fact_148_mult__is__0, fact_202_assms_I5_J, fact_222_set__times__mono2__b, fact_112_mult_Ocomm__neutral, fact_309_Sup_OSUP__id__eq, fact_237_mult__right__mono, fact_190_left__right__inverse__eq, fact_75_comp__eq__dest, fact_104_mult__left__cancel, fact_246_mult__mono_H, fact_204_mult__delta__left, fact_12_eq__id__iff, fact_265_artanh__0, fact_234_split__mult__neg__le, fact_195_left__right__inverse__eq, help_If_2_1_If_001t__Complex__Ocomplex_T, fact_220_zero__le, fact_110_comp__eq__id__dest, fact_292_equalityD1, fact_191_left__right__inverse__eq, fact_90_mult_Oassoc, fact_98_divisors__zero, fact_338_ord__le__eq__trans, fact_10_id__def, fact_160_mult__eq__self__implies__10, fact_336_order__class_Oorder_Oantisym, fact_228_mult__nonpos__nonneg, fact_290_equalityE, fact_176_holomorphic__on__linear, fact_329_dual__order_Orefl, fact_45_mult_Oright__neutral, fact_17_one__reorient, help_If_3_1_If_001t__Complex__Ocomplex_T, fact_180_isomorphism__expand, fact_301_image__subsetI, fact_77_funpow__swap1, fact_92_mult_Ocommute, fact_150_nat__1__eq__mult__iff, fact_316_nat__le__linear, fact_255_deriv__left__inverse, fact_332_order__trans, fact_95_mult_Oleft__commute, fact_181_isomorphism__expand, fact_48_mult_Oleft__neutral, fact_226_mult__nonneg__nonpos2, fact_117_funpow__simps__right_I1_J, fact_8_id__def, fact_216_set__times__mono2, fact_311_Sup_OSUP__id__eq, fact_9_id__def, fact_278_mult__le__mono1, fact_43_mult__cancel__right, fact_322_dual__order_Oeq__iff, fact_40_mult__cancel__left, fact_193_left__right__inverse__eq, fact_201_holomorphic__transform, fact_221_holomorphic__on__subset, fact_128_vector__space__over__itself_Oscale__zero__right, fact_23_calculation, fact_297_subset__trans, fact_19_id__funpow, fact_179_isomorphism__expand, fact_315_le__antisym, fact_111_mult_Ocomm__neutral, fact_187_left__right__inverse__eq, fact_175_holomorphic__on__id, fact_155_nat__mult__1__right, fact_288_in__mono, fact_275_bot__nat__0_Oextremum__unique, fact_281_le__cube, fact_6_id__apply, fact_291_subset__eq, fact_174_complex__derivative__transform__within__open, fact_21_id__funpow, fact_34_mult__zero__right, fact_88_Collect__mem__eq, fact_250_zero__le__one, fact_199_rewriteR__comp__comp2, fact_52_comp__id, fact_293_equalityD2, fact_156_nat__mult__1, fact_144_assms_I2_J, fact_254_holomorphic__on__compose, fact_30_mult__zero__left, fact_16_one__reorient, fact_188_left__right__inverse__eq, fact_313_le__trans
% 17.78/5.20 % No. of inferences in proof: 510
% 17.78/5.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4816 ms resp. 3960 ms w/o parsing
% 18.68/5.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.68/5.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------