%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP148^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n002.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 08:06:57 AM UTC 2026
% Result : Theorem 69.04s 40.69s
% Output : Refutation 70.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 284
% Syntax : Number of formulae : 598 ( 175 unt; 0 typ; 0 def)
% Number of atoms : 2079 ( 727 equ; 4 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 8487 ( 123 ~; 39 |; 127 &;7475 @)
% ( 0 <=>; 723 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 698 ( 698 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 41 usr; 5 con; 0-8 aty)
% Number of variables : 2300 ( 69 ^;2193 !; 38 ?;2300 :)
% Comments :
%------------------------------------------------------------------------------
thf(complex_type,type,
complex: $tType ).
thf(real_type,type,
real: $tType ).
thf(int_type,type,
int: $tType ).
thf(a_type,type,
a: $tType ).
thf(type_decl,type,
type:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(top_decl,type,
top:
!>[TA: $tType] : $o ).
thf(inner_real_inner_decl,type,
inner_real_inner:
!>[TA: $tType] : $o ).
thf(real_V1076094709vector_decl,type,
real_V1076094709vector:
!>[TA: $tType] : $o ).
thf(euclid925273238_space_decl,type,
euclid925273238_space:
!>[TA: $tType] : $o ).
thf(topolo503727757_space_decl,type,
topolo503727757_space:
!>[TA: $tType] : $o ).
thf(real_V55928688vector_decl,type,
real_V55928688vector:
!>[TA: $tType] : $o ).
thf(execut510477386_space_decl,type,
execut510477386_space:
!>[TA: $tType] : $o ).
thf(aff_dim_decl,type,
aff_dim:
!>[TA: $tType] : ( ( set @ TA ) > int ) ).
thf(bij_betw_decl,type,
bij_betw:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > ( set @ TA ) > $o ) ).
thf(comp_decl,type,
comp:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB ) > ( TA > TC ) > TA > TB ) ).
thf(id_decl,type,
id:
!>[TA: $tType] : ( TA > TA ) ).
thf(inj_on_decl,type,
inj_on:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > $o ) ).
thf(swap_decl,type,
swap:
!>[TA: $tType,TB: $tType] : ( TB > TB > ( TB > TA ) > TB > TA ) ).
thf(the_inv_into_decl,type,
the_inv_into:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( TB > TA ) > TA > TB ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(hilbert_inv_into_decl,type,
hilbert_inv_into:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( TB > TA ) > TA > TB ) ).
thf(inner_780170721_inner_decl,type,
inner_780170721_inner:
!>[TA: $tType] : ( TA > TA > real ) ).
thf(linear_adjoint_decl,type,
linear_adjoint:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > TA > TB ) ).
thf(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
thf(path_arc_decl,type,
path_arc:
!>[TA: $tType] : ( ( real > TA ) > $o ) ).
thf(path_path_decl,type,
path_path:
!>[TA: $tType] : ( ( real > TA ) > $o ) ).
thf(path_pathfinish_decl,type,
path_pathfinish:
!>[TA: $tType] : ( ( real > TA ) > TA ) ).
thf(path_pathstart_decl,type,
path_pathstart:
!>[TA: $tType] : ( ( real > TA ) > TA ) ).
thf(path_rectpath_decl,type,
path_rectpath: complex > complex > real > complex ).
thf(path_simple_path_decl,type,
path_simple_path:
!>[TA: $tType] : ( ( real > TA ) > $o ) ).
thf(poinca1076805489pen_R2_decl,type,
poinca1076805489pen_R2:
!>[TA: $tType] : ( ( TA > TA ) > ( TA > ( bounde2145540817linfun @ TA @ TA ) ) > ( set @ TA ) > $o ) ).
thf(poinca1531302022lex_of_decl,type,
poinca1531302022lex_of:
!>[TA: $tType] : ( TA > complex ) ).
thf(poinca179318102eal_of_decl,type,
poinca179318102eal_of:
!>[TA: $tType] : ( complex > TA ) ).
thf(real_V1632203528linear_decl,type,
real_V1632203528linear:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > $o ) ).
thf(real_V1072672427axioms_decl,type,
real_V1072672427axioms:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > $o ) ).
thf(real_Vector_linear_decl,type,
real_Vector_linear:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > $o ) ).
thf(iso_tu2011167877assist_decl,type,
iso_tu2011167877assist:
!>[TA: $tType,TB: $tType] : ( ( ( TB > TB ) > TA > TA ) > ( TA > TB ) > TA > ( TB > TB ) > TA > TB > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(image_decl,type,
image:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > ( set @ TA ) ) ).
thf(coplanar_decl,type,
coplanar:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(c_decl,type,
c: real > a ).
thf(257,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC] :
( ( inj_on @ TC @ TB @ A @ ( top_top @ ( set @ TC ) ) )
=> ( ( inj_on @ TA @ TC @ B @ ( top_top @ ( set @ TA ) ) )
=> ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_inj__compose) ).
thf(1036,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC] :
( ( inj_on @ TC @ TB @ A @ ( top_top @ ( set @ TC ) ) )
=> ( ( inj_on @ TA @ TC @ B @ ( top_top @ ( set @ TA ) ) )
=> ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(175,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V1076094709vector @ TA )
& ( topolo503727757_space @ TA )
& ( real_V1076094709vector @ TB )
& ( topolo503727757_space @ TB ) )
=> ! [A: TA > TB,B: real > TA] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( path_pathfinish @ TB @ ( comp @ TA @ TB @ real @ A @ B ) )
= ( A @ ( path_pathfinish @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_pathfinish__linear__image) ).
thf(809,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V1076094709vector @ TA )
& ( topolo503727757_space @ TA )
& ( real_V1076094709vector @ TB )
& ( topolo503727757_space @ TB ) )
=> ! [A: TA > TB,B: real > TA] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( path_pathfinish @ TB @ ( comp @ TA @ TB @ real @ A @ B ) )
= ( A @ ( path_pathfinish @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( A @ B )
= C )
=> ( ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_inv__f__eq) ).
thf(629,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( A @ B )
= C )
=> ( ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( bij_betw @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TB ) ) )
=> ~ ! [C: TA] :
( ( B
= ( A @ C ) )
=> ~ ! [D: TA] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_bij__pointE) ).
thf(365,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( bij_betw @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TB ) ) )
=> ~ ! [C: TA] :
( ( B
= ( A @ C ) )
=> ~ ! [D: TA] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(279,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TB,B: TA > TE,C: TA,D: TD > TB,E: TA > TD,F: TB > TC] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp @ TE @ TC @ TA @ ( comp @ TB @ TC @ TE @ F @ A ) @ B @ C )
= ( comp @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ F @ D ) @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_type__copy__map__cong0) ).
thf(1105,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TB,B: TA > TE,C: TA,D: TD > TB,E: TA > TD,F: TB > TC] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp @ TE @ TC @ TA @ ( comp @ TB @ TC @ TE @ F @ A ) @ B @ C )
= ( comp @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ F @ D ) @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(206,axiom,
inj_on @ complex @ a @ ( poinca179318102eal_of @ a ) @ ( top_top @ ( set @ complex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_real__of__inj) ).
thf(893,plain,
inj_on @ complex @ a @ ( poinca179318102eal_of @ a ) @ ( top_top @ ( set @ complex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA,D: TA] :
( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ( ( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ( member @ TA @ D @ C ) )
=> ( ( A @ ( the_inv_into @ TB @ TA @ B @ A @ D ) )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_f__the__inv__into__f__bij__betw) ).
thf(518,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA,D: TA] :
( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ( ( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ( member @ TA @ D @ C ) )
=> ( ( A @ ( the_inv_into @ TB @ TA @ B @ A @ D ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TA )
& ( real_V55928688vector @ TB ) )
=> ! [A: TA > TB] :
( ( real_V1632203528linear @ TA @ TB @ A )
=> ( real_V1072672427axioms @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_bounded__linear_Oaxioms_I2_J) ).
thf(468,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TA )
& ( real_V55928688vector @ TB ) )
=> ! [A: TA > TB] :
( ( real_V1632203528linear @ TA @ TB @ A )
=> ( real_V1072672427axioms @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(163,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA > TB] :
( ( swap @ TA @ TB @ A @ B @ ( swap @ TA @ TB @ A @ B @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_swap__nilpotent) ).
thf(777,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA > TB] :
( ( swap @ TA @ TB @ A @ B @ ( swap @ TA @ TB @ A @ B @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(238,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: set @ TA] :
( ( image @ TC @ TB @ A @ ( image @ TA @ TC @ B @ C ) )
= ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_image__comp) ).
thf(977,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: set @ TA] :
( ( image @ TC @ TB @ A @ ( image @ TA @ TC @ B @ C ) )
= ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(248,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ( ( path_arc @ TA )
= ( ^ [A: real > TA] :
( ( path_simple_path @ TA @ A )
& ( ( path_pathfinish @ TA @ A )
!= ( path_pathstart @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_arc__simple__path) ).
thf(1005,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ( ( path_arc @ TA )
= ( ^ [A: real > TA] :
( ( path_simple_path @ TA @ A )
& ( ( path_pathfinish @ TA @ A )
!= ( path_pathstart @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_rev__image__eqI) ).
thf(597,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( C != D )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_inj__on__contraD) ).
thf(582,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( C != D )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(158,axiom,
! [TA: $tType,A: set @ TA] : ( inj_on @ TA @ TA @ ( id @ TA ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_inj__on__id) ).
thf(762,plain,
! [TA: $tType,A: set @ TA] : ( inj_on @ TA @ TA @ ( id @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(197,axiom,
! [TA: $tType] :
( ( inner_real_inner @ TA )
=> ! [A: TA] :
( ( ( inner_780170721_inner @ TA @ A @ A )
= ( zero_zero @ real ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_inner__eq__zero__iff) ).
thf(873,plain,
! [TA: $tType] :
( ( inner_real_inner @ TA )
=> ! [A: TA] :
( ( ( inner_780170721_inner @ TA @ A @ A )
= ( zero_zero @ real ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
( ! [C: TA] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_surjI) ).
thf(449,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
( ! [C: TA] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(259,axiom,
bij_betw @ complex @ a @ ( poinca179318102eal_of @ a ) @ ( top_top @ ( set @ complex ) ) @ ( top_top @ ( set @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_real__of__bij) ).
thf(1041,plain,
bij_betw @ complex @ a @ ( poinca179318102eal_of @ a ) @ ( top_top @ ( set @ complex ) ) @ ( top_top @ ( set @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(192,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB,E: TA] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_comp__eq__dest) ).
thf(861,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB,E: TA] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V1076094709vector @ TA )
& ( real_V1076094709vector @ TB ) )
=> ! [A: TB > TA] :
( ( real_Vector_linear @ TB @ TA @ A )
=> ( ( A @ ( zero_zero @ TB ) )
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_linear__0) ).
thf(500,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V1076094709vector @ TA )
& ( real_V1076094709vector @ TB ) )
=> ! [A: TB > TA] :
( ( real_Vector_linear @ TB @ TA @ A )
=> ( ( A @ ( zero_zero @ TB ) )
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(170,axiom,
real_Vector_linear @ a @ complex @ ( poinca1531302022lex_of @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_complex__of__linear) ).
thf(797,plain,
real_Vector_linear @ a @ complex @ ( poinca1531302022lex_of @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(227,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TB,B: TE > TD,C: TE,D: TC > TB,E: TA > TC,F: TA] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ F ) ) )
=> ( ( comp @ TD @ TB @ TE @ A @ B @ C )
= ( comp @ TC @ TB @ TA @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_comp__cong) ).
thf(945,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TB,B: TE > TD,C: TE,D: TC > TB,E: TA > TC,F: TA] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ F ) ) )
=> ( ( comp @ TD @ TB @ TE @ A @ B @ C )
= ( comp @ TC @ TB @ TA @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(221,axiom,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ! [A: TA > TA,B: TA > ( bounde2145540817linfun @ TA @ TA ),C: set @ TA] :
( ( poinca1076805489pen_R2 @ TA @ A @ B @ C )
=> ( real_V1632203528linear @ complex @ TA @ ( poinca179318102eal_of @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_c1__on__open__R2_Oreal__of__bounded__linear) ).
thf(930,plain,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ! [A: TA > TA,B: TA > ( bounde2145540817linfun @ TA @ TA ),C: set @ TA] :
( ( poinca1076805489pen_R2 @ TA @ A @ B @ C )
=> ( real_V1632203528linear @ complex @ TA @ ( poinca179318102eal_of @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(141,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA,C: TA] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_inj__def) ).
thf(709,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA,C: TA] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(201,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_comp__apply) ).
thf(883,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(884,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TC @ TB @ TA )
= ( ^ [A: TC > TB,B: TA > TC,C: TA] : ( A @ ( B @ C ) ) ) ),
inference(cnf,[status(esa)],[883]) ).
thf(885,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TC @ TB @ TA )
= ( ^ [A: TC > TB,B: TA > TC,C: TA] : ( A @ ( B @ C ) ) ) ),
inference(lifteq,[status(thm)],[884]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: ( TA > TA ) > TB > TB,B: TB > TA,C: TB,D: TA > TA,E: TB,F: TA] :
( ( iso_tu2011167877assist @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( iso_tu2011167877assist @ TA @ TB @ A @ B @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_iso__tuple__update__accessor__eq__assist__triv) ).
thf(288,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_top__conj_I2_J) ).
thf(301,plain,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB,B: set @ TA] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( coplanar @ TB @ ( image @ TA @ TB @ A @ B ) )
= ( coplanar @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_coplanar__linear__image__eq) ).
thf(389,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB,B: set @ TA] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( coplanar @ TB @ ( image @ TA @ TB @ A @ B ) )
= ( coplanar @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(264,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( comp @ TB @ TA @ TA @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A ) @ A )
= ( id @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_inv__o__cancel) ).
thf(1055,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( comp @ TB @ TA @ TA @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A ) @ A )
= ( id @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: TA] :
( ( inj_on @ TB @ TA @ A @ B )
=> ( ( member @ TA @ C @ ( image @ TB @ TA @ A @ B ) )
=> ( ( A @ ( the_inv_into @ TB @ TA @ B @ A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_f__the__inv__into__f) ).
thf(372,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: TA] :
( ( inj_on @ TB @ TA @ A @ B )
=> ( ( member @ TA @ C @ ( image @ TB @ TA @ A @ B ) )
=> ( ( A @ ( the_inv_into @ TB @ TA @ B @ A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(113,axiom,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: TA > TA] :
( ( real_V1632203528linear @ TA @ TA @ A )
=> ( ( inj_on @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) )
=> ( real_V1632203528linear @ TA @ TA @ ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_inj__linear__imp__inv__bounded__linear) ).
thf(619,plain,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: TA > TA] :
( ( real_V1632203528linear @ TA @ TA @ A )
=> ( ( inj_on @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) )
=> ( real_V1632203528linear @ TA @ TA @ ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(266,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V1076094709vector @ TA )
& ( topolo503727757_space @ TA )
& ( real_V1076094709vector @ TB )
& ( topolo503727757_space @ TB ) )
=> ! [A: TA > TB,B: real > TA] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( path_pathstart @ TB @ ( comp @ TA @ TB @ real @ A @ B ) )
= ( A @ ( path_pathstart @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_pathstart__linear__image__eq) ).
thf(1059,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V1076094709vector @ TA )
& ( topolo503727757_space @ TA )
& ( real_V1076094709vector @ TB )
& ( topolo503727757_space @ TB ) )
=> ! [A: TA > TB,B: real > TA] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( path_pathstart @ TB @ ( comp @ TA @ TB @ real @ A @ B ) )
= ( A @ ( path_pathstart @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(215,axiom,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ! [A: TA > TA,B: TA > ( bounde2145540817linfun @ TA @ TA ),C: set @ TA] :
( ( poinca1076805489pen_R2 @ TA @ A @ B @ C )
=> ( real_Vector_linear @ complex @ TA @ ( poinca179318102eal_of @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_c1__on__open__R2_Oreal__of__linear) ).
thf(917,plain,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ! [A: TA > TA,B: TA > ( bounde2145540817linfun @ TA @ TA ),C: set @ TA] :
( ( poinca1076805489pen_R2 @ TA @ A @ B @ C )
=> ( real_Vector_linear @ complex @ TA @ ( poinca179318102eal_of @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(137,axiom,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ( inner_real_inner @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Executable__Euclidean__Space_Oexecutable__euclidean__space___Inner__Product_Oreal__inner) ).
thf(702,plain,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ( inner_real_inner @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(155,axiom,
! [TA: $tType] :
( ( real_V1076094709vector @ TA )
=> ( real_Vector_linear @ TA @ TA @ ( id @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_module__hom__id) ).
thf(751,plain,
! [TA: $tType] :
( ( real_V1076094709vector @ TA )
=> ( real_Vector_linear @ TA @ TA @ ( id @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(189,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
= ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_Sup_OSUP__image) ).
thf(853,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
= ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ C ) )
= ( member @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_inj__image__mem__iff) ).
thf(416,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ C ) )
= ( member @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_top__conj_I1_J) ).
thf(289,plain,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(157,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_ball__imageD) ).
thf(756,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(167,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( real_V55928688vector @ TB ) )
=> ( ( real_Vector_linear @ TA @ TB )
= ( real_V1632203528linear @ TA @ TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_linear__conv__bounded__linear) ).
thf(789,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( real_V55928688vector @ TB ) )
=> ( ( real_Vector_linear @ TA @ TB )
= ( real_V1632203528linear @ TA @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( ( image @ TB @ TA @ ( linear_adjoint @ TA @ TB @ A ) @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_surj__adjoint__iff__inj) ).
thf(591,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( ( image @ TB @ TA @ ( linear_adjoint @ TA @ TB @ A ) @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(184,axiom,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ! [A: TA > TA,B: TA > ( bounde2145540817linfun @ TA @ TA ),C: set @ TA] :
( ( poinca1076805489pen_R2 @ TA @ A @ B @ C )
=> ( real_V1632203528linear @ TA @ complex @ ( poinca1531302022lex_of @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_c1__on__open__R2_Ocomplex__of__bounded__linear) ).
thf(834,plain,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ! [A: TA > TA,B: TA > ( bounde2145540817linfun @ TA @ TA ),C: set @ TA] :
( ( poinca1076805489pen_R2 @ TA @ A @ B @ C )
=> ( real_V1632203528linear @ TA @ complex @ ( poinca1531302022lex_of @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(224,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: set @ TD,C: TA > TC,D: set @ TA,E: TC > TB] :
( ( ( image @ TD @ TC @ A @ B )
= ( image @ TA @ TC @ C @ D ) )
=> ( ( image @ TD @ TB @ ( comp @ TC @ TB @ TD @ E @ A ) @ B )
= ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ E @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_image__eq__imp__comp) ).
thf(937,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: set @ TD,C: TA > TC,D: set @ TA,E: TC > TB] :
( ( ( image @ TD @ TC @ A @ B )
= ( image @ TA @ TC @ C @ D ) )
=> ( ( image @ TD @ TB @ ( comp @ TC @ TB @ TD @ E @ A ) @ B )
= ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ E @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(179,axiom,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: TA > TA,B: TA > TA] :
( ( real_Vector_linear @ TA @ TA @ A )
=> ( ( real_Vector_linear @ TA @ TA @ B )
=> ( ( ( comp @ TA @ TA @ TA @ A @ B )
= ( id @ TA ) )
= ( ( comp @ TA @ TA @ TA @ B @ A )
= ( id @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_linear__inverse__left) ).
thf(821,plain,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: TA > TA,B: TA > TA] :
( ( real_Vector_linear @ TA @ TA @ A )
=> ( ( real_Vector_linear @ TA @ TA @ B )
=> ( ( ( comp @ TA @ TA @ TA @ A @ B )
= ( id @ TA ) )
= ( ( comp @ TA @ TA @ TA @ B @ A )
= ( id @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(281,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: real > TA] :
( ( ( path_pathfinish @ TA @ A )
!= ( path_pathstart @ TA @ A ) )
=> ( ( path_simple_path @ TA @ A )
= ( path_arc @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_simple__path__eq__arc) ).
thf(1109,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: real > TA] :
( ( ( path_pathfinish @ TA @ A )
!= ( path_pathstart @ TA @ A ) )
=> ( ( path_simple_path @ TA @ A )
= ( path_arc @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TA )
& ( real_V55928688vector @ TB ) )
=> ( ( real_V1632203528linear @ TA @ TB )
= ( ^ [A: TA > TB] :
( ( real_Vector_linear @ TA @ TB @ A )
& ( real_V1072672427axioms @ TA @ TB @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_bounded__linear__def) ).
thf(321,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TA )
& ( real_V55928688vector @ TB ) )
=> ( ( real_V1632203528linear @ TA @ TB )
= ( ^ [A: TA > TB] :
( ( real_Vector_linear @ TA @ TB @ A )
& ( real_V1072672427axioms @ TA @ TB @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(250,axiom,
real_V1076094709vector @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Real__Vector__Spaces_Oreal__vector) ).
thf(1020,plain,
real_V1076094709vector @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
= ( ( inj_on @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
& ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_bij__def) ).
thf(348,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
= ( ( inj_on @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
& ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ? [C: TA] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_surjD) ).
thf(353,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ? [C: TA] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(234,axiom,
( ( path_pathfinish @ a @ c )
= ( path_pathstart @ a @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I2_J) ).
thf(966,plain,
( ( path_pathfinish @ a @ c )
= ( path_pathstart @ a @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(240,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TB > TC,C: TB > TC] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( comp @ TB @ TC @ TA @ B @ A )
= ( comp @ TB @ TC @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_fun_Omap__cong0) ).
thf(981,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TB > TC,C: TB > TC] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( comp @ TB @ TC @ TA @ B @ A )
= ( comp @ TB @ TC @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(199,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB,B: TA > TD,C: TA,D: TC > TB,E: TA > TC] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp @ TD @ TB @ TA @ A @ B @ C )
= ( comp @ TC @ TB @ TA @ D @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_comp__apply__eq) ).
thf(877,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB,B: TA > TD,C: TA,D: TC > TB,E: TA > TC] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp @ TD @ TB @ TA @ A @ B @ C )
= ( comp @ TC @ TB @ TA @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(6,axiom,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_top1I) ).
thf(293,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(162,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ ( swap @ TA @ TA @ A @ B @ ( id @ TA ) ) )
= ( swap @ TA @ TA @ A @ B @ ( id @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_inv__swap__id) ).
thf(774,plain,
! [TA: $tType,A: TA,B: TA] :
( ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ ( swap @ TA @ TA @ A @ B @ ( id @ TA ) ) )
= ( swap @ TA @ TA @ A @ B @ ( id @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(127,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( image @ TB @ TA @ ( the_inv_into @ TA @ TB @ B @ A ) @ ( image @ TA @ TB @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_the__inv__into__onto) ).
thf(660,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( image @ TB @ TA @ ( the_inv_into @ TA @ TB @ B @ A ) @ ( image @ TA @ TB @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType] :
( ( ( inner_real_inner @ TA )
& ( inner_real_inner @ TB ) )
=> ! [A: TB > TA,B: TA > TB] :
( ! [C: TB,D: TA] :
( ( inner_780170721_inner @ TA @ ( A @ C ) @ D )
= ( inner_780170721_inner @ TB @ C @ ( B @ D ) ) )
=> ( ( linear_adjoint @ TB @ TA @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_adjoint__unique) ).
thf(411,plain,
! [TA: $tType,TB: $tType] :
( ( ( inner_real_inner @ TA )
& ( inner_real_inner @ TB ) )
=> ! [A: TB > TA,B: TA > TB] :
( ! [C: TB,D: TA] :
( ( inner_780170721_inner @ TA @ ( A @ C ) @ D )
= ( inner_780170721_inner @ TB @ C @ ( B @ D ) ) )
=> ( ( linear_adjoint @ TB @ TA @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB,C: TB > TA] :
( ( ( image @ TB @ TA @ ( swap @ TB @ TA @ A @ B @ C ) @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( ( image @ TB @ TA @ C @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_surj__swap__iff) ).
thf(527,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB,C: TB > TA] :
( ( ( image @ TB @ TA @ ( swap @ TB @ TA @ A @ B @ C ) @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( ( image @ TB @ TA @ C @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(13,axiom,
! [TA: $tType] :
( ( inner_real_inner @ TA )
=> ! [A: TA,B: TA] :
( ( ! [C: TA] :
( ( inner_780170721_inner @ TA @ A @ C )
= ( inner_780170721_inner @ TA @ B @ C ) ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_vector__eq__rdot) ).
thf(312,plain,
! [TA: $tType] :
( ( inner_real_inner @ TA )
=> ! [A: TA,B: TA] :
( ( ! [C: TA] :
( ( inner_780170721_inner @ TA @ A @ C )
= ( inner_780170721_inner @ TA @ B @ C ) ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Otop) ).
thf(307,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
top @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Otop_5) ).
thf(292,plain,
top @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( image @ TA @ TB @ A @ B )
= ( image @ TA @ TB @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_inj__image__eq__iff) ).
thf(452,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( image @ TA @ TB @ A @ B )
= ( image @ TA @ TB @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB,D: TA] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ( ( member @ TA @ D @ B )
=> ( ( hilbert_inv_into @ TA @ TB @ B @ A @ ( A @ D ) )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_bij__betw__inv__into__left) ).
thf(380,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB,D: TA] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ( ( member @ TA @ D @ B )
=> ( ( hilbert_inv_into @ TA @ TB @ B @ A @ ( A @ D ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(89,axiom,
! [TA: $tType] :
( ( id @ TA )
= ( ^ [A: TA] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_id__apply) ).
thf(546,plain,
! [TA: $tType] :
( ( id @ TA )
= ( ^ [A: TA] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(218,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TB > TA] :
( ( bij_betw @ TC @ TB @ A @ ( top_top @ ( set @ TC ) ) @ ( top_top @ ( set @ TB ) ) )
=> ( ( bij_betw @ TB @ TA @ B @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
=> ( bij_betw @ TC @ TA @ ( comp @ TB @ TA @ TC @ B @ A ) @ ( top_top @ ( set @ TC ) ) @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_bij__comp) ).
thf(925,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TB > TA] :
( ( bij_betw @ TC @ TB @ A @ ( top_top @ ( set @ TC ) ) @ ( top_top @ ( set @ TB ) ) )
=> ( ( bij_betw @ TB @ TA @ B @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
=> ( bij_betw @ TC @ TA @ ( comp @ TB @ TA @ TC @ B @ A ) @ ( top_top @ ( set @ TC ) ) @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(269,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: set @ TC,C: set @ TB,D: TB > TA,E: set @ TA] :
( ( bij_betw @ TC @ TB @ A @ B @ C )
=> ( ( bij_betw @ TB @ TA @ D @ C @ E )
=> ( bij_betw @ TC @ TA @ ( comp @ TB @ TA @ TC @ D @ A ) @ B @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_bij__betw__trans) ).
thf(1067,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: set @ TC,C: set @ TB,D: TB > TA,E: set @ TA] :
( ( bij_betw @ TC @ TB @ A @ B @ C )
=> ( ( bij_betw @ TB @ TA @ D @ C @ E )
=> ( bij_betw @ TC @ TA @ ( comp @ TB @ TA @ TC @ D @ A ) @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(143,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ozero_3) ).
thf(714,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(171,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB,C: TA] :
( ( ( comp @ TB @ TA @ TA @ A @ B )
= ( id @ TA ) )
=> ( ( A @ ( B @ C ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_pointfree__idE) ).
thf(798,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB,C: TA] :
( ( ( comp @ TB @ TA @ TA @ A @ B )
= ( id @ TA ) )
=> ( ( A @ ( B @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TB] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( ( A @ C )
= D )
=> ( ( hilbert_inv_into @ TA @ TB @ B @ A @ D )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_inv__into__f__eq) ).
thf(512,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TB] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( ( A @ C )
= D )
=> ( ( hilbert_inv_into @ TA @ TB @ B @ A @ D )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(226,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( image @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ ( top_top @ ( set @ TA ) ) )
= ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_fun_Oset__map) ).
thf(942,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( image @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ ( top_top @ ( set @ TA ) ) )
= ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(20,axiom,
! [TA: $tType] :
( ( id @ TA )
= ( ^ [A: TA] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_id__def) ).
thf(332,plain,
! [TA: $tType] :
( ( id @ TA )
= ( ^ [A: TA] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(333,plain,
! [TA: $tType] :
( ( id @ TA )
= ( ^ [A: TA] : A ) ),
inference(cnf,[status(esa)],[332]) ).
thf(334,plain,
! [TA: $tType] :
( ( id @ TA )
= ( ^ [A: TA] : A ) ),
inference(lifteq,[status(thm)],[333]) ).
thf(251,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC] :
( ( inj_on @ TB @ TC @ A @ ( top_top @ ( set @ TB ) ) )
=> ( inj_on @ ( TA > TB ) @ ( TA > TC ) @ ( comp @ TB @ TC @ TA @ A ) @ ( top_top @ ( set @ ( TA > TB ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_fun_Oinj__map) ).
thf(1021,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC] :
( ( inj_on @ TB @ TC @ A @ ( top_top @ ( set @ TB ) ) )
=> ( inj_on @ ( TA > TB ) @ ( TA > TC ) @ ( comp @ TB @ TC @ TA @ A ) @ ( top_top @ ( set @ ( TA > TB ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(260,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( A != B )
=> ( ( A != C )
=> ( ( D != B )
=> ( ( D != C )
=> ( ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ A @ D @ ( id @ TA ) ) @ ( swap @ TA @ TA @ B @ C @ ( id @ TA ) ) )
= ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ B @ C @ ( id @ TA ) ) @ ( swap @ TA @ TA @ A @ D @ ( id @ TA ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_swap__id__independent) ).
thf(1042,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( A != B )
=> ( ( A != C )
=> ( ( D != B )
=> ( ( D != C )
=> ( ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ A @ D @ ( id @ TA ) ) @ ( swap @ TA @ TA @ B @ C @ ( id @ TA ) ) )
= ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ B @ C @ ( id @ TA ) ) @ ( swap @ TA @ TA @ A @ D @ ( id @ TA ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_bij__is__surj) ).
thf(392,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(52,axiom,
! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
( ( A @ ( image @ TA @ TA @ ( id @ TA ) @ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_Sup_OSUP__id__eq) ).
thf(424,plain,
! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
( ( A @ ( image @ TA @ TA @ ( id @ TA ) @ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(134,axiom,
! [TA: $tType] :
( ( inner_real_inner @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ( inner_780170721_inner @ TA @ A @ A )
= ( inner_780170721_inner @ TA @ A @ B ) )
& ( ( inner_780170721_inner @ TA @ B @ B )
= ( inner_780170721_inner @ TA @ A @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_vector__eq) ).
thf(693,plain,
! [TA: $tType] :
( ( inner_real_inner @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ( inner_780170721_inner @ TA @ A @ A )
= ( inner_780170721_inner @ TA @ A @ B ) )
& ( ( inner_780170721_inner @ TA @ B @ B )
= ( inner_780170721_inner @ TA @ A @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(54,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_UNIV__eq__I) ).
thf(429,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(231,axiom,
! [TA: $tType] :
( ( inner_real_inner @ TA )
=> ! [A: TA] :
( ( inner_780170721_inner @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_inner__zero__right) ).
thf(957,plain,
! [TA: $tType] :
( ( inner_real_inner @ TA )
=> ! [A: TA] :
( ( inner_780170721_inner @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(207,axiom,
path_simple_path @ a @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I1_J) ).
thf(894,plain,
path_simple_path @ a @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(255,axiom,
real_Vector_linear @ complex @ a @ ( poinca179318102eal_of @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_real__of__linear) ).
thf(1032,plain,
real_Vector_linear @ complex @ a @ ( poinca179318102eal_of @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ( inj_on @ TA @ TB @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_bij__betw__imp__inj__on) ).
thf(361,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ( inj_on @ TA @ TB @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: set @ TA] :
( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ! [E: TB] :
( ( member @ TB @ E @ A )
=> ( ( ( B @ D )
= ( B @ E ) )
= ( D = E ) ) ) )
=> ( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ( member @ TA @ ( B @ D ) @ C ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ C )
=> ? [E: TB] :
( ( member @ TB @ E @ A )
& ( D
= ( B @ E ) ) ) )
=> ( bij_betw @ TB @ TA @ B @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_bij__betwI_H) ).
thf(435,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: set @ TA] :
( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ! [E: TB] :
( ( member @ TB @ E @ A )
=> ( ( ( B @ D )
= ( B @ E ) )
= ( D = E ) ) ) )
=> ( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ( member @ TA @ ( B @ D ) @ C ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ C )
=> ? [E: TB] :
( ( member @ TB @ E @ A )
& ( D
= ( B @ E ) ) ) )
=> ( bij_betw @ TB @ TA @ B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(19,axiom,
! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
( ( A @ ( image @ TA @ TA @ ( id @ TA ) @ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_Inf_OINF__id__eq) ).
thf(329,plain,
! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
( ( A @ ( image @ TA @ TA @ ( id @ TA ) @ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(182,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ( ( path_pathstart @ TA )
= ( ^ [A: real > TA] : ( A @ ( zero_zero @ real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_pathstart__def) ).
thf(830,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ( ( path_pathstart @ TA )
= ( ^ [A: real > TA] : ( A @ ( zero_zero @ real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB,B: TB,C: TA] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( inner_780170721_inner @ TA @ ( linear_adjoint @ TA @ TB @ A @ B ) @ C )
= ( inner_780170721_inner @ TB @ B @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_adjoint__clauses_I2_J) ).
thf(461,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB,B: TB,C: TA] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( inner_780170721_inner @ TA @ ( linear_adjoint @ TA @ TB @ A @ B ) @ C )
= ( inner_780170721_inner @ TB @ B @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(273,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > TA,C: TA > TB] :
( ( ( comp @ TA @ TB @ TB @ A @ B )
= ( id @ TB ) )
=> ( ( ( comp @ TB @ TA @ TA @ B @ C )
= ( id @ TA ) )
=> ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_left__right__inverse__eq) ).
thf(1079,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > TA,C: TA > TB] :
( ( ( comp @ TA @ TB @ TB @ A @ B )
= ( id @ TB ) )
=> ( ( ( comp @ TB @ TA @ TA @ B @ C )
= ( id @ TA ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(132,axiom,
! [TA: $tType,TB: $tType] :
( ( bij_betw @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA,C: set @ TB] :
? [D: TB > TA] :
( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( member @ TB @ ( A @ E ) @ C )
& ( ( D @ ( A @ E ) )
= E ) ) )
& ! [E: TB] :
( ( member @ TB @ E @ C )
=> ( ( member @ TA @ ( D @ E ) @ B )
& ( ( A @ ( D @ E ) )
= E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_bij__betw__iff__bijections) ).
thf(682,plain,
! [TA: $tType,TB: $tType] :
( ( bij_betw @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA,C: set @ TB] :
? [D: TB > TA] :
( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( member @ TB @ ( A @ E ) @ C )
& ( ( D @ ( A @ E ) )
= E ) ) )
& ! [E: TB] :
( ( member @ TB @ E @ C )
=> ( ( member @ TA @ ( D @ E ) @ B )
& ( ( A @ ( D @ E ) )
= E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA,D: TA > TB] :
( ( A != B )
=> ( ( A != C )
=> ( ( swap @ TA @ TB @ B @ C @ D @ A )
= ( D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_swap__apply_I3_J) ).
thf(566,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA,D: TA > TB] :
( ( A != B )
=> ( ( A != C )
=> ( ( swap @ TA @ TB @ B @ C @ D @ A )
= ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(71,axiom,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ( real_V1076094709vector @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Executable__Euclidean__Space_Oexecutable__euclidean__space___Real__Vector__Spaces_Oreal__vector) ).
thf(484,plain,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ( real_V1076094709vector @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(17,axiom,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: TA > TA] :
( ( real_Vector_linear @ TA @ TA @ A )
=> ( ( inj_on @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_linear__inj__imp__surj) ).
thf(324,plain,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: TA > TA] :
( ( real_Vector_linear @ TA @ TA @ A )
=> ( ( inj_on @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(237,axiom,
! [A: complex,B: complex] :
( ( path_pathfinish @ complex @ ( path_rectpath @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_pathfinish__rectpath) ).
thf(974,plain,
! [A: complex,B: complex] :
( ( path_pathfinish @ complex @ ( path_rectpath @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TB] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ( A @ C )
= D )
=> ( ( member @ TA @ C @ B )
=> ( ( the_inv_into @ TA @ TB @ B @ A @ D )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_the__inv__into__f__eq) ).
thf(578,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TB] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ( A @ C )
= D )
=> ( ( member @ TA @ C @ B )
=> ( ( the_inv_into @ TA @ TB @ B @ A @ D )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(138,axiom,
topolo503727757_space @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Topological__Spaces_Otopological__space_1) ).
thf(704,plain,
topolo503727757_space @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(200,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: real > TA] :
( ( path_arc @ TA @ A )
=> ( ( path_pathfinish @ TA @ A )
!= ( path_pathstart @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_arc__distinct__ends) ).
thf(880,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: real > TA] :
( ( path_arc @ TA @ A )
=> ( ( path_pathfinish @ TA @ A )
!= ( path_pathstart @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(881,plain,
! [TA: $tType,A: real > TA] :
( ~ ( topolo503727757_space @ TA )
| ~ ( path_arc @ TA @ A )
| ( ( path_pathfinish @ TA @ A )
!= ( path_pathstart @ TA @ A ) ) ),
inference(cnf,[status(esa)],[880]) ).
thf(882,plain,
! [TA: $tType,A: real > TA] :
( ( ( path_pathstart @ TA @ A )
!= ( path_pathfinish @ TA @ A ) )
| ~ ( topolo503727757_space @ TA )
| ~ ( path_arc @ TA @ A ) ),
inference(lifteq,[status(thm)],[881]) ).
thf(1119,plain,
! [TA: $tType,A: real > TA] :
( ( ( path_pathstart @ TA @ A )
!= ( path_pathfinish @ TA @ A ) )
| ~ $true
| ~ ( path_arc @ TA @ A )
| ( ( topolo503727757_space @ int )
!= ( topolo503727757_space @ TA ) ) ),
inference(paramod_ordered,[status(thm)],[704,882]) ).
thf(1120,plain,
! [TA: $tType,A: real > TA] :
( ( ( path_pathstart @ TA @ A )
!= ( path_pathfinish @ TA @ A ) )
| ~ ( path_arc @ TA @ A )
| ( ( topolo503727757_space @ int )
!= ( topolo503727757_space @ TA ) ) ),
inference(simp,[status(thm)],[1119]) ).
thf(1121,plain,
! [A: real > int] :
( ( ( path_pathstart @ int @ A )
!= ( path_pathfinish @ int @ A ) )
| ~ ( path_arc @ int @ A ) ),
inference(pattern_uni,[status(thm)],[1120:[bind_type(TA,$thf( int ))]]) ).
thf(268,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ A @ B @ ( id @ TA ) ) @ ( swap @ TA @ TA @ A @ B @ ( id @ TA ) ) )
= ( id @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_swap__id__idempotent) ).
thf(1064,plain,
! [TA: $tType,A: TA,B: TA] :
( ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ A @ B @ ( id @ TA ) ) @ ( swap @ TA @ TA @ A @ B @ ( id @ TA ) ) )
= ( id @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(148,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ ( A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_inv__f__f) ).
thf(725,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ ( A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(28,axiom,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ( real_V55928688vector @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Executable__Euclidean__Space_Oexecutable__euclidean__space___Real__Vector__Spaces_Oreal__normed__vector) ).
thf(356,plain,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ( real_V55928688vector @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(195,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( comp @ TB @ TB @ TA @ ( id @ TB ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_id__comp) ).
thf(869,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( comp @ TB @ TB @ TA @ ( id @ TB ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(165,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] :
? [C: TB] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_surj__def) ).
thf(783,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] :
? [C: TB] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(242,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( comp @ TB @ TB @ TA @ ( id @ TB ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_fun_Omap__id) ).
thf(989,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( comp @ TB @ TB @ TA @ ( id @ TB ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(124,axiom,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: TA > TA] :
( ( real_Vector_linear @ TA @ TA @ A )
=> ( ( ( image @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( inj_on @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_linear__surj__imp__inj) ).
thf(650,plain,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: TA > TA] :
( ( real_Vector_linear @ TA @ TA @ A )
=> ( ( ( image @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( inj_on @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(228,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: set @ TC,C: set @ TB,D: TB > TA,E: set @ TA] :
( ( bij_betw @ TC @ TB @ A @ B @ C )
=> ( ( bij_betw @ TB @ TA @ D @ C @ E )
= ( bij_betw @ TC @ TA @ ( comp @ TB @ TA @ TC @ D @ A ) @ B @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_bij__betw__comp__iff) ).
thf(948,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: set @ TC,C: set @ TB,D: TB > TA,E: set @ TA] :
( ( bij_betw @ TC @ TB @ A @ B @ C )
=> ( ( bij_betw @ TB @ TA @ D @ C @ E )
= ( bij_betw @ TC @ TA @ ( comp @ TB @ TA @ TC @ D @ A ) @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(239,axiom,
bij_betw @ a @ complex @ ( poinca1531302022lex_of @ a ) @ ( top_top @ ( set @ a ) ) @ ( top_top @ ( set @ complex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_complex__of__bij) ).
thf(980,plain,
bij_betw @ a @ complex @ ( poinca1531302022lex_of @ a ) @ ( top_top @ ( set @ a ) ) @ ( top_top @ ( set @ complex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_top__apply) ).
thf(403,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(274,axiom,
! [TA: $tType] :
( ( inner_real_inner @ TA )
=> ! [A: TA] :
( ( ! [B: TA] :
( ( inner_780170721_inner @ TA @ A @ B )
= ( zero_zero @ real ) ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_all__zero__iff) ).
thf(1082,plain,
! [TA: $tType] :
( ( inner_real_inner @ TA )
=> ! [A: TA] :
( ( ! [B: TA] :
( ( inner_780170721_inner @ TA @ A @ B )
= ( zero_zero @ real ) ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ~ ! [C: TA] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_surjE) ).
thf(339,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ~ ! [C: TA] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(156,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V1076094709vector @ TA )
& ( real_V1076094709vector @ TB ) )
=> ! [A: TA > TB] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] :
( ( ( A @ B )
= ( zero_zero @ TB ) )
=> ( B
= ( zero_zero @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_linear__inj__iff__eq__0) ).
thf(753,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V1076094709vector @ TA )
& ( real_V1076094709vector @ TB ) )
=> ! [A: TA > TB] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] :
( ( ( A @ B )
= ( zero_zero @ TB ) )
=> ( B
= ( zero_zero @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( inj_on @ TB @ TA @ ( the_inv_into @ TA @ TB @ B @ A ) @ ( image @ TA @ TB @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_inj__on__the__inv__into) ).
thf(642,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( inj_on @ TB @ TA @ ( the_inv_into @ TA @ TB @ B @ A ) @ ( image @ TA @ TB @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(131,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > TA] :
( ! [C: TB] :
( ( A @ ( B @ C ) )
= C )
=> ( ! [C: TA] :
( ( B @ ( A @ C ) )
= C )
=> ( ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_inv__equality) ).
thf(679,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > TA] :
( ! [C: TB] :
( ( A @ ( B @ C ) )
= C )
=> ( ! [C: TA] :
( ( B @ ( A @ C ) )
= C )
=> ( ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(271,axiom,
euclid925273238_space @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Complex_Ocomplex___Euclidean__Space_Oeuclidean__space_10) ).
thf(1075,plain,
euclid925273238_space @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(69,axiom,
! [TA: $tType] : ( top @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Otop_2) ).
thf(476,plain,
! [TA: $tType] : ( top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(186,axiom,
! [TA: $tType] :
( ( inner_real_inner @ TA )
=> ! [A: TA] :
( ( inner_780170721_inner @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_inner__zero__left) ).
thf(837,plain,
! [TA: $tType] :
( ( inner_real_inner @ TA )
=> ! [A: TA] :
( ( inner_780170721_inner @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(284,axiom,
! [TA: $tType,TB: $tType] :
( ( comp @ TB @ TB @ TA @ ( id @ TB ) )
= ( id @ ( TA > TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_fun_Omap__id0) ).
thf(1114,plain,
! [TA: $tType,TB: $tType] :
( ( comp @ TB @ TB @ TA @ ( id @ TB ) )
= ( id @ ( TA > TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(122,axiom,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: TA > TA] :
( ( real_Vector_linear @ TA @ TA @ A )
=> ( ( inj_on @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) )
=> ( real_Vector_linear @ TA @ TA @ ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_inj__linear__imp__inv__linear) ).
thf(647,plain,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: TA > TA] :
( ( real_Vector_linear @ TA @ TA @ A )
=> ( ( inj_on @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) )
=> ( real_Vector_linear @ TA @ TA @ ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(153,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on @ TA @ TB @ B @ A )
= ( inj_on @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_inj__on__cong) ).
thf(738,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on @ TA @ TB @ B @ A )
= ( inj_on @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(213,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > TA] :
( ( ( comp @ TA @ TB @ TB @ A @ B )
= ( id @ TB ) )
=> ( ( ( comp @ TB @ TA @ TA @ B @ A )
= ( id @ TA ) )
=> ( bij_betw @ TB @ TA @ B @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_o__bij) ).
thf(911,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > TA] :
( ( ( comp @ TA @ TB @ TB @ A @ B )
= ( id @ TB ) )
=> ( ( ( comp @ TB @ TA @ TA @ B @ A )
= ( id @ TA ) )
=> ( bij_betw @ TB @ TA @ B @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(246,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA,C: TA] :
( ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
=> ( bij_betw @ TB @ TA @ ( comp @ TA @ TA @ TB @ ( swap @ TA @ TA @ B @ C @ ( id @ TA ) ) @ A ) @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_bij__swap__compose__bij) ).
thf(1002,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA,C: TA] :
( ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
=> ( bij_betw @ TB @ TA @ ( comp @ TA @ TA @ TB @ ( swap @ TA @ TA @ B @ C @ ( id @ TA ) ) @ A ) @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA,D: TA] :
( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ C )
=> ( ( A @ ( hilbert_inv_into @ TB @ TA @ B @ A @ D ) )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_bij__betw__inv__into__right) ).
thf(569,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA,D: TA] :
( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ C )
=> ( ( A @ ( hilbert_inv_into @ TB @ TA @ B @ A @ D ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ A @ ( image @ TA @ TB @ ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_image__f__inv__f) ).
thf(503,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ A @ ( image @ TA @ TB @ ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TA )
& ( real_V55928688vector @ TB ) )
=> ! [A: TA > TB] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( real_V1072672427axioms @ TA @ TB @ A )
=> ( real_V1632203528linear @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_bounded__linear_Ointro) ).
thf(605,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TA )
& ( real_V55928688vector @ TB ) )
=> ! [A: TA > TB] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( real_V1072672427axioms @ TA @ TB @ A )
=> ( real_V1632203528linear @ TA @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(168,axiom,
( ( comp @ complex @ a @ a @ ( poinca179318102eal_of @ a ) @ ( poinca1531302022lex_of @ a ) )
= ( id @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_real__of__complex__of) ).
thf(792,plain,
( ( comp @ complex @ a @ a @ ( poinca179318102eal_of @ a ) @ ( poinca1531302022lex_of @ a ) )
= ( id @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ! [B: TB,C: TB] :
( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) )
=> ( ! [B: TA] :
? [C: TB] :
( B
= ( A @ C ) )
=> ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_bijI_H) ).
thf(633,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ! [B: TB,C: TB] :
( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) )
=> ( ! [B: TA] :
? [C: TB] :
( B
= ( A @ C ) )
=> ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ( ( image @ TB @ TA @ A @ B )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_bij__betw__imp__surj__on) ).
thf(541,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ( ( image @ TB @ TA @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(42,axiom,
! [TA: $tType] :
( ( inner_real_inner @ TA )
=> ! [A: TA,B: real] :
( ( A
!= ( zero_zero @ TA ) )
=> ~ ! [C: TA] :
( ( inner_780170721_inner @ TA @ A @ C )
!= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_hyperplane__eq__Ex) ).
thf(398,plain,
! [TA: $tType] :
( ( inner_real_inner @ TA )
=> ! [A: TA,B: real] :
( ( A
!= ( zero_zero @ TA ) )
=> ~ ! [C: TA] :
( ( inner_780170721_inner @ TA @ A @ C )
!= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(253,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: real > TA] :
( ( path_simple_path @ TA @ A )
=> ( ( ( path_pathfinish @ TA @ A )
!= ( path_pathstart @ TA @ A ) )
=> ( path_arc @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_simple__path__imp__arc) ).
thf(1026,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: real > TA] :
( ( path_simple_path @ TA @ A )
=> ( ( ( path_pathfinish @ TA @ A )
!= ( path_pathstart @ TA @ A ) )
=> ( path_arc @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ! [B: TA,C: TA] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_injI) ).
thf(530,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ! [B: TA,C: TA] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(169,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA,C: TA,D: TA > TB] :
( ( comp @ TB @ TC @ TA @ A @ ( swap @ TA @ TB @ B @ C @ D ) )
= ( swap @ TA @ TC @ B @ C @ ( comp @ TB @ TC @ TA @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_comp__swap) ).
thf(794,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA,C: TA,D: TA > TB] :
( ( comp @ TB @ TC @ TA @ A @ ( swap @ TA @ TB @ B @ C @ D ) )
= ( swap @ TA @ TC @ B @ C @ ( comp @ TB @ TC @ TA @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(145,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ! [D: TB] :
( ( member @ TB @ D @ B )
=> ( member @ TA @ ( A @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_bij__betwE) ).
thf(718,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ! [D: TB] :
( ( member @ TB @ D @ B )
=> ( member @ TA @ ( A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(204,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
( ( ( comp @ TC @ TB @ TA @ A @ B )
= ( comp @ TB @ TB @ TA @ ( id @ TB ) @ C ) )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_comp__eq__id__dest) ).
thf(888,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
( ( ( comp @ TC @ TB @ TA @ A @ B )
= ( comp @ TB @ TB @ TA @ ( id @ TB ) @ C ) )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: ( TA > TA ) > TB > TB,B: TB > TA,C: TB,D: TA > TA,E: TB,F: TA] :
( ( iso_tu2011167877assist @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ( B @ C )
= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_update__accessor__accessor__eqE) ).
thf(298,plain,
! [TA: $tType,TB: $tType,A: ( TA > TA ) > TB > TB,B: TB > TA,C: TB,D: TA > TA,E: TB,F: TA] :
( ( iso_tu2011167877assist @ TA @ TB @ A @ B @ C @ D @ E @ F )
=> ( ( B @ C )
= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(140,axiom,
topolo503727757_space @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Otopological__space_4) ).
thf(708,plain,
topolo503727757_space @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(1122,plain,
! [TA: $tType,A: real > TA] :
( ( ( path_pathstart @ TA @ A )
!= ( path_pathfinish @ TA @ A ) )
| ~ $true
| ~ ( path_arc @ TA @ A )
| ( ( topolo503727757_space @ $o )
!= ( topolo503727757_space @ TA ) ) ),
inference(paramod_ordered,[status(thm)],[708,882]) ).
thf(1123,plain,
! [TA: $tType,A: real > TA] :
( ( ( path_pathstart @ TA @ A )
!= ( path_pathfinish @ TA @ A ) )
| ~ ( path_arc @ TA @ A )
| ( ( topolo503727757_space @ $o )
!= ( topolo503727757_space @ TA ) ) ),
inference(simp,[status(thm)],[1122]) ).
thf(1124,plain,
! [A: real > $o] :
( ( ( path_pathstart @ $o @ A )
!= ( path_pathfinish @ $o @ A ) )
| ~ ( path_arc @ $o @ A ) ),
inference(pattern_uni,[status(thm)],[1123:[bind_type(TA,$thf( $o ))]]) ).
thf(1135,plain,
! [A: real > $o] :
( ~ ( path_arc @ $o @ A )
| ~ ( path_pathstart @ $o @ A )
| ~ ( path_pathfinish @ $o @ A ) ),
inference(bool_ext,[status(thm)],[1124]) ).
thf(180,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: set @ TA,C: TC > TB] :
( ( inj_on @ TA @ TC @ A @ B )
=> ( ( inj_on @ TC @ TB @ C @ ( image @ TA @ TC @ A @ B ) )
=> ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_comp__inj__on) ).
thf(824,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: set @ TA,C: TC > TB] :
( ( inj_on @ TA @ TC @ A @ B )
=> ( ( inj_on @ TC @ TB @ C @ ( image @ TA @ TC @ A @ B ) )
=> ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(190,axiom,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ! [A: TA > TA,B: TA > ( bounde2145540817linfun @ TA @ TA ),C: set @ TA] :
( ( poinca1076805489pen_R2 @ TA @ A @ B @ C )
=> ( real_Vector_linear @ TA @ complex @ ( poinca1531302022lex_of @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_c1__on__open__R2_Ocomplex__of__linear) ).
thf(856,plain,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ! [A: TA > TA,B: TA > ( bounde2145540817linfun @ TA @ TA ),C: set @ TA] :
( ( poinca1076805489pen_R2 @ TA @ A @ B @ C )
=> ( real_Vector_linear @ TA @ complex @ ( poinca1531302022lex_of @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ( bij_betw @ TB @ TA @ ( the_inv_into @ TA @ TB @ B @ A ) @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_bij__betw__the__inv__into) ).
thf(601,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ( bij_betw @ TB @ TA @ ( the_inv_into @ TA @ TB @ B @ A ) @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(34,axiom,
! [TA: $tType] :
( ( image @ TA @ TA @ ( id @ TA ) )
= ( id @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_image__id) ).
thf(375,plain,
! [TA: $tType] :
( ( image @ TA @ TA @ ( id @ TA ) )
= ( id @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(151,axiom,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ( euclid925273238_space @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Executable__Euclidean__Space_Oexecutable__euclidean__space___Euclidean__Space_Oeuclidean__space) ).
thf(733,plain,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ( euclid925273238_space @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(210,axiom,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ! [A: TA > TA,B: TA > ( bounde2145540817linfun @ TA @ TA ),C: set @ TA] :
( ( poinca1076805489pen_R2 @ TA @ A @ B @ C )
=> ( ( comp @ complex @ TA @ TA @ ( poinca179318102eal_of @ TA ) @ ( poinca1531302022lex_of @ TA ) )
= ( id @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_c1__on__open__R2_Oreal__of__complex__of) ).
thf(904,plain,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ! [A: TA > TA,B: TA > ( bounde2145540817linfun @ TA @ TA ),C: set @ TA] :
( ( poinca1076805489pen_R2 @ TA @ A @ B @ C )
=> ( ( comp @ complex @ TA @ TA @ ( poinca179318102eal_of @ TA ) @ ( poinca1531302022lex_of @ TA ) )
= ( id @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(188,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TA > TB,C: TB > TC,D: TB > TC] :
( ! [E: TB,F: TB] :
( ( member @ TB @ E @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( member @ TB @ F @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( C @ E )
= ( D @ F ) )
=> ( E = F ) ) ) )
=> ( ( ( comp @ TB @ TC @ TA @ C @ A )
= ( comp @ TB @ TC @ TA @ D @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_fun_Oinj__map__strong) ).
thf(843,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TA > TB,C: TB > TC,D: TB > TC] :
( ! [E: TB,F: TB] :
( ( member @ TB @ E @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( member @ TB @ F @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( C @ E )
= ( D @ F ) )
=> ( E = F ) ) ) )
=> ( ( ( comp @ TB @ TC @ TA @ C @ A )
= ( comp @ TB @ TC @ TA @ D @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(1,conjecture,
( ( path_pathfinish @ complex @ ( comp @ a @ complex @ real @ ( poinca1531302022lex_of @ a ) @ c ) )
= ( path_pathstart @ complex @ ( comp @ a @ complex @ real @ ( poinca1531302022lex_of @ a ) @ c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( path_pathfinish @ complex @ ( comp @ a @ complex @ real @ ( poinca1531302022lex_of @ a ) @ c ) )
!= ( path_pathstart @ complex @ ( comp @ a @ complex @ real @ ( poinca1531302022lex_of @ a ) @ c ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(286,plain,
( ( path_pathfinish @ complex @ ( comp @ a @ complex @ real @ ( poinca1531302022lex_of @ a ) @ c ) )
!= ( path_pathstart @ complex @ ( comp @ a @ complex @ real @ ( poinca1531302022lex_of @ a ) @ c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(181,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TC,B: TE > TD,C: TB > TC,D: TE > TB,E: TA > TE,F: TA > TB] :
( ( ( comp @ TD @ TC @ TE @ A @ B )
= ( comp @ TB @ TC @ TE @ C @ D ) )
=> ( ( ( comp @ TE @ TB @ TA @ D @ E )
= F )
=> ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TE @ TD @ TA @ B @ E ) )
= ( comp @ TB @ TC @ TA @ C @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_rewriteL__comp__comp2) ).
thf(826,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TC,B: TE > TD,C: TB > TC,D: TE > TB,E: TA > TE,F: TA > TB] :
( ( ( comp @ TD @ TC @ TE @ A @ B )
= ( comp @ TB @ TC @ TE @ C @ D ) )
=> ( ( ( comp @ TE @ TB @ TA @ D @ E )
= F )
=> ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TE @ TD @ TA @ B @ E ) )
= ( comp @ TB @ TC @ TA @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(223,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( real_V1076094709vector @ TA )
& ( real_V1076094709vector @ TB )
& ( real_V1076094709vector @ TC ) )
=> ! [A: TA > TB,B: TB > TC] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( real_Vector_linear @ TB @ TC @ B )
=> ( real_Vector_linear @ TA @ TC @ ( comp @ TB @ TC @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_linear__compose) ).
thf(935,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( real_V1076094709vector @ TA )
& ( real_V1076094709vector @ TB )
& ( real_V1076094709vector @ TC ) )
=> ! [A: TA > TB,B: TB > TC] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( real_Vector_linear @ TB @ TC @ B )
=> ( real_Vector_linear @ TA @ TC @ ( comp @ TB @ TC @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(936,plain,
! [TA: $tType,TB: $tType,TC: $tType,B: TB > TA,A: TC > TB] :
( ~ ( real_V1076094709vector @ TC )
| ~ ( real_V1076094709vector @ TB )
| ~ ( real_V1076094709vector @ TA )
| ~ ( real_Vector_linear @ TC @ TB @ A )
| ~ ( real_Vector_linear @ TB @ TA @ B )
| ( real_Vector_linear @ TC @ TA @ ( comp @ TB @ TA @ TC @ B @ A ) ) ),
inference(cnf,[status(esa)],[935]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_inj__on__eq__iff) ).
thf(572,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TA )
& ( real_V55928688vector @ TB ) )
=> ! [A: TA > TB] :
( ( real_V1632203528linear @ TA @ TB @ A )
=> ( real_Vector_linear @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_bounded__linear_Olinear) ).
thf(611,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TA )
& ( real_V55928688vector @ TB ) )
=> ! [A: TA > TB] :
( ( real_V1632203528linear @ TA @ TB @ A )
=> ( real_Vector_linear @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(265,axiom,
topolo503727757_space @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Topological__Spaces_Otopological__space_6) ).
thf(1058,plain,
topolo503727757_space @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( real_V55928688vector @ TB ) )
=> ! [A: set @ TA,B: TA > TB] :
( ( coplanar @ TA @ A )
=> ( ( real_Vector_linear @ TA @ TB @ B )
=> ( coplanar @ TB @ ( image @ TA @ TB @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_coplanar__linear__image) ).
thf(466,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( real_V55928688vector @ TB ) )
=> ! [A: set @ TA,B: TA > TB] :
( ( coplanar @ TA @ A )
=> ( ( real_Vector_linear @ TA @ TB @ B )
=> ( coplanar @ TB @ ( image @ TA @ TB @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(21,axiom,
! [TA: $tType,A: TA,B: TA > TA,C: TA] :
( ( A
= ( B @ C ) )
=> ( iso_tu2011167877assist @ TA @ TA @ ( id @ ( TA > TA ) ) @ ( id @ TA ) @ C @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_iso__tuple__update__accessor__eq__assist__idI) ).
thf(335,plain,
! [TA: $tType,A: TA,B: TA > TA,C: TA] :
( ( A
= ( B @ C ) )
=> ( iso_tu2011167877assist @ TA @ TA @ ( id @ ( TA > TA ) ) @ ( id @ TA ) @ C @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(216,axiom,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TB ) )
=> ! [A: TA > TB,B: real > TA] :
( ( path_pathstart @ TB @ ( comp @ TA @ TB @ real @ A @ B ) )
= ( A @ ( path_pathstart @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_pathstart__compose) ).
thf(919,plain,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TB ) )
=> ! [A: TA > TB,B: real > TA] :
( ( path_pathstart @ TB @ ( comp @ TA @ TB @ real @ A @ B ) )
= ( A @ ( path_pathstart @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(173,axiom,
! [TA: $tType,A: TA,B: TA,C: TA] :
( ( A != B )
=> ( ( A != C )
=> ( ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ A @ C @ ( id @ TA ) ) @ ( swap @ TA @ TA @ B @ C @ ( id @ TA ) ) )
= ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ B @ C @ ( id @ TA ) ) @ ( swap @ TA @ TA @ A @ B @ ( id @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_swap__id__common_H) ).
thf(804,plain,
! [TA: $tType,A: TA,B: TA,C: TA] :
( ( A != B )
=> ( ( A != C )
=> ( ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ A @ C @ ( id @ TA ) ) @ ( swap @ TA @ TA @ B @ C @ ( id @ TA ) ) )
= ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ B @ C @ ( id @ TA ) ) @ ( swap @ TA @ TA @ A @ B @ ( id @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(159,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( inj_on @ TB @ TA @ A @ B )
=> ( ( ( image @ TB @ TA @ A @ B )
= C )
=> ( bij_betw @ TB @ TA @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_bij__betw__imageI) ).
thf(764,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( inj_on @ TB @ TA @ A @ B )
=> ( ( ( image @ TB @ TA @ A @ B )
= C )
=> ( bij_betw @ TB @ TA @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_image__iff) ).
thf(406,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(285,axiom,
execut510477386_space @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
thf(1117,plain,
execut510477386_space @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(50,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(419,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(262,axiom,
! [A: real > a] :
( ( inj_on @ a @ complex @ ( poinca1531302022lex_of @ a ) @ ( top_top @ ( set @ a ) ) )
=> ( ( path_simple_path @ complex @ ( comp @ a @ complex @ real @ ( poinca1531302022lex_of @ a ) @ A ) )
= ( path_simple_path @ a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19__092_060open_062_092_060And_062g_O_Ainj_Acomplex__of_A_092_060Longrightarrow_062_Asimple__path_A_Icomplex__of_A_092_060circ_062_Ag_J_A_061_Asimple__path_Ag_092_060close_062) ).
thf(1048,plain,
! [A: real > a] :
( ( inj_on @ a @ complex @ ( poinca1531302022lex_of @ a ) @ ( top_top @ ( set @ a ) ) )
=> ( ( path_simple_path @ complex @ ( comp @ a @ complex @ real @ ( poinca1531302022lex_of @ a ) @ A ) )
= ( path_simple_path @ a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(244,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TA > TB] :
( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ C ) )
= ( comp @ TB @ TC @ TA @ ( comp @ TD @ TC @ TB @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_fun_Omap__comp) ).
thf(996,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TA > TB] :
( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ C ) )
= ( comp @ TB @ TC @ TA @ ( comp @ TD @ TC @ TB @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(1142,plain,
! [TA: $tType,A: real > TA] :
( ( ( path_pathstart @ TA @ A )
!= ( path_pathfinish @ TA @ A ) )
| ~ $true
| ~ ( path_arc @ TA @ A )
| ( ( topolo503727757_space @ real )
!= ( topolo503727757_space @ TA ) ) ),
inference(paramod_ordered,[status(thm)],[1058,882]) ).
thf(1143,plain,
! [TA: $tType,A: real > TA] :
( ( ( path_pathstart @ TA @ A )
!= ( path_pathfinish @ TA @ A ) )
| ~ ( path_arc @ TA @ A )
| ( ( topolo503727757_space @ real )
!= ( topolo503727757_space @ TA ) ) ),
inference(simp,[status(thm)],[1142]) ).
thf(1144,plain,
! [A: real > real] :
( ( ( path_pathstart @ real @ A )
!= ( path_pathfinish @ real @ A ) )
| ~ ( path_arc @ real @ A ) ),
inference(pattern_uni,[status(thm)],[1143:[bind_type(TA,$thf( real ))]]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB,C: TB > TA] :
( ( bij_betw @ TB @ TA @ ( swap @ TB @ TA @ A @ B @ C ) @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
= ( bij_betw @ TB @ TA @ C @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_bij__swap__iff) ).
thf(318,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB,C: TB > TA] :
( ( bij_betw @ TB @ TA @ ( swap @ TB @ TA @ A @ B @ C ) @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
= ( bij_betw @ TB @ TA @ C @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(112,axiom,
! [TA: $tType] :
( ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ ( id @ TA ) )
= ( id @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_inv__id) ).
thf(616,plain,
! [TA: $tType] :
( ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ ( id @ TA ) )
= ( id @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
( ( inj_on @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
=> ( ! [C: TA] :
( ( A @ ( B @ C ) )
= C )
=> ( ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_inj__imp__inv__eq) ).
thf(509,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
( ( inj_on @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
=> ( ! [C: TA] :
( ( A @ ( B @ C ) )
= C )
=> ( ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(123,axiom,
zero @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ozero) ).
thf(649,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(477,plain,
! [TA: $tType] : ( top @ ( set @ TA ) ),
inference(cnf,[status(esa)],[476]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB] :
( ( bij_betw @ TB @ TA @ A @ B @ ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_bij__betw__imp__surj) ).
thf(494,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB] :
( ( bij_betw @ TB @ TA @ A @ B @ ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(177,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( inj_on @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ C )
=> ( inj_on @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_inj__on__imageI) ).
thf(816,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( inj_on @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ C )
=> ( inj_on @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(109,axiom,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ( topolo503727757_space @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Executable__Euclidean__Space_Oexecutable__euclidean__space___Topological__Spaces_Otopological__space) ).
thf(609,plain,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ( topolo503727757_space @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType] :
( ( swap @ TA @ TB )
= ( ^ [A: TA,B: TA] : ( swap @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_swap__commute) ).
thf(594,plain,
! [TA: $tType,TB: $tType] :
( ( swap @ TA @ TB )
= ( ^ [A: TA,B: TA] : ( swap @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] :
? [C: TB] :
( ( ( A @ C )
= B )
& ! [D: TB] :
( ( ( A @ D )
= B )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_bij__iff) ).
thf(621,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] :
? [C: TB] :
( ( ( A @ C )
= B )
& ! [D: TB] :
( ( ( A @ D )
= B )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(222,axiom,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: TA > TA] :
( ( real_Vector_linear @ TA @ TA @ A )
=> ( ( ~ ( inj_on @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) ) )
= ( ? [B: TA] :
( ( B
!= ( zero_zero @ TA ) )
& ! [C: TA] :
( ( inner_780170721_inner @ TA @ B @ ( A @ C ) )
= ( zero_zero @ real ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_linear__singular__into__hyperplane) ).
thf(932,plain,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: TA > TA] :
( ( real_Vector_linear @ TA @ TA @ A )
=> ( ( ~ ( inj_on @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) ) )
= ( ? [B: TA] :
( ( B
!= ( zero_zero @ TA ) )
& ! [C: TA] :
( ( inner_780170721_inner @ TA @ B @ ( A @ C ) )
= ( zero_zero @ real ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(282,axiom,
zero @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_7) ).
thf(1112,plain,
zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( bij_betw @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TB ) ) )
=> ( ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_inv__inv__eq) ).
thf(345,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( bij_betw @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TB ) ) )
=> ( ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(191,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: TA > TB] :
( ( inj_on @ TA @ TC @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( comp @ TC @ TB @ TA @ ( comp @ TA @ TB @ TC @ B @ ( hilbert_inv_into @ TA @ TC @ ( top_top @ ( set @ TA ) ) @ A ) ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_o__inv__o__cancel) ).
thf(858,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: TA > TB] :
( ( inj_on @ TA @ TC @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( comp @ TC @ TB @ TA @ ( comp @ TA @ TB @ TC @ B @ ( hilbert_inv_into @ TA @ TC @ ( top_top @ ( set @ TA ) ) @ A ) ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image @ TA @ TB @ C @ A )
= ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_image__cong) ).
thf(552,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image @ TA @ TB @ C @ A )
= ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(254,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ! [E: TA] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_comp__eq__elim) ).
thf(1029,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ! [E: TA] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(208,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TB @ A @ B )
= C )
=> ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ D ) )
= ( comp @ TB @ TC @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_rewriteL__comp__comp) ).
thf(895,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TB @ A @ B )
= C )
=> ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ D ) )
= ( comp @ TB @ TC @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(133,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TA] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( ( B @ ( C @ D ) )
= ( B @ ( C @ E ) ) )
= ( ( B @ D )
= ( B @ E ) ) ) ) )
=> ( ( inj_on @ TA @ TA @ C @ A )
=> ( ( inj_on @ TA @ TB @ B @ ( image @ TA @ TA @ C @ A ) )
= ( inj_on @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_inj__on__image__iff) ).
thf(685,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TA] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( ( B @ ( C @ D ) )
= ( B @ ( C @ E ) ) )
= ( ( B @ D )
= ( B @ E ) ) ) ) )
=> ( ( inj_on @ TA @ TA @ C @ A )
=> ( ( inj_on @ TA @ TB @ B @ ( image @ TA @ TA @ C @ A ) )
= ( inj_on @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(160,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA > TB] :
( ( swap @ TA @ TB @ A @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_swap__self) ).
thf(768,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA > TB] :
( ( swap @ TA @ TB @ A @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType] :
( ( bij_betw @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA,C: set @ TB] :
( ( inj_on @ TA @ TB @ A @ B )
& ( ( image @ TA @ TB @ A @ B )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_bij__betw__def) ).
thf(636,plain,
! [TA: $tType,TB: $tType] :
( ( bij_betw @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA,C: set @ TB] :
( ( inj_on @ TA @ TB @ A @ B )
& ( ( image @ TA @ TB @ A @ B )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(164,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(780,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(278,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA,B: TB > TC,C: set @ TB,D: TA] :
( ( inj_on @ TC @ TA @ A @ ( image @ TB @ TC @ B @ C ) )
=> ( ( inj_on @ TB @ TC @ B @ C )
=> ( ( member @ TA @ D @ ( image @ TC @ TA @ A @ ( image @ TB @ TC @ B @ C ) ) )
=> ( ( the_inv_into @ TB @ TA @ C @ ( comp @ TC @ TA @ TB @ A @ B ) @ D )
= ( comp @ TC @ TB @ TA @ ( the_inv_into @ TB @ TC @ C @ B ) @ ( the_inv_into @ TC @ TA @ ( image @ TB @ TC @ B @ C ) @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_the__inv__into__comp) ).
thf(1102,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA,B: TB > TC,C: set @ TB,D: TA] :
( ( inj_on @ TC @ TA @ A @ ( image @ TB @ TC @ B @ C ) )
=> ( ( inj_on @ TB @ TC @ B @ C )
=> ( ( member @ TA @ D @ ( image @ TC @ TA @ A @ ( image @ TB @ TC @ B @ C ) ) )
=> ( ( the_inv_into @ TB @ TA @ C @ ( comp @ TC @ TA @ TB @ A @ B ) @ D )
= ( comp @ TC @ TB @ TA @ ( the_inv_into @ TB @ TC @ C @ B ) @ ( the_inv_into @ TC @ TA @ ( image @ TB @ TC @ B @ C ) @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(125,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( A @ ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_surj__f__inv__f) ).
thf(653,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( A @ ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(217,axiom,
! [A: complex,B: complex] :
( ( path_pathstart @ complex @ ( path_rectpath @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_pathstart__rectpath) ).
thf(922,plain,
! [A: complex,B: complex] :
( ( path_pathstart @ complex @ ( path_rectpath @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA] :
( ( A
= ( B @ C ) )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_range__eqI) ).
thf(455,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA] :
( ( A
= ( B @ C ) )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(283,axiom,
path_simple_path @ complex @ ( comp @ a @ complex @ real @ ( poinca1531302022lex_of @ a ) @ c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_a1) ).
thf(1113,plain,
path_simple_path @ complex @ ( comp @ a @ complex @ real @ ( poinca1531302022lex_of @ a ) @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( hilbert_inv_into @ TA @ TB @ B @ A @ ( A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_inv__into__f__f) ).
thf(563,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( hilbert_inv_into @ TA @ TB @ B @ A @ ( A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(147,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_zero__reorient) ).
thf(722,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(128,axiom,
! [TA: $tType,A: TA,B: TA,C: TA] :
( ( ( A = B )
=> ( ( swap @ TA @ TA @ B @ C @ ( id @ TA ) @ A )
= C ) )
& ( ( A != B )
=> ( ( ( A = C )
=> ( ( swap @ TA @ TA @ B @ C @ ( id @ TA ) @ A )
= B ) )
& ( ( A != C )
=> ( ( swap @ TA @ TA @ B @ C @ ( id @ TA ) @ A )
= A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_swap__id__eq) ).
thf(663,plain,
! [TA: $tType,A: TA,B: TA,C: TA] :
( ( ( A = B )
=> ( ( swap @ TA @ TA @ B @ C @ ( id @ TA ) @ A )
= C ) )
& ( ( A != B )
=> ( ( ( A = C )
=> ( ( swap @ TA @ TA @ B @ C @ ( id @ TA ) @ A )
= B ) )
& ( ( A != C )
=> ( ( swap @ TA @ TA @ B @ C @ ( id @ TA ) @ A )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(219,axiom,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ! [A: TA > TA,B: TA > ( bounde2145540817linfun @ TA @ TA ),C: set @ TA] :
( ( poinca1076805489pen_R2 @ TA @ A @ B @ C )
=> ( bij_betw @ complex @ TA @ ( poinca179318102eal_of @ TA ) @ ( top_top @ ( set @ complex ) ) @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_c1__on__open__R2_Oreal__of__bij) ).
thf(927,plain,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ! [A: TA > TA,B: TA > ( bounde2145540817linfun @ TA @ TA ),C: set @ TA] :
( ( poinca1076805489pen_R2 @ TA @ A @ B @ C )
=> ( bij_betw @ complex @ TA @ ( poinca179318102eal_of @ TA ) @ ( top_top @ ( set @ complex ) ) @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(198,axiom,
topolo503727757_space @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Complex_Ocomplex___Topological__Spaces_Otopological__space_9) ).
thf(876,plain,
topolo503727757_space @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(1132,plain,
! [TA: $tType,A: real > TA] :
( ( ( path_pathstart @ TA @ A )
!= ( path_pathfinish @ TA @ A ) )
| ~ $true
| ~ ( path_arc @ TA @ A )
| ( ( topolo503727757_space @ complex )
!= ( topolo503727757_space @ TA ) ) ),
inference(paramod_ordered,[status(thm)],[876,882]) ).
thf(1133,plain,
! [TA: $tType,A: real > TA] :
( ( ( path_pathstart @ TA @ A )
!= ( path_pathfinish @ TA @ A ) )
| ~ ( path_arc @ TA @ A )
| ( ( topolo503727757_space @ complex )
!= ( topolo503727757_space @ TA ) ) ),
inference(simp,[status(thm)],[1132]) ).
thf(1134,plain,
! [A: real > complex] :
( ( ( path_pathstart @ complex @ A )
!= ( path_pathfinish @ complex @ A ) )
| ~ ( path_arc @ complex @ A ) ),
inference(pattern_uni,[status(thm)],[1133:[bind_type(TA,$thf( complex ))]]) ).
thf(176,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
( ( ( comp @ TC @ TB @ TA @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_comp__eq__dest__lhs) ).
thf(812,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
( ( ( comp @ TC @ TB @ TA @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TA )
=> ( topolo503727757_space @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Topological__Spaces_Otopological__space) ).
thf(516,plain,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TA )
=> ( topolo503727757_space @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TB > TA,B: TB,C: TA] :
( ( real_Vector_linear @ TB @ TA @ A )
=> ( ( inner_780170721_inner @ TB @ B @ ( linear_adjoint @ TB @ TA @ A @ C ) )
= ( inner_780170721_inner @ TA @ ( A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_adjoint__works) ).
thf(342,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TB > TA,B: TB,C: TA] :
( ( real_Vector_linear @ TB @ TA @ A )
=> ( ( inner_780170721_inner @ TB @ B @ ( linear_adjoint @ TB @ TA @ A @ C ) )
= ( inner_780170721_inner @ TA @ ( A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(7,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_top__set__def) ).
thf(295,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(296,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(cnf,[status(esa)],[295]) ).
thf(297,plain,
! [TA: $tType] :
( ( collect @ TA @ ( top_top @ ( TA > $o ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(lifteq,[status(thm)],[296]) ).
thf(294,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(cnf,[status(esa)],[293]) ).
thf(1145,plain,
! [TA: $tType] :
( ( collect @ TA
@ ^ [A: TA] : $true )
= ( top_top @ ( set @ TA ) ) ),
inference(rewrite,[status(thm)],[297,294]) ).
thf(235,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB,B: real > TA] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( path_path @ TB @ ( comp @ TA @ TB @ real @ A @ B ) )
= ( path_path @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_path__linear__image__eq) ).
thf(968,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB,B: real > TA] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( path_path @ TB @ ( comp @ TA @ TB @ real @ A @ B ) )
= ( path_path @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(185,axiom,
real_V1076094709vector @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Complex_Ocomplex___Real__Vector__Spaces_Oreal__vector_11) ).
thf(836,plain,
real_V1076094709vector @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( image @ TA @ TB @ ( swap @ TA @ TB @ A @ C @ D ) @ B )
= ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_swap__image__eq) ).
thf(473,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( image @ TA @ TB @ ( swap @ TA @ TB @ A @ C @ D ) @ B )
= ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(272,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( comp @ TB @ TA @ TA @ ( the_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A ) @ A @ B )
= ( id @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_the__inv__f__o__f__id) ).
thf(1076,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( comp @ TB @ TA @ TA @ ( the_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A ) @ A @ B )
= ( id @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(142,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_UNIV__witness) ).
thf(712,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(196,axiom,
euclid925273238_space @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Euclidean__Space_Oeuclidean__space) ).
thf(872,plain,
euclid925273238_space @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(139,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TB > TA] :
( ( real_Vector_linear @ TB @ TA @ A )
=> ( ( inj_on @ TA @ TB @ ( linear_adjoint @ TB @ TA @ A ) @ ( top_top @ ( set @ TA ) ) )
= ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_inj__adjoint__iff__surj) ).
thf(705,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TB > TA] :
( ( real_Vector_linear @ TB @ TA @ A )
=> ( ( inj_on @ TA @ TB @ ( linear_adjoint @ TB @ TA @ A ) @ ( top_top @ ( set @ TA ) ) )
= ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(203,axiom,
inner_real_inner @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Complex_Ocomplex___Inner__Product_Oreal__inner_12) ).
thf(887,plain,
inner_real_inner @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(18,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: real > TA] :
( ( path_arc @ TA @ A )
=> ( path_simple_path @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_arc__imp__simple__path) ).
thf(327,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: real > TA] :
( ( path_arc @ TA @ A )
=> ( path_simple_path @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(230,axiom,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: TA > TA,B: TA > TA] :
( ( real_Vector_linear @ TA @ TA @ A )
=> ( ( ( comp @ TA @ TA @ TA @ B @ A )
= ( id @ TA ) )
=> ( real_Vector_linear @ TA @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_left__inverse__linear) ).
thf(954,plain,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: TA > TA,B: TA > TA] :
( ( real_Vector_linear @ TA @ TA @ A )
=> ( ( ( comp @ TA @ TA @ TA @ B @ A )
= ( id @ TA ) )
=> ( real_Vector_linear @ TA @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(46,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: real > TA] :
( ( path_simple_path @ TA @ A )
=> ( path_path @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_simple__path__imp__path) ).
thf(409,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: real > TA] :
( ( path_simple_path @ TA @ A )
=> ( path_path @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(48,axiom,
! [TA: $tType,A: set @ TA] : ( bij_betw @ TA @ TA @ ( id @ TA ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_bij__betw__id) ).
thf(414,plain,
! [TA: $tType,A: set @ TA] : ( bij_betw @ TA @ TA @ ( id @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(236,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD,B: TB > TC,C: TA > TB] :
( ( comp @ TB @ TD @ TA @ ( comp @ TC @ TD @ TB @ A @ B ) @ C )
= ( comp @ TC @ TD @ TA @ A @ ( comp @ TB @ TC @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_comp__assoc) ).
thf(971,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD,B: TB > TC,C: TA > TB] :
( ( comp @ TB @ TD @ TA @ ( comp @ TC @ TD @ TB @ A @ B ) @ C )
= ( comp @ TC @ TD @ TA @ A @ ( comp @ TB @ TC @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(129,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB,D: TA] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ( ( member @ TA @ D @ B )
=> ( ( hilbert_inv_into @ TB @ TA @ C @ ( hilbert_inv_into @ TA @ TB @ B @ A ) @ D )
= ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_inv__into__inv__into__eq) ).
thf(673,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB,D: TA] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ( ( member @ TA @ D @ B )
=> ( ( hilbert_inv_into @ TB @ TA @ C @ ( hilbert_inv_into @ TA @ TB @ B @ A ) @ D )
= ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(187,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > TA] :
( ( ( ( comp @ TA @ TB @ TB @ A @ B )
= ( id @ TB ) )
& ( ( comp @ TB @ TA @ TA @ B @ A )
= ( id @ TA ) ) )
= ( ! [C: TB] :
( ( A @ ( B @ C ) )
= C )
& ! [C: TA] :
( ( B @ ( A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_isomorphism__expand) ).
thf(840,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > TA] :
( ( ( ( comp @ TA @ TB @ TB @ A @ B )
= ( id @ TB ) )
& ( ( comp @ TB @ TA @ TA @ B @ A )
= ( id @ TA ) ) )
= ( ! [C: TB] :
( ( A @ ( B @ C ) )
= C )
& ! [C: TA] :
( ( B @ ( A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(229,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: set @ TA,C: TC > TB] :
( ( inj_on @ TA @ TC @ A @ B )
=> ( ( inj_on @ TC @ TB @ C @ ( image @ TA @ TC @ A @ B ) )
= ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_comp__inj__on__iff) ).
thf(951,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: set @ TA,C: TC > TB] :
( ( inj_on @ TA @ TC @ A @ B )
=> ( ( inj_on @ TC @ TB @ C @ ( image @ TA @ TC @ A @ B ) )
= ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(258,axiom,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ! [A: TA > TA,B: TA > ( bounde2145540817linfun @ TA @ TA ),C: set @ TA] :
( ( poinca1076805489pen_R2 @ TA @ A @ B @ C )
=> ( ( comp @ TA @ complex @ complex @ ( poinca1531302022lex_of @ TA ) @ ( poinca179318102eal_of @ TA ) )
= ( id @ complex ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_c1__on__open__R2_Ocomplex__of__real__of) ).
thf(1038,plain,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ! [A: TA > TA,B: TA > ( bounde2145540817linfun @ TA @ TA ),C: set @ TA] :
( ( poinca1076805489pen_R2 @ TA @ A @ B @ C )
=> ( ( comp @ TA @ complex @ complex @ ( poinca1531302022lex_of @ TA ) @ ( poinca179318102eal_of @ TA ) )
= ( id @ complex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TB] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ ( swap @ TB @ TA @ B @ C @ A ) @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_surj__imp__surj__swap) ).
thf(585,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TB] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ ( swap @ TB @ TA @ B @ C @ A ) @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(275,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_comp__def) ).
thf(1085,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_inj__eq) ).
thf(470,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( bij_betw @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TB ) ) )
=> ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_bij__is__inj) ).
thf(544,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( bij_betw @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TB ) ) )
=> ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(211,axiom,
execut510477386_space @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Executable__Euclidean__Space_Oexecutable__euclidean__space) ).
thf(907,plain,
execut510477386_space @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(154,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ? [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_bex__imageD) ).
thf(744,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ? [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(111,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( bij_betw @ TA @ TA @ ( id @ TA ) @ A @ B )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_bij__betw__id__iff) ).
thf(613,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( bij_betw @ TA @ TA @ ( id @ TA ) @ A @ B )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(263,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB,C: TB] :
( ( bij_betw @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TB ) ) )
=> ( ( comp @ TB @ TB @ TA @ ( swap @ TB @ TB @ B @ C @ ( id @ TB ) ) @ A )
= ( swap @ TA @ TB @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ B ) @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_bij__swap__comp) ).
thf(1052,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB,C: TB] :
( ( bij_betw @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TB ) ) )
=> ( ( comp @ TB @ TB @ TA @ ( swap @ TB @ TB @ B @ C @ ( id @ TB ) ) @ A )
= ( swap @ TA @ TB @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ B ) @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(193,axiom,
real_V1632203528linear @ complex @ a @ ( poinca179318102eal_of @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_real__of__bounded__linear) ).
thf(864,plain,
real_V1632203528linear @ complex @ a @ ( poinca179318102eal_of @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(249,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( A != B )
=> ( ( C != D )
=> ( ( ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ A @ B @ ( id @ TA ) ) @ ( swap @ TA @ TA @ C @ D @ ( id @ TA ) ) )
= ( id @ TA ) )
| ? [E: TA,F: TA,G: TA] :
( ( E != A )
& ( F != A )
& ( G != A )
& ( E != F )
& ( ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ A @ B @ ( id @ TA ) ) @ ( swap @ TA @ TA @ C @ D @ ( id @ TA ) ) )
= ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ E @ F @ ( id @ TA ) ) @ ( swap @ TA @ TA @ A @ G @ ( id @ TA ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_swap__general) ).
thf(1008,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( A != B )
=> ( ( C != D )
=> ( ( ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ A @ B @ ( id @ TA ) ) @ ( swap @ TA @ TA @ C @ D @ ( id @ TA ) ) )
= ( id @ TA ) )
| ? [E: TA,F: TA,G: TA] :
( ( E != A )
& ( F != A )
& ( G != A )
& ( E != F )
& ( ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ A @ B @ ( id @ TA ) ) @ ( swap @ TA @ TA @ C @ D @ ( id @ TA ) ) )
= ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ E @ F @ ( id @ TA ) ) @ ( swap @ TA @ TA @ A @ G @ ( id @ TA ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TA )
& ( real_V55928688vector @ TB ) )
=> ! [A: TA > TB] :
( ( real_V1632203528linear @ TA @ TB @ A )
=> ( real_V1632203528linear @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_bounded__linear_Obounded__linear) ).
thf(446,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(126,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_image__eqI) ).
thf(656,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(252,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( comp @ TA @ TB @ TA @ A @ ( id @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_comp__id) ).
thf(1023,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( comp @ TA @ TB @ TA @ A @ ( id @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(277,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TA > TB,C: TB > TC,D: TB > TC] :
( ( A = B )
=> ( ! [E: TB] :
( ( member @ TB @ E @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( comp @ TB @ TC @ TA @ C @ A )
= ( comp @ TB @ TC @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_fun_Omap__cong) ).
thf(1094,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TA > TB,C: TB > TC,D: TB > TC] :
( ( A = B )
=> ( ! [E: TB] :
( ( member @ TB @ E @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( comp @ TB @ TC @ TA @ C @ A )
= ( comp @ TB @ TC @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( ( image @ TB @ TA @ ( linear_adjoint @ TA @ TB @ A ) @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_linear__surj__adj__imp__inj) ).
thf(386,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( ( image @ TB @ TA @ ( linear_adjoint @ TA @ TB @ A ) @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(74,axiom,
! [TA: $tType] :
( ( inner_real_inner @ TA )
=> ! [A: TA,B: TA] :
( ( ! [C: TA] :
( ( inner_780170721_inner @ TA @ C @ A )
= ( inner_780170721_inner @ TA @ C @ B ) ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_vector__eq__ldot) ).
thf(497,plain,
! [TA: $tType] :
( ( inner_real_inner @ TA )
=> ! [A: TA,B: TA] :
( ( ! [C: TA] :
( ( inner_780170721_inner @ TA @ C @ A )
= ( inner_780170721_inner @ TA @ C @ B ) ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(31,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_UNIV__I) ).
thf(363,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(86,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_iso__tuple__UNIV__I) ).
thf(539,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TA )
& ( real_V55928688vector @ TB ) )
=> ! [A: TB > TA] :
( ( real_V1632203528linear @ TB @ TA @ A )
=> ( ( A @ ( zero_zero @ TB ) )
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_linear__simps_I3_J) ).
thf(524,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V55928688vector @ TA )
& ( real_V55928688vector @ TB ) )
=> ! [A: TB > TA] :
( ( real_V1632203528linear @ TB @ TA @ A )
=> ( ( A @ ( zero_zero @ TB ) )
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(205,axiom,
( ( comp @ a @ complex @ complex @ ( poinca1531302022lex_of @ a ) @ ( poinca179318102eal_of @ a ) )
= ( id @ complex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_complex__of__real__of) ).
thf(891,plain,
( ( comp @ a @ complex @ complex @ ( poinca1531302022lex_of @ a ) @ ( poinca179318102eal_of @ a ) )
= ( id @ complex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(161,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ TB,C: TB,D: TB > TA,E: set @ TA] :
( ( member @ TB @ A @ B )
=> ( ( member @ TB @ C @ B )
=> ( ( bij_betw @ TB @ TA @ ( swap @ TB @ TA @ A @ C @ D ) @ B @ E )
= ( bij_betw @ TB @ TA @ D @ B @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_bij__betw__swap__iff) ).
thf(771,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ TB,C: TB,D: TB > TA,E: set @ TA] :
( ( member @ TB @ A @ B )
=> ( ( member @ TB @ C @ B )
=> ( ( bij_betw @ TB @ TA @ ( swap @ TB @ TA @ A @ C @ D ) @ B @ E )
= ( bij_betw @ TB @ TA @ D @ B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(280,axiom,
real_V55928688vector @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Complex_Ocomplex___Real__Vector__Spaces_Oreal__normed__vector_8) ).
thf(1108,plain,
real_V55928688vector @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(233,axiom,
! [TA: $tType,A: TA,B: TA,C: TA] :
( ( A != B )
=> ( ( C != B )
=> ( ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ A @ C @ ( id @ TA ) ) @ ( swap @ TA @ TA @ A @ B @ ( id @ TA ) ) )
= ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ C @ B @ ( id @ TA ) ) @ ( swap @ TA @ TA @ A @ C @ ( id @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_swap__id__common) ).
thf(963,plain,
! [TA: $tType,A: TA,B: TA,C: TA] :
( ( A != B )
=> ( ( C != B )
=> ( ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ A @ C @ ( id @ TA ) ) @ ( swap @ TA @ TA @ A @ B @ ( id @ TA ) ) )
= ( comp @ TA @ TA @ TA @ ( swap @ TA @ TA @ C @ B @ ( id @ TA ) ) @ ( swap @ TA @ TA @ A @ C @ ( id @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,A: ( TB > TB ) > TA > TA,B: TA > TB,C: TA,D: TB > TB,E: TA,F: TB] :
( ( iso_tu2011167877assist @ TB @ TA @ A @ B @ C @ D @ E @ F )
=> ( ( A @ D @ C )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_update__accessor__updator__eqE) ).
thf(304,plain,
! [TA: $tType,TB: $tType,A: ( TB > TB ) > TA > TA,B: TA > TB,C: TA,D: TB > TB,E: TA,F: TB] :
( ( iso_tu2011167877assist @ TB @ TA @ A @ B @ C @ D @ E @ F )
=> ( ( A @ D @ C )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(267,axiom,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ! [A: TA > TA,B: TA > ( bounde2145540817linfun @ TA @ TA ),C: set @ TA] :
( ( poinca1076805489pen_R2 @ TA @ A @ B @ C )
=> ( inj_on @ complex @ TA @ ( poinca179318102eal_of @ TA ) @ ( top_top @ ( set @ complex ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_c1__on__open__R2_Oreal__of__inj) ).
thf(1062,plain,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ! [A: TA > TA,B: TA > ( bounde2145540817linfun @ TA @ TA ),C: set @ TA] :
( ( poinca1076805489pen_R2 @ TA @ A @ B @ C )
=> ( inj_on @ complex @ TA @ ( poinca179318102eal_of @ TA ) @ ( top_top @ ( set @ complex ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(26,axiom,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ( type @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Executable__Euclidean__Space_Oexecutable__euclidean__space___HOL_Otype) ).
thf(351,plain,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ( type @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_imageI) ).
thf(401,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB,B: set @ TA] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( aff_dim @ TB @ ( image @ TA @ TB @ A @ B ) )
= ( aff_dim @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_aff__dim__injective__linear__image) ).
thf(588,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB,B: set @ TA] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( aff_dim @ TB @ ( image @ TA @ TB @ A @ B ) )
= ( aff_dim @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(136,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] :
( ( A @ ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_surj__iff__all) ).
thf(699,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] :
( ( A @ ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(150,axiom,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ( zero @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Executable__Euclidean__Space_Oexecutable__euclidean__space___Groups_Ozero) ).
thf(731,plain,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ( zero @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(166,axiom,
! [TA: $tType] :
( ( image @ TA @ TA @ ( id @ TA ) @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_surj__id) ).
thf(786,plain,
! [TA: $tType] :
( ( image @ TA @ TA @ ( id @ TA ) @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(220,axiom,
real_V55928688vector @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector) ).
thf(929,plain,
real_V55928688vector @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: TB > TA,D: set @ TA] :
( ! [E: TB] :
( ( member @ TB @ E @ A )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( bij_betw @ TB @ TA @ B @ A @ D )
= ( bij_betw @ TB @ TA @ C @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_bij__betw__cong) ).
thf(478,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: TB > TA,D: set @ TA] :
( ! [E: TB] :
( ( member @ TB @ E @ A )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( bij_betw @ TB @ TA @ B @ A @ D )
= ( bij_betw @ TB @ TA @ C @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType] :
( ( inj_on @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_inj__on__def) ).
thf(383,plain,
! [TA: $tType,TB: $tType] :
( ( inj_on @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(209,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V1076094709vector @ TA )
& ( real_V1076094709vector @ TB ) )
=> ! [A: TA > TB] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ? [B: TB > TA] :
( ( real_Vector_linear @ TB @ TA @ B )
& ( ( comp @ TB @ TA @ TA @ B @ A )
= ( id @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_linear__injective__left__inverse) ).
thf(899,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V1076094709vector @ TA )
& ( real_V1076094709vector @ TB ) )
=> ! [A: TA > TB] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ? [B: TB > TA] :
( ( real_Vector_linear @ TB @ TA @ B )
& ( ( comp @ TB @ TA @ TA @ B @ A )
= ( id @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( inj_on @ TA @ TB @ ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A ) @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_surj__imp__inj__inv) ).
thf(549,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( inj_on @ TA @ TB @ ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A ) @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( member @ TB @ B @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
= ( ? [C: TA] :
( ( B
= ( A @ C ) )
& ! [D: TA] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_range__ex1__eq) ).
thf(536,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( member @ TB @ B @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
= ( ? [C: TA] :
( ( B
= ( A @ C ) )
& ! [D: TA] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(261,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: real > TA] :
( ( path_simple_path @ TA @ A )
=> ( ( path_arc @ TA @ A )
| ( ( path_pathfinish @ TA @ A )
= ( path_pathstart @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_simple__path__cases) ).
thf(1045,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: real > TA] :
( ( path_simple_path @ TA @ A )
=> ( ( path_arc @ TA @ A )
| ( ( path_pathfinish @ TA @ A )
= ( path_pathstart @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(214,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
= ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_Inf_OINF__image) ).
thf(914,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
= ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( inj_on @ TA @ TB @ ( swap @ TA @ TB @ C @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_inj__on__imp__inj__on__swap) ).
thf(378,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( inj_on @ TA @ TB @ ( swap @ TA @ TB @ C @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(144,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( bij_betw @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TB ) ) )
=> ( bij_betw @ TB @ TA @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A ) @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_bij__imp__bij__inv) ).
thf(716,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( bij_betw @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TB ) ) )
=> ( bij_betw @ TB @ TA @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A ) @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(287,plain,
( ( path_pathstart @ complex @ ( comp @ a @ complex @ real @ ( poinca1531302022lex_of @ a ) @ c ) )
!= ( path_pathfinish @ complex @ ( comp @ a @ complex @ real @ ( poinca1531302022lex_of @ a ) @ c ) ) ),
inference(lifteq,[status(thm)],[286]) ).
thf(245,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB,B: real > TA] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( path_simple_path @ TB @ ( comp @ TA @ TB @ real @ A @ B ) )
= ( path_simple_path @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_simple__path__linear__image__eq) ).
thf(999,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB,B: real > TA] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( path_simple_path @ TB @ ( comp @ TA @ TB @ real @ A @ B ) )
= ( path_simple_path @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ? [D: TB > TA] : ( bij_betw @ TB @ TA @ D @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_bij__betw__inv) ).
thf(447,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ? [D: TB > TA] : ( bij_betw @ TB @ TA @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(14,axiom,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_top__empty__eq) ).
thf(315,plain,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_inj__onD) ).
thf(432,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(183,axiom,
zero @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Complex_Ocomplex___Groups_Ozero_13) ).
thf(833,plain,
zero @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(178,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TB > TA] :
( ( ( image @ TC @ TB @ A @ ( top_top @ ( set @ TC ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ( ( ( image @ TB @ TA @ B @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TC @ TA @ ( comp @ TB @ TA @ TC @ B @ A ) @ ( top_top @ ( set @ TC ) ) )
= ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_comp__surj) ).
thf(818,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TB > TA] :
( ( ( image @ TC @ TB @ A @ ( top_top @ ( set @ TC ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ( ( ( image @ TB @ TA @ B @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TC @ TA @ ( comp @ TB @ TA @ TC @ B @ A ) @ ( top_top @ ( set @ TC ) ) )
= ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(51,axiom,
! [TA: $tType] : ( bij_betw @ TA @ TA @ ( id @ TA ) @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_bij__id) ).
thf(422,plain,
! [TA: $tType] : ( bij_betw @ TA @ TA @ ( id @ TA ) @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(194,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TD,B: TA > TE,C: TB > TD,D: TA > TB,E: TD > TC,F: TB > TC] :
( ( ( comp @ TE @ TD @ TA @ A @ B )
= ( comp @ TB @ TD @ TA @ C @ D ) )
=> ( ( ( comp @ TD @ TC @ TB @ E @ C )
= F )
=> ( ( comp @ TE @ TC @ TA @ ( comp @ TD @ TC @ TE @ E @ A ) @ B )
= ( comp @ TB @ TC @ TA @ F @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_rewriteR__comp__comp2) ).
thf(865,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TD,B: TA > TE,C: TB > TD,D: TA > TB,E: TD > TC,F: TB > TC] :
( ( ( comp @ TE @ TD @ TA @ A @ B )
= ( comp @ TB @ TD @ TA @ C @ D ) )
=> ( ( ( comp @ TD @ TC @ TB @ E @ C )
= F )
=> ( ( comp @ TE @ TC @ TA @ ( comp @ TD @ TC @ TE @ E @ A ) @ B )
= ( comp @ TB @ TC @ TA @ F @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] : ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_rangeI) ).
thf(603,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] : ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(152,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( inj_on @ TA @ TB @ ( swap @ TA @ TB @ A @ C @ D ) @ B )
= ( inj_on @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_inj__on__swap__iff) ).
thf(735,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( inj_on @ TA @ TB @ ( swap @ TA @ TB @ A @ C @ D ) @ B )
= ( inj_on @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( linear_adjoint @ TB @ TA @ ( linear_adjoint @ TA @ TB @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_adjoint__adjoint) ).
thf(506,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( linear_adjoint @ TB @ TA @ ( linear_adjoint @ TA @ TB @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(256,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( comp @ ( TA > TB ) @ ( TA > TB ) @ ( TA > TB ) @ ( swap @ TA @ TB @ A @ B ) @ ( swap @ TA @ TB @ A @ B ) )
= ( id @ ( TA > TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_swap__comp__involutory) ).
thf(1033,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( comp @ ( TA > TB ) @ ( TA > TB ) @ ( TA > TB ) @ ( swap @ TA @ TB @ A @ B ) @ ( swap @ TA @ TB @ A @ B ) )
= ( id @ ( TA > TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(232,axiom,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: TA > TA,B: TA > TA] :
( ( real_Vector_linear @ TA @ TA @ A )
=> ( ( ( comp @ TA @ TA @ TA @ A @ B )
= ( id @ TA ) )
=> ( real_Vector_linear @ TA @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_right__inverse__linear) ).
thf(960,plain,
! [TA: $tType] :
( ( euclid925273238_space @ TA )
=> ! [A: TA > TA,B: TA > TA] :
( ( real_Vector_linear @ TA @ TA @ A )
=> ( ( ( comp @ TA @ TA @ TA @ A @ B )
= ( id @ TA ) )
=> ( real_Vector_linear @ TA @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(135,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA,D: TA > TB] :
( ( A != B )
=> ( ( C != B )
=> ( ( swap @ TA @ TB @ A @ C @ ( swap @ TA @ TB @ C @ B @ ( swap @ TA @ TB @ A @ C @ D ) ) )
= ( swap @ TA @ TB @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_swap__triple) ).
thf(696,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA,D: TA > TB] :
( ( A != B )
=> ( ( C != B )
=> ( ( swap @ TA @ TB @ A @ C @ ( swap @ TA @ TB @ C @ B @ ( swap @ TA @ TB @ A @ C @ D ) ) )
= ( swap @ TA @ TB @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(146,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ( bij_betw @ TB @ TA @ ( hilbert_inv_into @ TA @ TB @ B @ A ) @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_bij__betw__inv__into) ).
thf(720,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ( bij_betw @ TB @ TA @ ( hilbert_inv_into @ TA @ TB @ B @ A ) @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(202,axiom,
inner_real_inner @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Inner__Product_Oreal__inner) ).
thf(886,plain,
inner_real_inner @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(172,axiom,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TB ) )
=> ! [A: TA > TB,B: real > TA] :
( ( path_pathfinish @ TB @ ( comp @ TA @ TB @ real @ A @ B ) )
= ( A @ ( path_pathfinish @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_pathfinish__compose) ).
thf(801,plain,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo503727757_space @ TB ) )
=> ! [A: TA > TB,B: real > TA] :
( ( path_pathfinish @ TB @ ( comp @ TA @ TB @ real @ A @ B ) )
= ( A @ ( path_pathfinish @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_injD) ).
thf(358,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(174,axiom,
! [A: complex,B: complex] : ( path_path @ complex @ ( path_rectpath @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_path__rectpath) ).
thf(807,plain,
! [A: complex,B: complex] : ( path_path @ complex @ ( path_rectpath @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(149,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ! [C: TB] :
( ( B @ ( A @ C ) )
= C )
=> ( ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_surj__imp__inv__eq) ).
thf(728,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ! [C: TB] :
( ( B @ ( A @ C ) )
= C )
=> ( ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(241,axiom,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ! [A: TA > TA,B: TA > ( bounde2145540817linfun @ TA @ TA ),C: set @ TA] :
( ( poinca1076805489pen_R2 @ TA @ A @ B @ C )
=> ( bij_betw @ TA @ complex @ ( poinca1531302022lex_of @ TA ) @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ complex ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_c1__on__open__R2_Ocomplex__of__bij) ).
thf(987,plain,
! [TA: $tType] :
( ( execut510477386_space @ TA )
=> ! [A: TA > TA,B: TA > ( bounde2145540817linfun @ TA @ TA ),C: set @ TA] :
( ( poinca1076805489pen_R2 @ TA @ A @ B @ C )
=> ( bij_betw @ TA @ complex @ ( poinca1531302022lex_of @ TA ) @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ complex ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( real_Vector_linear @ TB @ TA @ ( linear_adjoint @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_adjoint__linear) ).
thf(464,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( real_Vector_linear @ TB @ TA @ ( linear_adjoint @ TA @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TA] :
( ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
=> ( ( B
= ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A @ C ) )
= ( ( A @ B )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_bij__inv__eq__iff) ).
thf(575,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TA] :
( ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
=> ( ( B
= ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A @ C ) )
= ( ( A @ B )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA,D: TB] :
( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ( ( member @ TB @ D @ B )
=> ( member @ TA @ ( A @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_bij__betw__apply) ).
thf(427,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA,D: TB] :
( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ( ( member @ TB @ D @ B )
=> ( member @ TA @ ( A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(595,plain,
! [TA: $tType,TB: $tType] :
( ( swap @ TB @ TA )
= ( ^ [A: TB,B: TB] : ( swap @ TB @ TA @ B @ A ) ) ),
inference(cnf,[status(esa)],[594]) ).
thf(596,plain,
! [TA: $tType,TB: $tType] :
( ( swap @ TB @ TA )
= ( ^ [A: TB,B: TB] : ( swap @ TB @ TA @ B @ A ) ) ),
inference(lifteq,[status(thm)],[595]) ).
thf(121,axiom,
! [TA: $tType,A: TA > TA] :
( ( ! [B: TA] :
( ( A @ B )
= B ) )
= ( A
= ( id @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_eq__id__iff) ).
thf(644,plain,
! [TA: $tType,A: TA > TA] :
( ( ! [B: TA] :
( ( A @ B )
= B ) )
= ( A
= ( id @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( bij_betw @ TA @ TB @ A @ B @ ( image @ TA @ TB @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_inj__on__imp__bij__betw) ).
thf(459,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( bij_betw @ TA @ TB @ A @ B @ ( image @ TA @ TB @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(247,axiom,
real_V1632203528linear @ a @ complex @ ( poinca1531302022lex_of @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_complex__of__bounded__linear) ).
thf(1004,plain,
real_V1632203528linear @ a @ complex @ ( poinca1531302022lex_of @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(108,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: real > TA] :
( ( path_arc @ TA @ A )
=> ( path_path @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_arc__imp__path) ).
thf(607,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: real > TA] :
( ( path_arc @ TA @ A )
=> ( path_path @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( the_inv_into @ TA @ TB @ B @ A @ ( A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_the__inv__into__f__f) ).
thf(395,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( the_inv_into @ TA @ TB @ B @ A @ ( A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(115,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TB > TA,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on @ TA @ TB @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_inj__on__inverseI) ).
thf(624,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TB > TA,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on @ TA @ TB @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(212,axiom,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB,B: real > TA] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( path_arc @ TB @ ( comp @ TA @ TB @ real @ A @ B ) )
= ( path_arc @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_arc__linear__image__eq) ).
thf(908,plain,
! [TA: $tType,TB: $tType] :
( ( ( euclid925273238_space @ TA )
& ( euclid925273238_space @ TB ) )
=> ! [A: TA > TB,B: real > TA] :
( ( real_Vector_linear @ TA @ TB @ A )
=> ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( path_arc @ TB @ ( comp @ TA @ TB @ real @ A @ B ) )
= ( path_arc @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(243,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB,B: TA > TD,C: TA > TB,D: TB > TC] :
( ( ( comp @ TD @ TB @ TA @ A @ B )
= C )
=> ( ( comp @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ D @ A ) @ B )
= ( comp @ TB @ TC @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_rewriteR__comp__comp) ).
thf(992,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB,B: TA > TD,C: TA > TB,D: TB > TC] :
( ( ( comp @ TD @ TB @ TA @ A @ B )
= C )
=> ( ( comp @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ D @ A ) @ B )
= ( comp @ TB @ TC @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on @ TA @ TB @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_inj__onI) ).
thf(486,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on @ TA @ TB @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(225,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( inj_on @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ C )
=> ( inj_on @ TA @ TB @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_inj__on__imageI2) ).
thf(940,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( inj_on @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ C )
=> ( inj_on @ TA @ TB @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(12,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(309,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(92,axiom,
! [TA: $tType] :
( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
? [C: TA] :
( ( member @ TA @ C @ ( top_top @ ( set @ TA ) ) )
& ( ( id @ TA @ C )
= A )
& ( ( id @ TA @ C )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_DEADID_Oin__rel) ).
thf(560,plain,
! [TA: $tType] :
( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
? [C: TA] :
( ( member @ TA @ C @ ( top_top @ ( set @ TA ) ) )
& ( ( id @ TA @ C )
= A )
& ( ( id @ TA @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(119,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( the_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ ( A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_the__inv__f__f) ).
thf(639,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( the_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ ( A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( inj_on @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
=> ( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_bijI) ).
thf(676,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( inj_on @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
=> ( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(276,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA,B: set @ TC,C: TA > TB,D: TA > TB] :
( ( ( image @ TC @ TA @ A @ B )
= ( top_top @ ( set @ TA ) ) )
=> ( ! [E: TC] :
( ( member @ TC @ E @ B )
=> ( ( comp @ TA @ TB @ TC @ C @ A @ E )
= ( comp @ TA @ TB @ TC @ D @ A @ E ) ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_surj__fun__eq) ).
thf(1088,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA,B: set @ TC,C: TA > TB,D: TA > TB] :
( ( ( image @ TC @ TA @ A @ B )
= ( top_top @ ( set @ TA ) ) )
=> ( ! [E: TC] :
( ( member @ TC @ E @ B )
=> ( ( comp @ TA @ TB @ TC @ C @ A @ E )
= ( comp @ TA @ TB @ TC @ D @ A @ E ) ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(270,axiom,
! [TA: $tType,TB: $tType] :
( ( ( real_V1076094709vector @ TA )
& ( real_V1076094709vector @ TB ) )
=> ! [A: TB > TA] :
( ( real_Vector_linear @ TB @ TA @ A )
=> ( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ? [B: TA > TB] :
( ( real_Vector_linear @ TA @ TB @ B )
& ( ( comp @ TB @ TA @ TA @ A @ B )
= ( id @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_linear__surjective__right__inverse) ).
thf(1069,plain,
! [TA: $tType,TB: $tType] :
( ( ( real_V1076094709vector @ TA )
& ( real_V1076094709vector @ TB ) )
=> ! [A: TB > TA] :
( ( real_Vector_linear @ TB @ TA @ A )
=> ( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ? [B: TA > TB] :
( ( real_Vector_linear @ TA @ TB @ B )
& ( ( comp @ TB @ TA @ TA @ A @ B )
= ( id @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(1646,plain,
$false,
inference(e,[status(thm)],[1036,809,629,365,1105,893,518,468,777,977,1005,597,582,762,873,449,1041,861,500,797,945,930,709,885,288,301,389,1055,372,619,1059,917,702,751,853,416,289,756,789,591,834,937,821,1109,321,1020,348,353,966,981,877,293,774,660,411,527,312,307,292,452,380,546,925,1067,714,798,512,942,334,1021,1042,392,424,693,429,957,894,1032,361,435,329,830,461,1079,682,566,484,324,974,578,1121,1064,725,356,869,783,989,650,948,980,403,1082,339,753,642,679,1075,476,837,1114,647,738,911,1002,569,503,605,792,633,541,398,1026,530,794,718,888,298,1135,824,856,601,375,733,904,843,286,826,1124,936,572,611,1058,466,335,704,919,804,764,406,1117,419,1048,996,1144,318,616,509,880,649,477,494,816,609,594,621,932,1112,345,858,552,1029,895,685,768,636,780,1102,653,922,455,883,1113,563,722,663,927,1134,812,516,342,1145,968,836,473,1076,712,295,872,705,887,327,954,409,414,971,673,840,951,1038,585,1085,470,544,907,744,613,1052,864,1008,446,656,1023,1094,386,497,876,363,539,524,891,771,1108,963,304,1062,351,401,588,699,731,786,929,478,383,899,549,536,1045,914,378,716,287,999,447,315,432,833,818,422,865,603,735,506,1033,960,696,720,886,294,801,358,807,728,987,464,332,575,427,596,644,459,1004,607,395,624,908,992,486,940,935,309,560,639,676,1088,1069,708,882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP148^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n002.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 20:03:42 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.01/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.96/1.17 % [INFO] Parsing done (366ms).
% 1.96/1.18 % [INFO] Running in sequential loop mode.
% 2.97/1.57 % [INFO] eprover registered as external prover.
% 2.97/1.58 % [INFO] Scanning for conjecture ...
% 3.37/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 284 axioms. Running axiom selection ...
% 3.56/1.87 % [INFO] Axiom selection finished. Selected 283 axioms (removed 1 axioms).
% 4.58/2.19 % [INFO] Problem is higher-order (TPTP THF).
% 4.80/2.22 % [INFO] Type checking passed.
% 4.80/2.23 % [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 ...
% 69.04/40.69 % External prover 'e' found a proof!
% 69.04/40.69 % [INFO] Killing All external provers ...
% 69.04/40.69 % Time passed: 40333ms (effective reasoning time: 39499ms)
% 69.04/40.69 % 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)>
% 69.04/40.69 % Axioms used in derivation (283): fact_40_simple__path__linear__image__eq, fact_242_bij__betw__inv__into__left, fact_65_fun_Omap__comp, fact_62_simple__path__eq__arc, fact_103_simple__path__imp__path, fact_202_linear__surj__imp__inj, fact_196_inj__on__imp__bij__betw, fact_126_c1__on__open__R2_Oreal__of__inj, fact_191_comp__inj__on__iff, tcon_Complex_Ocomplex___Euclidean__Space_Oeuclidean__space_10, fact_119_c1__on__open__R2_Ocomplex__of__real__of, fact_249_inv__f__eq, fact_122_c1__on__open__R2_Ocomplex__of__bounded__linear, subcl_Executable__Euclidean__Space_Oexecutable__euclidean__space___Groups_Ozero, fact_69_complex__of__bij, fact_186_comp__surj, fact_151_bij__betw__imp__surj__on, tfree_0, fact_30_inj__def, fact_211_surj__adjoint__iff__inj, fact_227_all__zero__iff, fact_79_fun_Omap__id, fact_0_assms_I2_J, fact_172_range__eqI, fact_199_the__inv__f__f, fact_170_surj__def, fact_192_inj__on__imageI, fact_230_bij__swap__comp, fact_6_complex__of__bounded__linear, fact_4_pathfinish__compose, fact_160_rev__image__eqI, fact_59_UNIV__eq__I, fact_231_inj__linear__imp__inv__bounded__linear, fact_94_o__bij, fact_77_comp__id, fact_101_arc__imp__path, fact_27_injD, fact_136_swap__apply_I3_J, tcon_Int_Oint___Groups_Ozero, fact_110_right__inverse__linear, fact_237_inv__id, fact_85_fun_Omap__id0, fact_124_c1__on__open__R2_Oreal__of__linear, fact_173_inj__on__imp__inj__on__swap, fact_248_inv__f__f, fact_114_left__right__inverse__eq, fact_12_comp__cong, fact_221_vector__eq, fact_66_complex__of__real__of, fact_97_bij__betw__comp__iff, fact_50_top__apply, fact_209_Sup_OSUP__image, fact_25_rewriteR__comp__comp, fact_138_swap__image__eq, fact_190_surj__id, fact_253_inv__inv__eq, fact_159_update__accessor__updator__eqE, fact_74_id__apply, fact_14_pathstart__linear__image__eq, fact_225_inner__eq__zero__iff, fact_95_bij__pointE, tcon_fun___Topological__Spaces_Otopological__space, fact_93_bij__betw__iff__bijections, fact_92_bij__betw__id__iff, fact_142_surj__swap__iff, subcl_Executable__Euclidean__Space_Oexecutable__euclidean__space___Real__Vector__Spaces_Oreal__normed__vector, fact_13_comp__eq__dest__lhs, fact_102_inj__on__id, fact_71_path__linear__image__eq, fact_219_adjoint__works, fact_232_inv__swap__id, fact_18_linear__compose, fact_72_linear__inj__iff__eq__0, fact_117_bijI_H, fact_1_assms_I1_J, fact_244_surj__f__inv__f, fact_228_inner__zero__left, tcon_Complex_Ocomplex___Topological__Spaces_Otopological__space_9, fact_78_id__comp, fact_20_pathfinish__rectpath, fact_145_the__inv__into__onto, fact_123_c1__on__open__R2_Ocomplex__of__linear, fact_107_pathstart__def, tcon_Real_Oreal___Inner__Product_Oreal__inner, fact_198_bij__betw__def, fact_51_bounded__linear_Ointro, fact_2_a1, fact_11_comp__eq__elim, tcon_Set_Oset___Orderings_Otop_2, fact_90_bij__betw__cong, fact_10_comp__eq__dest, fact_169_surjI, fact_41_fun_Oinj__map, fact_204_surj__fun__eq, fact_247_surj__imp__inv__eq, subcl_Executable__Euclidean__Space_Oexecutable__euclidean__space___HOL_Otype, fact_127_c1__on__open__R2_Oreal__of__complex__of, fact_46_Collect__mem__eq, fact_109_bij__is__inj, fact_53_arc__linear__image__eq, tcon_Real_Oreal___Real__Vector__Spaces_Oreal__vector, fact_224_coplanar__linear__image, fact_201_bijI, fact_31_inj__onD, fact_239_inv__into__f__eq, fact_100_comp__eq__id__dest, fact_75_top1I, fact_216_linear__singular__into__hyperplane, fact_178_swap__general, fact_152_surj__imp__surj__swap, fact_33_inj__on__def, fact_7_complex__of__linear, tcon_Int_Oint___Topological__Spaces_Otopological__space_1, fact_82_DEADID_Oin__rel, fact_89_bij__betw__inv, fact_177_bij__betw__the__inv__into, fact_141_swap__comp__involutory, fact_194_bij__betw__imp__surj, fact_212_adjoint__adjoint, subcl_Executable__Euclidean__Space_Oexecutable__euclidean__space___Real__Vector__Spaces_Oreal__vector, fact_214_linear__surj__adj__imp__inj, fact_179_swap__id__common, fact_112_left__inverse__linear, fact_182_fun_Oinj__map__strong, fact_26_rewriteL__comp__comp, fact_3_comp__apply, fact_197_bij__betw__imageI, fact_73_type__copy__map__cong0, fact_147_comp__swap, fact_240_bij__betw__inv__into, fact_121_c1__on__open__R2_Oreal__of__bounded__linear, fact_246_image__f__inv__f, fact_161_ball__imageD, fact_39_inj__on__imageI2, fact_15_pathfinish__linear__image, tcon_Real_Oreal___Euclidean__Space_Oeuclidean__space, fact_143_bij__swap__iff, fact_134_swap__nilpotent, fact_86_id__def, fact_32_inj__onI, fact_241_inv__into__inv__into__eq, tcon_HOL_Obool___Orderings_Otop_5, tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector, fact_222_vector__eq__ldot, fact_57_arc__distinct__ends, fact_164_image__iff, fact_166_inj__on__image__iff, subcl_Executable__Euclidean__Space_Oexecutable__euclidean__space___Inner__Product_Oreal__inner, fact_184_fun_Omap__cong, fact_38_inj__compose, fact_8_comp__def, fact_125_comp__apply__eq, fact_238_inv__equality, fact_171_rangeI, fact_34_inj__on__cong, tcon_Complex_Ocomplex___Real__Vector__Spaces_Oreal__vector_11, fact_45_mem__Collect__eq, fact_206_Sup_OSUP__id__eq, fact_137_image__id, fact_215_coplanar__linear__image__eq, fact_28_injI, fact_200_bij__def, fact_54_real__of__inj, fact_133_image__eqI, fact_88_eq__id__iff, fact_203_linear__inj__imp__surj, fact_176_f__the__inv__into__f__bij__betw, fact_148_the__inv__into__comp, fact_165_imageI, fact_131_iso__tuple__update__accessor__eq__assist__idI, fact_140_bij__betw__swap__iff, fact_118_bij__iff, fact_29_inj__eq, fact_158_update__accessor__accessor__eqE, fact_16_bounded__linear_Olinear, fact_130_linear__surjective__right__inverse, fact_17_linear__conv__bounded__linear, fact_47_Collect__cong, fact_80_bij__betw__id, fact_139_inj__on__swap__iff, fact_168_surjE, fact_61_simple__path__imp__arc, fact_163_bex__imageD, fact_233_inj__linear__imp__inv__linear, fact_150_image__comp, tcon_fun___Orderings_Otop, tcon_HOL_Obool___Topological__Spaces_Otopological__space_4, fact_210_inj__adjoint__iff__surj, fact_223_vector__eq__rdot, tcon_Real_Oreal___Topological__Spaces_Otopological__space_6, fact_104_module__hom__id, fact_189_range__ex1__eq, fact_81_bij__id, fact_35_inj__on__eq__iff, fact_111_linear__inverse__left, fact_68_real__of__bij, fact_87_bij__betwE, fact_252_bij__inv__eq__iff, fact_205_Inf_OINF__id__eq, tcon_Complex_Ocomplex___Groups_Ozero_13, fact_157_iso__tuple__update__accessor__eq__assist__triv, fact_243_bij__betw__inv__into__right, fact_235_o__inv__o__cancel, tcon_Real_Oreal___Executable__Euclidean__Space_Oexecutable__euclidean__space, fact_154_f__the__inv__into__f, fact_105_linear__simps_I3_J, fact_67_real__of__complex__of, fact_43_real__of__linear, fact_52_bounded__linear__def, fact_254_surj__imp__inj__inv, fact_108_bij__comp, fact_167_surjD, fact_23_rewriteR__comp__comp2, fact_83_top__conj_I1_J, fact_180_swap__id__common_H, fact_207_Inf_OINF__image, fact_5_pathstart__compose, fact_19__092_060open_062_092_060And_062g_O_Ainj_Acomplex__of_A_092_060Longrightarrow_062_Asimple__path_A_Icomplex__of_A_092_060circ_062_Ag_J_A_061_Asimple__path_Ag_092_060close_062, fact_220_adjoint__clauses_I2_J, fact_70_linear__injective__left__inverse, fact_174_the__inv__into__f__eq, fact_106_linear__0, fact_162_image__cong, fact_155_swap__commute, tcon_Set_Oset___Groups_Ozero_3, fact_185_fun_Oset__map, fact_21_pathstart__rectpath, fact_98_bij__betw__imp__inj__on, fact_236_inv__into__f__f, fact_9_comp__assoc, fact_149_image__eq__imp__comp, fact_91_bij__betw__apply, fact_44_iso__tuple__UNIV__I, fact_251_bij__imp__bij__inv, fact_113_top__empty__eq, fact_99_pointfree__idE, fact_175_the__inv__into__f__f, fact_193_comp__inj__on, fact_153_inj__on__the__inv__into, fact_250_inj__imp__inv__eq, fact_208_bij__betwI_H, fact_24_rewriteL__comp__comp2, fact_64_arc__simple__path, subcl_Executable__Euclidean__Space_Oexecutable__euclidean__space___Topological__Spaces_Otopological__space, tcon_Complex_Ocomplex___Real__Vector__Spaces_Oreal__normed__vector_8, fact_195_bij__is__surj, fact_234_inv__o__cancel, fact_56_arc__imp__simple__path, fact_58_bounded__linear_Oaxioms_I2_J, fact_60_UNIV__witness, fact_116_isomorphism__expand, fact_96_bij__betw__trans, subcl_Executable__Euclidean__Space_Oexecutable__euclidean__space___Euclidean__Space_Oeuclidean__space, fact_144_swap__id__idempotent, fact_181_swap__id__independent, fact_22_bounded__linear_Obounded__linear, fact_129_the__inv__f__o__f__id, fact_187_inj__image__mem__iff, fact_55_top__set__def, fact_229_aff__dim__injective__linear__image, fact_37_inj__on__inverseI, fact_84_top__conj_I2_J, fact_183_fun_Omap__cong0, fact_156_swap__triple, fact_213_adjoint__linear, fact_226_inner__zero__right, fact_63_simple__path__cases, fact_128_c1__on__open__R2_Ocomplex__of__bij, fact_188_inj__image__eq__iff, fact_217_adjoint__unique, fact_115_zero__reorient, fact_218_hyperplane__eq__Ex, fact_146_swap__id__eq, fact_42_real__of__bounded__linear, fact_36_inj__on__contraD, tcon_Complex_Ocomplex___Inner__Product_Oreal__inner_12, tcon_Real_Oreal___Groups_Ozero_7, fact_132_bij__swap__compose__bij, fact_49_UNIV__I, fact_245_surj__iff__all, fact_120_c1__on__open__R2_Oreal__of__bij, fact_76_path__rectpath, fact_135_swap__self
% 69.04/40.69 % No. of inferences in proof: 598
% 69.04/40.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 40333 ms resp. 39499 ms w/o parsing
% 70.87/40.99 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 70.87/40.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------