%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP023^7 : TPTP v9.3.1. Bugfixed 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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:27 AM UTC 2026
% Result : Theorem 57.99s 18.67s
% Output : Refutation 61.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 410
% Syntax : Number of formulae : 822 ( 425 unt; 0 typ; 0 def)
% Number of atoms : 3583 ( 936 equ; 0 cnn)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 10342 ( 90 ~; 42 |; 658 &;9058 @)
% ( 0 <=>; 494 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 24 ( 23 usr)
% Number of type conns : 1144 (1144 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 46 usr; 2 con; 0-10 aty)
% Number of variables : 2892 ( 56 ^;2678 !; 158 ?;2892 :)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Eind_type,type,
tyop_2Emin_2Eind: $tType ).
thf(tyop_2Enum_2Enum_type,type,
tyop_2Enum_2Enum: $tType ).
thf(tyop_2Eone_2Eone_type,type,
tyop_2Eone_2Eone: $tType ).
thf(tyop_2Estring_2Echar_type,type,
tyop_2Estring_2Echar: $tType ).
thf(tyop_2EternaryComparisons_2Eordering_type,type,
tyop_2EternaryComparisons_2Eordering: $tType ).
thf(tyop_2Ehrat_2Ehrat_type,type,
tyop_2Ehrat_2Ehrat: $tType ).
thf(tyop_2Einteger_2Eint_type,type,
tyop_2Einteger_2Eint: $tType ).
thf(tyop_2Equote_2Eindex_type,type,
tyop_2Equote_2Eindex: $tType ).
thf(tyop_2Etoto_2Enum__dt_type,type,
tyop_2Etoto_2Enum__dt: $tType ).
thf(tyop_2Ehreal_2Ehreal_type,type,
tyop_2Ehreal_2Ehreal: $tType ).
thf(tyop_2EDeepSyntax_2Edeep__form_type,type,
tyop_2EDeepSyntax_2Edeep__form: $tType ).
thf(tyop_2Erealax_2Ereal_type,type,
tyop_2Erealax_2Ereal: $tType ).
thf(tyop_2Efrac_2Efrac_type,type,
tyop_2Efrac_2Efrac: $tType ).
thf(tyop_2Erat_2Erat_type,type,
tyop_2Erat_2Erat: $tType ).
thf(tyop_2Ebinary__ieee_2Eflags_type,type,
tyop_2Ebinary__ieee_2Eflags: $tType ).
thf(tyop_2Ebinary__ieee_2Efloat__compare_type,type,
tyop_2Ebinary__ieee_2Efloat__compare: $tType ).
thf(tyop_2Ebinary__ieee_2Efloat__value_type,type,
tyop_2Ebinary__ieee_2Efloat__value: $tType ).
thf(tyop_2Ebinary__ieee_2Erounding_type,type,
tyop_2Ebinary__ieee_2Erounding: $tType ).
thf(tyop_2Eieee_2Eccode_type,type,
tyop_2Eieee_2Eccode: $tType ).
thf(tyop_2Eieee_2Efloat_type,type,
tyop_2Eieee_2Efloat: $tType ).
thf(tyop_2Eieee_2Eroundmode_type,type,
tyop_2Eieee_2Eroundmode: $tType ).
thf(tyop_2Eextreal_2Eextreal_type,type,
tyop_2Eextreal_2Eextreal: $tType ).
thf(c_2Ebool_2EIN_decl,type,
c_2Ebool_2EIN:
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf(c_2Epair_2E_2C_decl,type,
c_2Epair_2E_2C:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( tyop_2Epair_2Eprod @ TB @ TA ) ) ).
thf(c_2Epair_2ECURRY_decl,type,
c_2Epair_2ECURRY:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( ( tyop_2Epair_2Eprod @ TC @ TB ) > TA ) > TC > TB > TA ) ).
thf(c_2Epair_2ELEX_decl,type,
c_2Epair_2ELEX:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( TA > TA > $o ) > ( tyop_2Epair_2Eprod @ TB @ TA ) > ( tyop_2Epair_2Eprod @ TB @ TA ) > $o ) ).
thf(c_2Epair_2EPROD__ALL_decl,type,
c_2Epair_2EPROD__ALL:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TA > $o ) > ( tyop_2Epair_2Eprod @ TB @ TA ) > $o ) ).
thf(c_2Eposet_2Erelation_decl,type,
c_2Eposet_2Erelation:
!>[TA: $tType] : ( ( tyop_2Epair_2Eprod @ ( TA > $o ) @ ( TA > TA > $o ) ) > TA > TA > $o ) ).
thf(c_2Epred__set_2EBIGINTER_decl,type,
c_2Epred__set_2EBIGINTER:
!>[TA: $tType] : ( ( ( TA > $o ) > $o ) > TA > $o ) ).
thf(c_2Epred__set_2EDIFF_decl,type,
c_2Epred__set_2EDIFF:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA > $o ) ).
thf(c_2Epred__set_2EEMPTY_decl,type,
c_2Epred__set_2EEMPTY:
!>[TA: $tType] : ( TA > $o ) ).
thf(c_2Epred__set_2EGSPEC_decl,type,
c_2Epred__set_2EGSPEC:
!>[TA: $tType,TB: $tType] : ( ( TA > ( tyop_2Epair_2Eprod @ TB @ $o ) ) > TB > $o ) ).
thf(c_2Epred__set_2EIMAGE_decl,type,
c_2Epred__set_2EIMAGE:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( TB > $o ) > TA > $o ) ).
thf(c_2Epred__set_2EINTER_decl,type,
c_2Epred__set_2EINTER:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA > $o ) ).
thf(c_2Epred__set_2ESUBSET_decl,type,
c_2Epred__set_2ESUBSET:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > $o ) ).
thf(c_2Epred__set_2EUNION_decl,type,
c_2Epred__set_2EUNION:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA > $o ) ).
thf(c_2Estate__transformer_2EREAD_decl,type,
c_2Estate__transformer_2EREAD:
!>[TA: $tType,TB: $tType] : ( ( TA > TB ) > TA > ( tyop_2Epair_2Eprod @ TB @ TA ) ) ).
thf(c_2Etransfer_2EPAIR__REL_decl,type,
c_2Etransfer_2EPAIR__REL:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > TC > $o ) > ( TB > TA > $o ) > ( tyop_2Epair_2Eprod @ TD @ TB ) > ( tyop_2Epair_2Eprod @ TC @ TA ) > $o ) ).
thf(c_2Ewellorder_2EChain_decl,type,
c_2Ewellorder_2EChain:
!>[TA: $tType] : ( ( ( tyop_2Epair_2Eprod @ TA @ TA ) > $o ) > ( TA > $o ) > $o ) ).
thf(c_2Ewellorder_2Efl_decl,type,
c_2Ewellorder_2Efl:
!>[TA: $tType] : ( ( ( tyop_2Epair_2Eprod @ TA @ TA ) > $o ) > TA > $o ) ).
thf(c_2Ewellorder_2Eposet_decl,type,
c_2Ewellorder_2Eposet:
!>[TA: $tType] : ( ( ( tyop_2Epair_2Eprod @ TA @ TA ) > $o ) > $o ) ).
thf(c_2Epath_2Eparallel__comp_decl,type,
c_2Epath_2Eparallel__comp:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( ( TE > TD > TC > $o ) > ( TB > TD > TA > $o ) > ( tyop_2Epair_2Eprod @ TE @ TB ) > TD > ( tyop_2Epair_2Eprod @ TC @ TA ) > $o ) ).
thf(c_2EternaryComparisons_2Epair__compare_decl,type,
c_2EternaryComparisons_2Epair__compare:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > TC > tyop_2EternaryComparisons_2Eordering ) > ( TB > TA > tyop_2EternaryComparisons_2Eordering ) > ( tyop_2Epair_2Eprod @ TD @ TB ) > ( tyop_2Epair_2Eprod @ TC @ TA ) > tyop_2EternaryComparisons_2Eordering ) ).
thf(c_2Efmapal_2EAP__SND_decl,type,
c_2Efmapal_2EAP__SND:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB > TA ) > ( tyop_2Epair_2Eprod @ TC @ TB ) > ( tyop_2Epair_2Eprod @ TC @ TA ) ) ).
thf(c_2Erealax_2Ereal__add_decl,type,
c_2Erealax_2Ereal__add: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Erealax_2Ereal__lt_decl,type,
c_2Erealax_2Ereal__lt: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o ).
thf(c_2Erealax_2Ereal__mul_decl,type,
c_2Erealax_2Ereal__mul: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Ereal_2Emax_decl,type,
c_2Ereal_2Emax: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Ereal_2Emin_decl,type,
c_2Ereal_2Emin: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Ereal_2Ereal__lte_decl,type,
c_2Ereal_2Ereal__lte: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o ).
thf(c_2Elim_2Econtl_decl,type,
c_2Elim_2Econtl: ( tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal > $o ).
thf(c_2Etransc_2EDint_decl,type,
c_2Etransc_2EDint: ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) > ( tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal > $o ).
thf(c_2Eintegral_2Eintegrable_decl,type,
c_2Eintegral_2Eintegrable: ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) > ( tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ) > $o ).
thf(c_2Eintegral_2Eintegral_decl,type,
c_2Eintegral_2Eintegral: ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) > ( tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
thf(c_2Ereal__topology_2EClosed_decl,type,
c_2Ereal__topology_2EClosed: ( tyop_2Erealax_2Ereal > $o ) > $o ).
thf(c_2Ereal__topology_2EDist_decl,type,
c_2Ereal__topology_2EDist: ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
thf(c_2Ereal__topology_2EOpen_decl,type,
c_2Ereal__topology_2EOpen: ( tyop_2Erealax_2Ereal > $o ) > $o ).
thf(c_2Ereal__topology_2Eball_decl,type,
c_2Ereal__topology_2Eball: ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal > $o ).
thf(c_2Ereal__topology_2Ebetween_decl,type,
c_2Ereal__topology_2Ebetween: tyop_2Erealax_2Ereal > ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) > $o ).
thf(c_2Ereal__topology_2Ebounded__def_decl,type,
c_2Ereal__topology_2Ebounded__def: ( tyop_2Erealax_2Ereal > $o ) > $o ).
thf(c_2Ereal__topology_2Ecball_decl,type,
c_2Ereal__topology_2Ecball: ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal > $o ).
thf(c_2Ereal__topology_2Eclosure_decl,type,
c_2Ereal__topology_2Eclosure: ( tyop_2Erealax_2Ereal > $o ) > tyop_2Erealax_2Ereal > $o ).
thf(c_2Ereal__topology_2Econnected_decl,type,
c_2Ereal__topology_2Econnected: ( tyop_2Erealax_2Ereal > $o ) > $o ).
thf(c_2Ereal__topology_2Efrontier_decl,type,
c_2Ereal__topology_2Efrontier: ( tyop_2Erealax_2Ereal > $o ) > tyop_2Erealax_2Ereal > $o ).
thf(c_2Ereal__topology_2Einterior_decl,type,
c_2Ereal__topology_2Einterior: ( tyop_2Erealax_2Ereal > $o ) > tyop_2Erealax_2Ereal > $o ).
thf(c_2Ereal__topology_2Emidpoint_decl,type,
c_2Ereal__topology_2Emidpoint: ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
thf(c_2Ereal__topology_2Esphere_decl,type,
c_2Ereal__topology_2Esphere: ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal > $o ).
thf(258,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Einterior @ A ) @ ( c_2Ereal__topology_2Einterior @ B ) ) @ ( c_2Ereal__topology_2Einterior @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EUNION__INTERIOR__SUBSET) ).
thf(1322,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Einterior @ A ) @ ( c_2Ereal__topology_2Einterior @ B ) ) @ ( c_2Ereal__topology_2Einterior @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(182,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B )
& ( c_2Ereal__topology_2EClosed @ B ) )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__MINIMAL) ).
thf(1036,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B )
& ( c_2Ereal__topology_2EClosed @ B ) )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(311,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EClosed @ A )
& ( ( c_2Ereal__topology_2Einterior @ B )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) )
=> ( ( c_2Ereal__topology_2Einterior @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Ereal__topology_2Einterior @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__CLOSED__UNION__EMPTY__INTERIOR) ).
thf(1501,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EClosed @ A )
& ( ( c_2Ereal__topology_2Einterior @ B )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) )
=> ( ( c_2Ereal__topology_2Einterior @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Ereal__topology_2Einterior @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(221,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte @ B @ ( c_2Ereal_2Emax @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__MAX2) ).
thf(1190,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte @ B @ ( c_2Ereal_2Emax @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(104,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ A @ B )
= ( c_2Erealax_2Ereal__mul @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MUL__COMM) ).
thf(760,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ A @ B )
= ( c_2Erealax_2Ereal__mul @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(386,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( ( ( c_2Ereal__topology_2Emidpoint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
= A )
= ( A = B ) )
& ( ( ( c_2Ereal__topology_2Emidpoint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
= B )
= ( A = B ) )
& ( ( A
= ( c_2Ereal__topology_2Emidpoint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( A = B ) )
& ( ( B
= ( c_2Ereal__topology_2Emidpoint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EMIDPOINT__EQ__ENDPOINT) ).
thf(1767,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( ( ( c_2Ereal__topology_2Emidpoint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
= A )
= ( A = B ) )
& ( ( ( c_2Ereal__topology_2Emidpoint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
= B )
= ( A = B ) )
& ( ( A
= ( c_2Ereal__topology_2Emidpoint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( A = B ) )
& ( ( B
= ( c_2Ereal__topology_2Emidpoint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o] :
( ( ! [C: TB,D: TB] :
( ( ( c_2Ebool_2EIN @ TB @ C @ B )
& ( c_2Ebool_2EIN @ TB @ D @ B )
& ( ( A @ C )
= ( A @ D ) ) )
=> ( C = D ) ) )
= ( ? [C: TA > TB] :
! [D: TB] :
( ( c_2Ebool_2EIN @ TB @ D @ B )
=> ( ( C @ ( A @ D ) )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EINJECTIVE__ON__LEFT__INVERSE) ).
thf(468,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o] :
( ( ! [C: TB,D: TB] :
( ( ( c_2Ebool_2EIN @ TB @ C @ B )
& ( c_2Ebool_2EIN @ TB @ D @ B )
& ( ( A @ C )
= ( A @ D ) ) )
=> ( C = D ) ) )
= ( ? [C: TA > TB] :
! [D: TB] :
( ( c_2Ebool_2EIN @ TB @ D @ B )
=> ( ( C @ ( A @ D ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(156,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__APP) ).
thf(941,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(254,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Emax @ A @ B )
= ( c_2Ereal_2Emax @ B @ A ) )
& ( ( c_2Ereal_2Emax @ ( c_2Ereal_2Emax @ A @ B ) @ C )
= ( c_2Ereal_2Emax @ A @ ( c_2Ereal_2Emax @ B @ C ) ) )
& ( ( c_2Ereal_2Emax @ A @ ( c_2Ereal_2Emax @ B @ C ) )
= ( c_2Ereal_2Emax @ B @ ( c_2Ereal_2Emax @ A @ C ) ) )
& ( ( c_2Ereal_2Emax @ A @ A )
= A )
& ( ( c_2Ereal_2Emax @ A @ ( c_2Ereal_2Emax @ A @ B ) )
= ( c_2Ereal_2Emax @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MAX__ACI) ).
thf(1295,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Emax @ A @ B )
= ( c_2Ereal_2Emax @ B @ A ) )
& ( ( c_2Ereal_2Emax @ ( c_2Ereal_2Emax @ A @ B ) @ C )
= ( c_2Ereal_2Emax @ A @ ( c_2Ereal_2Emax @ B @ C ) ) )
& ( ( c_2Ereal_2Emax @ A @ ( c_2Ereal_2Emax @ B @ C ) )
= ( c_2Ereal_2Emax @ B @ ( c_2Ereal_2Emax @ A @ C ) ) )
& ( ( c_2Ereal_2Emax @ A @ A )
= A )
& ( ( c_2Ereal_2Emax @ A @ ( c_2Ereal_2Emax @ A @ B ) )
= ( c_2Ereal_2Emax @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(324,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( tyop_2Epair_2Eprod @ TC @ TB ) > TA,B: ( tyop_2Epair_2Eprod @ TC @ TB ) > TA] :
( ( ( c_2Epair_2ECURRY @ TC @ TB @ TA @ B )
= ( c_2Epair_2ECURRY @ TC @ TB @ TA @ A ) )
= ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2ECURRY__ONE__ONE__THM) ).
thf(1549,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( tyop_2Epair_2Eprod @ TC @ TB ) > TA,B: ( tyop_2Epair_2Eprod @ TC @ TB ) > TA] :
( ( ( c_2Epair_2ECURRY @ TC @ TB @ TA @ B )
= ( c_2Epair_2ECURRY @ TC @ TB @ TA @ A ) )
= ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(200,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Einterior @ A ) )
= ( c_2Ereal__topology_2EOpen @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESUBSET__INTERIOR__EQ) ).
thf(1110,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Einterior @ A ) )
= ( c_2Ereal__topology_2EOpen @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(363,axiom,
! [A: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Einterior @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__SUBSET) ).
thf(1686,plain,
! [A: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Einterior @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(178,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Eclosure @ A )
= A )
= ( c_2Ereal__topology_2EClosed @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__EQ) ).
thf(1024,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Eclosure @ A )
= A )
= ( c_2Ereal__topology_2EClosed @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(301,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ B )
= ( c_2Epred__set_2EUNION @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__COMM) ).
thf(1469,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ B )
= ( c_2Epred__set_2EUNION @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(164,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EClosed @ A )
& ( c_2Ereal__topology_2EClosed @ B )
& ( c_2Ereal__topology_2Econnected @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) )
& ( c_2Ereal__topology_2Econnected @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) )
=> ( ( c_2Ereal__topology_2Econnected @ A )
& ( c_2Ereal__topology_2Econnected @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__FROM__CLOSED__UNION__AND__INTER) ).
thf(977,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EClosed @ A )
& ( c_2Ereal__topology_2EClosed @ B )
& ( c_2Ereal__topology_2Econnected @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) )
& ( c_2Ereal__topology_2Econnected @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) )
=> ( ( c_2Ereal__topology_2Econnected @ A )
& ( c_2Ereal__topology_2Econnected @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(230,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( c_2Ereal_2Ereal__lte @ B @ A ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__ANTISYM) ).
thf(1211,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( c_2Ereal_2Ereal__lte @ B @ A ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(171,axiom,
! [TA: $tType,A: TA > $o] :
( ( ? [B: TA] : ( c_2Ebool_2EIN @ TA @ B @ A ) )
= ( A
!= ( c_2Epred__set_2EEMPTY @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EMEMBER__NOT__EMPTY) ).
thf(1005,plain,
! [TA: $tType,A: TA > $o] :
( ( ? [B: TA] : ( c_2Ebool_2EIN @ TA @ B @ A ) )
= ( A
!= ( c_2Epred__set_2EEMPTY @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(284,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ A )
& ( c_2Ereal__topology_2EOpen @ B ) )
=> ( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ A ) ) @ ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__CLOSURE__INTER__OPEN) ).
thf(1406,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ A )
& ( c_2Ereal__topology_2EOpen @ B ) )
=> ( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ A ) ) @ ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(253,axiom,
! [TA: $tType] :
( ! [A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) )
& ! [A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__UNION) ).
thf(1290,plain,
! [TA: $tType] :
( ! [A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) )
& ! [A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(282,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ ( c_2Epred__set_2EINTER @ TA @ B @ C ) )
= ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EINTER @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__ASSOC) ).
thf(1401,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ ( c_2Epred__set_2EINTER @ TA @ B @ C ) )
= ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EINTER @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(227,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) ) ) @ D )
=> ( c_2Erealax_2Ereal__lt @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EDIST__TRIANGLE__LT) ).
thf(1205,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) ) ) @ D )
=> ( c_2Erealax_2Ereal__lt @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(13,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
~ ( ( c_2Erealax_2Ereal__lt @ A @ B )
& ( c_2Ereal_2Ereal__lte @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LET__ANTISYM) ).
thf(440,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
~ ( ( c_2Erealax_2Ereal__lt @ A @ B )
& ( c_2Ereal_2Ereal__lte @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(391,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TA > TA > $o,C: tyop_2Epair_2Eprod @ TB @ TA,D: tyop_2Epair_2Eprod @ TB @ TA,E: TB > TB > $o,F: TA > TA > $o,G: tyop_2Epair_2Eprod @ TB @ TA,H: tyop_2Epair_2Eprod @ TB @ TA] :
( ( ( C = G )
& ( D = H )
& ! [I: TB,J: TA,K: TB,L: TA] :
( ( ( G
= ( c_2Epair_2E_2C @ TB @ TA @ I @ J ) )
& ( H
= ( c_2Epair_2E_2C @ TB @ TA @ K @ L ) ) )
=> ( ( A @ I @ K )
= ( E @ I @ K ) ) )
& ! [I: TB,J: TA,K: TB,L: TA] :
( ( ( G
= ( c_2Epair_2E_2C @ TB @ TA @ I @ J ) )
& ( H
= ( c_2Epair_2E_2C @ TB @ TA @ K @ L ) )
& ( I = K ) )
=> ( ( B @ J @ L )
= ( F @ J @ L ) ) ) )
=> ( ( c_2Epair_2ELEX @ TB @ TA @ A @ B @ C @ D )
= ( c_2Epair_2ELEX @ TB @ TA @ E @ F @ G @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2ELEX__CONG) ).
thf(1793,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TA > TA > $o,C: tyop_2Epair_2Eprod @ TB @ TA,D: tyop_2Epair_2Eprod @ TB @ TA,E: TB > TB > $o,F: TA > TA > $o,G: tyop_2Epair_2Eprod @ TB @ TA,H: tyop_2Epair_2Eprod @ TB @ TA] :
( ( ( C = G )
& ( D = H )
& ! [I: TB,J: TA,K: TB,L: TA] :
( ( ( G
= ( c_2Epair_2E_2C @ TB @ TA @ I @ J ) )
& ( H
= ( c_2Epair_2E_2C @ TB @ TA @ K @ L ) ) )
=> ( ( A @ I @ K )
= ( E @ I @ K ) ) )
& ! [I: TB,J: TA,K: TB,L: TA] :
( ( ( G
= ( c_2Epair_2E_2C @ TB @ TA @ I @ J ) )
& ( H
= ( c_2Epair_2E_2C @ TB @ TA @ K @ L ) )
& ( I = K ) )
=> ( ( B @ J @ L )
= ( F @ J @ L ) ) ) )
=> ( ( c_2Epair_2ELEX @ TB @ TA @ A @ B @ C @ D )
= ( c_2Epair_2ELEX @ TB @ TA @ E @ F @ G @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(63,axiom,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2EIN @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ENOT__IN__EMPTY) ).
thf(597,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2EIN @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(185,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ! [D: tyop_2Erealax_2Ereal] :
( ( ? [E: tyop_2Erealax_2Ereal] :
( ( ^ [F: tyop_2Erealax_2Ereal] : ( A @ ( c_2Erealax_2Ereal__add @ F @ C ) )
@ E )
& ( c_2Erealax_2Ereal__lt @ D @ E ) ) )
= ( c_2Erealax_2Ereal__lt @ D @ B ) )
=> ! [D: tyop_2Erealax_2Ereal] :
( ( ? [E: tyop_2Erealax_2Ereal] :
( ( A @ E )
& ( c_2Erealax_2Ereal__lt @ D @ E ) ) )
= ( c_2Erealax_2Ereal__lt @ D @ ( c_2Erealax_2Ereal__add @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2ESUP__LEMMA1) ).
thf(1041,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ! [D: tyop_2Erealax_2Ereal] :
( ( ? [E: tyop_2Erealax_2Ereal] :
( ( A @ ( c_2Erealax_2Ereal__add @ E @ C ) )
& ( c_2Erealax_2Ereal__lt @ D @ E ) ) )
= ( c_2Erealax_2Ereal__lt @ D @ B ) )
=> ! [D: tyop_2Erealax_2Ereal] :
( ( ? [E: tyop_2Erealax_2Ereal] :
( ( A @ E )
& ( c_2Erealax_2Ereal__lt @ D @ E ) ) )
= ( c_2Erealax_2Ereal__lt @ D @ ( c_2Erealax_2Ereal__add @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(399,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Epair_2Eprod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( c_2Epair_2E_2C @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2EABS__PAIR__THM) ).
thf(1855,plain,
! [TA: $tType,TB: $tType,A: tyop_2Epair_2Eprod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( c_2Epair_2E_2C @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(225,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ( c_2Ereal_2Ereal__lte @ C @ D )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A ) )
=> ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ D ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EINTEGRABLE__COMBINE) ).
thf(1200,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ( c_2Ereal_2Ereal__lte @ C @ D )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A ) )
=> ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(206,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ! [B: TB > $o,C: TB > $o] :
( ( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ B )
= ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ C ) )
=> ( B = C ) ) )
= ( ! [B: TB,C: TB] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EINJECTIVE__IMAGE) ).
thf(1142,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ! [B: TB > $o,C: TB > $o] :
( ( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ B )
= ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ C ) )
=> ( B = C ) ) )
= ( ! [B: TB,C: TB] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(245,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Emax @ B @ C ) @ A )
= ( ( c_2Ereal_2Ereal__lte @ B @ A )
& ( c_2Ereal_2Ereal__lte @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MAX__LE) ).
thf(1269,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Emax @ B @ C ) @ A )
= ( ( c_2Ereal_2Ereal__lte @ B @ A )
& ( c_2Ereal_2Ereal__lte @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(369,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Ebounded__def @ A )
=> ( c_2Ereal__topology_2Ebounded__def @ ( c_2Ereal__topology_2Eclosure @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__CLOSURE) ).
thf(1705,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Ebounded__def @ A )
=> ( c_2Ereal__topology_2Ebounded__def @ ( c_2Ereal__topology_2Eclosure @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(192,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ A @ B )
= ( ~ ( c_2Erealax_2Ereal__lt @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2Ereal__lte) ).
thf(1078,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ A @ B )
= ( ~ ( c_2Erealax_2Ereal__lt @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(35,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EGSPEC @ TA @ TA
@ ^ [B: TA] : ( c_2Epair_2E_2C @ TA @ $o @ B @ ( A @ B ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EGSPEC__ETA) ).
thf(500,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EGSPEC @ TA @ TA
@ ^ [B: TA] : ( c_2Epair_2E_2C @ TA @ $o @ B @ ( A @ B ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(95,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ A @ B )
= ( c_2Erealax_2Ereal__mul @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erealax_2EREAL__MUL__SYM) ).
thf(715,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ A @ B )
= ( c_2Erealax_2Ereal__mul @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(118,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__lt @ A @ B )
& ( c_2Erealax_2Ereal__lt @ B @ C ) )
=> ( c_2Erealax_2Ereal__lt @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__TRANS) ).
thf(814,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__lt @ A @ B )
& ( c_2Erealax_2Ereal__lt @ B @ C ) )
=> ( c_2Erealax_2Ereal__lt @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(313,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) ) ) @ D )
=> ( c_2Ereal_2Ereal__lte @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EDIST__TRIANGLE__LE) ).
thf(1507,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) ) ) @ D )
=> ( c_2Ereal_2Ereal__lte @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(265,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( ( c_2Epred__set_2EINTER @ TA @ B @ A )
= B )
= ( c_2Epred__set_2ESUBSET @ TA @ B @ A ) )
& ( ( ( c_2Epred__set_2EINTER @ TA @ B @ A )
= A )
= ( c_2Epred__set_2ESUBSET @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__SUBSET__EQN) ).
thf(1342,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( ( c_2Epred__set_2EINTER @ TA @ B @ A )
= B )
= ( c_2Epred__set_2ESUBSET @ TA @ B @ A ) )
& ( ( ( c_2Epred__set_2EINTER @ TA @ B @ A )
= A )
= ( c_2Epred__set_2ESUBSET @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(149,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( A = B )
| ( c_2Erealax_2Ereal__lt @ A @ B )
| ( c_2Erealax_2Ereal__lt @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erealax_2EREAL__LT__TOTAL) ).
thf(913,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( A = B )
| ( c_2Erealax_2Ereal__lt @ A @ B )
| ( c_2Erealax_2Ereal__lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(411,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Ebounded__def @ B )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B ) )
=> ( c_2Ereal__topology_2Ebounded__def @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__SUBSET) ).
thf(1914,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Ebounded__def @ B )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B ) )
=> ( c_2Ereal__topology_2Ebounded__def @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(278,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESET__EQ__SUBSET) ).
thf(1391,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(93,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
| ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__UNION) ).
thf(709,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
| ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(4,axiom,
( ( c_2Ereal__topology_2Efrontier @ ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__EMPTY) ).
thf(417,plain,
( ( c_2Ereal__topology_2Efrontier @ ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(344,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ ( c_2Ereal__topology_2Efrontier @ B ) ) @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ A ) @ ( c_2Ereal__topology_2Eclosure @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__INTER__SUBSET__INTER) ).
thf(1613,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ ( c_2Ereal__topology_2Efrontier @ B ) ) @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ A ) @ ( c_2Ereal__topology_2Eclosure @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(303,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ ( c_2Epred__set_2EINTER @ TA @ B @ C ) )
= ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ ( c_2Epred__set_2EUNION @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__OVER__UNION) ).
thf(1475,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ ( c_2Epred__set_2EINTER @ TA @ B @ C ) )
= ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ ( c_2Epred__set_2EUNION @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(340,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EClosed @ A )
& ( c_2Ereal__topology_2EClosed @ B ) )
=> ( ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ A ) ) @ ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__INTERIOR__UNION__CLOSED) ).
thf(1601,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EClosed @ A )
& ( c_2Ereal__topology_2EClosed @ B ) )
=> ( ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ A ) ) @ ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(276,axiom,
! [TA: $tType,A: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__REFL) ).
thf(1386,plain,
! [TA: $tType,A: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(252,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Econnected @ A )
& ( c_2Ereal__topology_2Econnected @ B )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) )
=> ( c_2Ereal__topology_2Econnected @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__UNION) ).
thf(1287,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Econnected @ A )
& ( c_2Ereal__topology_2Econnected @ B )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) )
=> ( c_2Ereal__topology_2Econnected @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(356,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__IDEMPOT) ).
thf(1660,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(405,axiom,
! [A: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Emidpoint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EMIDPOINT__REFL) ).
thf(1871,plain,
! [A: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Emidpoint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(401,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( c_2Estate__transformer_2EREAD @ TB @ TA @ A )
= ( ^ [B: TA] : ( c_2Epair_2E_2C @ TB @ TA @ ( A @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Estate__transformer_2EREAD__def) ).
thf(1860,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( c_2Estate__transformer_2EREAD @ TB @ TA @ A )
= ( ^ [B: TA] : ( c_2Epair_2E_2C @ TB @ TA @ ( A @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(127,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__lt @ A @ B )
& ( c_2Ereal_2Ereal__lte @ B @ C ) )
=> ( c_2Erealax_2Ereal__lt @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LTE__TRANS) ).
thf(838,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__lt @ A @ B )
& ( c_2Ereal_2Ereal__lte @ B @ C ) )
=> ( c_2Erealax_2Ereal__lt @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(315,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Epair_2Eprod @ TB @ TA,B: TA > $o,C: TA > $o,D: TB > $o,E: TB > $o] :
( ( ! [F: TB] :
( ( E @ F )
=> ( D @ F ) )
& ! [F: TA] :
( ( C @ F )
=> ( B @ F ) ) )
=> ( ( c_2Epair_2EPROD__ALL @ TB @ TA @ E @ C @ A )
=> ( c_2Epair_2EPROD__ALL @ TB @ TA @ D @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2EPROD__ALL__MONO) ).
thf(1511,plain,
! [TA: $tType,TB: $tType,A: tyop_2Epair_2Eprod @ TB @ TA,B: TA > $o,C: TA > $o,D: TB > $o,E: TB > $o] :
( ( ! [F: TB] :
( ( E @ F )
=> ( D @ F ) )
& ! [F: TA] :
( ( C @ F )
=> ( B @ F ) ) )
=> ( ( c_2Epair_2EPROD__ALL @ TB @ TA @ E @ C @ A )
=> ( c_2Epair_2EPROD__ALL @ TB @ TA @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(113,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ B )
=> ( A @ D ) )
& ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
=> ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EFORALL__IN__UNION) ).
thf(802,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ B )
=> ( A @ D ) )
& ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
=> ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(249,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Emin @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MIN__LE1) ).
thf(1279,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Emin @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(332,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ A )
& ( c_2Ereal__topology_2EOpen @ B )
& ( c_2Ereal__topology_2Econnected @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) )
& ( c_2Ereal__topology_2Econnected @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) )
=> ( ( c_2Ereal__topology_2Econnected @ A )
& ( c_2Ereal__topology_2Econnected @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__FROM__OPEN__UNION__AND__INTER) ).
thf(1577,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ A )
& ( c_2Ereal__topology_2EOpen @ B )
& ( c_2Ereal__topology_2Econnected @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) )
& ( c_2Ereal__topology_2Econnected @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) )
=> ( ( c_2Ereal__topology_2Econnected @ A )
& ( c_2Ereal__topology_2Econnected @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(47,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ B @ C )
=> ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ A @ B ) @ ( c_2Erealax_2Ereal__add @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erealax_2EREAL__LT__IADD) ).
thf(542,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ B @ C )
=> ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ A @ B ) @ ( c_2Erealax_2Ereal__add @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(285,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ A ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( ! [B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ B )
& ( B
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) )
=> ? [C: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ C )
& ( C
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ C @ B )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ C @ A )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ENOWHERE__DENSE) ).
thf(1409,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ A ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( ! [B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ B )
& ( B
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) )
=> ? [C: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ C )
& ( C
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ C @ B )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ C @ A )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(98,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ C )
= ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__COMM) ).
thf(724,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ C )
= ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(145,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ B @ A )
=> ( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__DIFF__SUBSET) ).
thf(902,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ B @ A )
=> ( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(239,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A ) )
=> ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ D ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EINTEGRABLE__SUBINTERVAL__LEFT) ).
thf(1247,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A ) )
=> ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(174,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ! [B: TA] :
? [C: TB] :
( ( A @ C )
= B ) )
= ( ! [B: TA > $o] :
( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A
@ ( c_2Epred__set_2EGSPEC @ TB @ TB
@ ^ [C: TB] : ( c_2Epair_2E_2C @ TB @ $o @ C @ ( B @ ( A @ C ) ) ) ) )
= ( c_2Epred__set_2EGSPEC @ TA @ TA
@ ^ [C: TA] : ( c_2Epair_2E_2C @ TA @ $o @ C @ ( B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ESURJECTIVE__IMAGE__THM) ).
thf(1013,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ! [B: TA] :
? [C: TB] :
( ( A @ C )
= B ) )
= ( ! [B: TA > $o] :
( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A
@ ( c_2Epred__set_2EGSPEC @ TB @ TB
@ ^ [C: TB] : ( c_2Epair_2E_2C @ TB @ $o @ C @ ( B @ ( A @ C ) ) ) ) )
= ( c_2Epred__set_2EGSPEC @ TA @ TA
@ ^ [C: TA] : ( c_2Epair_2E_2C @ TA @ $o @ C @ ( B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(381,axiom,
! [TA: $tType,TB: $tType,A: ( tyop_2Epair_2Eprod @ TB @ TA ) > $o] :
( ! [B: TB,C: TA] : ( A @ ( c_2Epair_2E_2C @ TB @ TA @ B @ C ) )
=> ! [B: tyop_2Epair_2Eprod @ TB @ TA] : ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2Epair__induction) ).
thf(1741,plain,
! [TA: $tType,TB: $tType,A: ( tyop_2Epair_2Eprod @ TB @ TA ) > $o] :
( ! [B: TB,C: TA] : ( A @ ( c_2Epair_2E_2C @ TB @ TA @ B @ C ) )
=> ! [B: tyop_2Epair_2Eprod @ TB @ TA] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(202,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( ( c_2Epred__set_2EINTER @ TA @ B @ C )
= ( c_2Epred__set_2EINTER @ TA @ C @ B ) )
& ( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EINTER @ TA @ B @ C ) @ A )
= ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EINTER @ TA @ B @ C ) @ A ) )
& ( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EINTER @ TA @ B @ C ) @ A )
= ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EINTER @ TA @ C @ B ) @ A ) )
& ( ( c_2Epred__set_2EINTER @ TA @ B @ B )
= B )
& ( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EINTER @ TA @ B @ B ) @ C )
= ( c_2Epred__set_2EINTER @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EINTER__ACI) ).
thf(1115,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( ( c_2Epred__set_2EINTER @ TA @ B @ C )
= ( c_2Epred__set_2EINTER @ TA @ C @ B ) )
& ( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EINTER @ TA @ B @ C ) @ A )
= ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EINTER @ TA @ C @ B ) @ A ) )
& ( ( c_2Epred__set_2EINTER @ TA @ B @ B )
= B )
& ( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EINTER @ TA @ B @ B ) @ C )
= ( c_2Epred__set_2EINTER @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(271,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ? [B: tyop_2Erealax_2Ereal] : ( A @ B )
& ? [B: tyop_2Erealax_2Ereal] :
! [C: tyop_2Erealax_2Ereal] :
( ( A @ C )
=> ( c_2Ereal_2Ereal__lte @ C @ B ) ) )
=> ? [B: tyop_2Erealax_2Ereal] :
( ! [C: tyop_2Erealax_2Ereal] :
( ( A @ C )
=> ( c_2Ereal_2Ereal__lte @ C @ B ) )
& ! [C: tyop_2Erealax_2Ereal] :
( ! [D: tyop_2Erealax_2Ereal] :
( ( A @ D )
=> ( c_2Ereal_2Ereal__lte @ D @ C ) )
=> ( c_2Ereal_2Ereal__lte @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eiterate_2EREAL__COMPLETE) ).
thf(1362,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ? [B: tyop_2Erealax_2Ereal] : ( A @ B )
& ? [B: tyop_2Erealax_2Ereal] :
! [C: tyop_2Erealax_2Ereal] :
( ( A @ C )
=> ( c_2Ereal_2Ereal__lte @ C @ B ) ) )
=> ? [B: tyop_2Erealax_2Ereal] :
( ! [C: tyop_2Erealax_2Ereal] :
( ( A @ C )
=> ( c_2Ereal_2Ereal__lte @ C @ B ) )
& ! [C: tyop_2Erealax_2Ereal] :
( ! [D: tyop_2Erealax_2Ereal] :
( ( A @ D )
=> ( c_2Ereal_2Ereal__lte @ D @ C ) )
=> ( c_2Ereal_2Ereal__lte @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(196,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o,C: TB > $o,D: TA > $o] :
( ( ( c_2Epred__set_2ESUBSET @ TB @ B @ C )
& ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ C ) @ D ) )
=> ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ B ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__SUBSET__gen) ).
thf(1100,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o,C: TB > $o,D: TA > $o] :
( ( ( c_2Epred__set_2ESUBSET @ TB @ B @ C )
& ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ C ) @ D ) )
=> ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(235,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TB ) )
= ( c_2Epred__set_2EEMPTY @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__EMPTY) ).
thf(1232,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TB ) )
= ( c_2Epred__set_2EEMPTY @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(396,axiom,
c_2Ereal__topology_2Ebounded__def @ ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__EMPTY) ).
thf(1847,plain,
c_2Ereal__topology_2Ebounded__def @ ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(257,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ A ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESUBSET__ANTISYM__EQ) ).
thf(1319,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ A ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(6,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
=> ! [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ A )
=> ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__THM) ).
thf(421,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
=> ! [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ A )
=> ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ C @ ( c_2Ereal_2Emin @ A @ B ) )
= ( ( c_2Erealax_2Ereal__lt @ C @ A )
& ( c_2Erealax_2Ereal__lt @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__MIN) ).
thf(448,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ C @ ( c_2Ereal_2Emin @ A @ B ) )
= ( ( c_2Erealax_2Ereal__lt @ C @ A )
& ( c_2Erealax_2Ereal__lt @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(308,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EDIST__TRIANGLE) ).
thf(1494,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(297,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EUNION @ TA @ B @ A ) @ B )
= B )
& ( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ B )
= B )
& ( ( c_2Epred__set_2EINTER @ TA @ B @ ( c_2Epred__set_2EUNION @ TA @ B @ A ) )
= B )
& ( ( c_2Epred__set_2EINTER @ TA @ B @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__UNION) ).
thf(1450,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EUNION @ TA @ B @ A ) @ B )
= B )
& ( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ B )
= B )
& ( ( c_2Epred__set_2EINTER @ TA @ B @ ( c_2Epred__set_2EUNION @ TA @ B @ A ) )
= B )
& ( ( c_2Epred__set_2EINTER @ TA @ B @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(61,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
~ ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( c_2Erealax_2Ereal__lt @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LTE__ANTSYM) ).
thf(591,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
~ ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( c_2Erealax_2Ereal__lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(14,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EClosed @ A )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__SUBSET__CLOSED) ).
thf(443,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EClosed @ A )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(184,axiom,
c_2Ereal__topology_2Econnected @ ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__EMPTY) ).
thf(1040,plain,
c_2Ereal__topology_2Econnected @ ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(288,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__add @ A @ B ) @ C ) )
= ( c_2Epred__set_2EIMAGE @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__add @ A ) @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECBALL__TRANSLATION) ).
thf(1418,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__add @ A @ B ) @ C ) )
= ( c_2Epred__set_2EIMAGE @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__add @ A ) @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(262,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ A )
& ( c_2Ereal__topology_2EOpen @ B ) )
=> ( c_2Ereal__topology_2EOpen @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__INTER) ).
thf(1334,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ A )
& ( c_2Ereal__topology_2EOpen @ B ) )
=> ( c_2Ereal__topology_2EOpen @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(30,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ C )
= ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EINTER @ TA @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__INTER) ).
thf(485,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ C )
= ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EINTER @ TA @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(400,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Ebounded__def @ A )
=> ( c_2Ereal__topology_2Ebounded__def @ ( c_2Ereal__topology_2Einterior @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__INTERIOR) ).
thf(1858,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Ebounded__def @ A )
=> ( c_2Ereal__topology_2Ebounded__def @ ( c_2Ereal__topology_2Einterior @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(209,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__ANTISYM) ).
thf(1151,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(275,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal_2Emin @ B @ C ) ) )
= ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECBALL__MIN__INTER) ).
thf(1383,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal_2Emin @ B @ C ) ) )
= ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(333,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ A ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__SUBSET__EQ) ).
thf(1581,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ A ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(306,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ ( c_2Ereal__topology_2Eclosure @ B ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
=> ( ( c_2Ereal__topology_2Efrontier @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ A ) @ ( c_2Ereal__topology_2Efrontier @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__UNION) ).
thf(1489,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ ( c_2Ereal__topology_2Eclosure @ B ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
=> ( ( c_2Ereal__topology_2Efrontier @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ A ) @ ( c_2Ereal__topology_2Efrontier @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(287,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ A )
=> ( ( c_2Ereal__topology_2Econnected @ A )
= ( ~ ? [B: tyop_2Erealax_2Ereal > $o,C: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ B )
& ( c_2Ereal__topology_2EOpen @ C )
& ( B
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( C
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ B @ C )
= A )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ B @ C )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__OPEN__SET) ).
thf(1415,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ A )
=> ( ( c_2Ereal__topology_2Econnected @ A )
= ( ~ ? [B: tyop_2Erealax_2Ereal > $o,C: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ B )
& ( c_2Ereal__topology_2EOpen @ C )
& ( B
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( C
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ B @ C )
= A )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ B @ C )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(146,axiom,
! [A: tyop_2Erealax_2Ereal > $o] : ( c_2Ereal__topology_2EClosed @ ( c_2Ereal__topology_2Eclosure @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSED__CLOSURE) ).
thf(905,plain,
! [A: tyop_2Erealax_2Ereal > $o] : ( c_2Ereal__topology_2EClosed @ ( c_2Ereal__topology_2Eclosure @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(28,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ B @ C )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
& ~ ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__applied) ).
thf(480,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ B @ C )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
& ~ ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(213,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ A ) ) ) )
= ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__CLOSURE__IDEMP) ).
thf(1169,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ A ) ) ) )
= ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(133,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EClosed @ A )
& ( c_2Ereal__topology_2EClosed @ B ) )
=> ( c_2Ereal__topology_2EClosed @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSED__INTER) ).
thf(866,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EClosed @ A )
& ( c_2Ereal__topology_2EClosed @ B ) )
=> ( c_2Ereal__topology_2EClosed @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(18,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EClosed @ B )
=> ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ B )
= ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__MINIMAL__EQ) ).
thf(453,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EClosed @ B )
=> ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ B )
= ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(348,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( c_2Ereal_2Ereal__lte @ C @ D ) )
=> ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ A @ C ) @ ( c_2Erealax_2Ereal__add @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__ADD2) ).
thf(1622,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( c_2Ereal_2Ereal__lte @ C @ D ) )
=> ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ A @ C ) @ ( c_2Erealax_2Ereal__add @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(279,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ C )
& ( c_2Ereal_2Ereal__lte @ B @ D ) )
=> ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Emax @ A @ B ) @ ( c_2Ereal_2Emax @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__IMP__MAX__LE2) ).
thf(1394,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ C )
& ( c_2Ereal_2Ereal__lte @ B @ D ) )
=> ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Emax @ A @ B ) @ ( c_2Ereal_2Emax @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(168,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ A @ B ) @ ( c_2Erealax_2Ereal__add @ A @ C ) )
= ( c_2Erealax_2Ereal__lt @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__LADD) ).
thf(988,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ A @ B ) @ ( c_2Erealax_2Ereal__add @ A @ C ) )
= ( c_2Erealax_2Ereal__lt @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > TB,C: TA > $o] :
( ( ? [D: TB] :
( ( c_2Ebool_2EIN @ TB @ D @ ( c_2Epred__set_2EIMAGE @ TA @ TB @ B @ C ) )
& ( A @ D ) ) )
= ( ? [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
& ( A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EEXISTS__IN__IMAGE) ).
thf(428,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > TB,C: TA > $o] :
( ( ? [D: TB] :
( ( c_2Ebool_2EIN @ TB @ D @ ( c_2Epred__set_2EIMAGE @ TA @ TB @ B @ C ) )
& ( A @ D ) ) )
= ( ? [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
& ( A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(366,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__SUBSET__CBALL) ).
thf(1697,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(42,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ A @ ( c_2Erealax_2Ereal__add @ B @ C ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ A @ B ) @ ( c_2Erealax_2Ereal__mul @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LDISTRIB) ).
thf(527,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ A @ ( c_2Erealax_2Ereal__add @ B @ C ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ A @ B ) @ ( c_2Erealax_2Ereal__mul @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(329,axiom,
! [TA: $tType] :
( ! [A: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A )
= A )
& ! [A: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__EMPTY) ).
thf(1564,plain,
! [TA: $tType] :
( ! [A: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A )
= A )
& ! [A: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(65,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Econnected @ A )
= ( ~ ? [B: tyop_2Erealax_2Ereal > $o,C: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EClosed @ B )
& ( c_2Ereal__topology_2EClosed @ C )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ B @ C ) )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ B @ C ) @ A )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ B @ A )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ C @ A )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__CLOSED) ).
thf(602,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Econnected @ A )
= ( ~ ? [B: tyop_2Erealax_2Ereal > $o,C: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EClosed @ B )
& ( c_2Ereal__topology_2EClosed @ C )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ B @ C ) )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ B @ C ) @ A )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ B @ A )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ C @ A )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(165,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal,F: tyop_2Erealax_2Ereal,G: tyop_2Erealax_2Ereal,H: tyop_2Erealax_2Ereal] :
( ( ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ E @ F ) @ C @ G )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ E @ F ) @ D @ H ) )
=> ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ E @ F )
@ ^ [I: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ B @ ( C @ I ) ) @ ( c_2Erealax_2Ereal__mul @ A @ ( D @ I ) ) )
@ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ B @ G ) @ ( c_2Erealax_2Ereal__mul @ A @ H ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EDINT__LINEAR) ).
thf(981,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal,F: tyop_2Erealax_2Ereal,G: tyop_2Erealax_2Ereal,H: tyop_2Erealax_2Ereal] :
( ( ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ E @ F ) @ C @ G )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ E @ F ) @ D @ H ) )
=> ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ E @ F )
@ ^ [I: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ B @ ( C @ I ) ) @ ( c_2Erealax_2Ereal__mul @ A @ ( D @ I ) ) )
@ ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ B @ G ) @ ( c_2Erealax_2Ereal__mul @ A @ H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(106,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ B )
= ( c_2Epred__set_2EDIFF @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__DIFF) ).
thf(766,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ B )
= ( c_2Epred__set_2EDIFF @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(296,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Eclosure @ A )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( A
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__EQ__EMPTY) ).
thf(1447,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Eclosure @ A )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( A
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(160,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A @ D ) )
=> ( ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EDINT__INTEGRAL) ).
thf(956,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A @ D ) )
=> ( ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(402,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB > TA] :
? [B: ( tyop_2Epair_2Eprod @ TC @ TB ) > TA] :
! [C: TC,D: TB] :
( ( B @ ( c_2Epair_2E_2C @ TC @ TB @ C @ D ) )
= ( A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2Epair__Axiom) ).
thf(1863,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB > TA] :
? [B: ( tyop_2Epair_2Eprod @ TC @ TB ) > TA] :
! [C: TC,D: TB] :
( ( B @ ( c_2Epair_2E_2C @ TC @ TB @ C @ D ) )
= ( A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(353,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
= ( ( c_2Epred__set_2EUNION @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__UNION__ABSORPTION) ).
thf(1651,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
= ( ( c_2Epred__set_2EUNION @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(341,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Einterior @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Einterior @ A ) @ ( c_2Ereal__topology_2Einterior @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__INTER) ).
thf(1604,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Einterior @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Einterior @ A ) @ ( c_2Ereal__topology_2Einterior @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(39,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal,F: tyop_2Erealax_2Ereal] :
( ( ! [G: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ G )
& ( c_2Ereal_2Ereal__lte @ G @ D )
& ( G != E ) )
=> ( ( A @ G )
= ( B @ G ) ) )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A @ F ) )
=> ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EDINT__POINT__SPIKE) ).
thf(512,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal,F: tyop_2Erealax_2Ereal] :
( ( ! [G: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ G )
& ( c_2Ereal_2Ereal__lte @ G @ D )
& ( G != E ) )
=> ( ( A @ G )
= ( B @ G ) ) )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A @ F ) )
=> ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o] :
( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ B )
= ( c_2Epred__set_2EGSPEC @ TA @ TB
@ ^ [C: TB] : ( c_2Epair_2E_2C @ TA @ $o @ ( A @ C ) @ ( c_2Ebool_2EIN @ TB @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__DEF) ).
thf(678,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o] :
( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ B )
= ( c_2Epred__set_2EGSPEC @ TA @ TB
@ ^ [C: TB] : ( c_2Epair_2E_2C @ TA @ $o @ ( A @ C ) @ ( c_2Ebool_2EIN @ TB @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(81,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Efrontier @ A )
= ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ ( c_2Ereal__topology_2Einterior @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2Efrontier) ).
thf(661,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Efrontier @ A )
= ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ ( c_2Ereal__topology_2Einterior @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o,C: TB] :
( ( c_2Ebool_2EIN @ TB @ C @ B )
=> ( c_2Ebool_2EIN @ TA @ ( A @ C ) @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFUN__IN__IMAGE) ).
thf(810,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o,C: TB] :
( ( c_2Ebool_2EIN @ TB @ C @ B )
=> ( c_2Ebool_2EIN @ TA @ ( A @ C ) @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(187,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ! [D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C ) )
=> ( c_2Elim_2Econtl @ A @ D ) ) )
=> ? [D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ D @ E )
& ! [F: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ D @ F )
& ( c_2Ereal_2Ereal__lte @ F @ E ) )
=> ? [G: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ G )
& ( c_2Ereal_2Ereal__lte @ G @ C )
& ( ( A @ G )
= F ) ) )
& ! [F: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ F )
& ( c_2Ereal_2Ereal__lte @ F @ C ) )
=> ( ( c_2Ereal_2Ereal__lte @ D @ ( A @ F ) )
& ( c_2Ereal_2Ereal__lte @ ( A @ F ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Elim_2ECONT__ATTAINS__ALL) ).
thf(1047,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ! [D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C ) )
=> ( c_2Elim_2Econtl @ A @ D ) ) )
=> ? [D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ D @ E )
& ! [F: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ D @ F )
& ( c_2Ereal_2Ereal__lte @ F @ E ) )
=> ? [G: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ G )
& ( c_2Ereal_2Ereal__lte @ G @ C )
& ( ( A @ G )
= F ) ) )
& ! [F: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ F )
& ( c_2Ereal_2Ereal__lte @ F @ C ) )
=> ( ( c_2Ereal_2Ereal__lte @ D @ ( A @ F ) )
& ( c_2Ereal_2Ereal__lte @ ( A @ F ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(378,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal__topology_2Ebounded__def @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__CBALL) ).
thf(1730,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal__topology_2Ebounded__def @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(247,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ A ) @ A )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( c_2Ereal__topology_2EOpen @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__DISJOINT__EQ) ).
thf(1274,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ A ) @ A )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( c_2Ereal__topology_2EOpen @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(148,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Ereal_2Emin @ A @ B ) @ C )
= ( ( c_2Erealax_2Ereal__lt @ A @ C )
| ( c_2Erealax_2Ereal__lt @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MIN__LT) ).
thf(910,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Ereal_2Emin @ A @ B ) @ C )
= ( ( c_2Erealax_2Ereal__lt @ A @ C )
| ( c_2Erealax_2Ereal__lt @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(268,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__add @ C @ B ) @ A )
= ( c_2Erealax_2Ereal__add @ C @ ( c_2Erealax_2Ereal__add @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er218) ).
thf(1355,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__add @ C @ B ) @ A )
= ( c_2Erealax_2Ereal__add @ C @ ( c_2Erealax_2Ereal__add @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(232,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ A ) )
= A )
& ( ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ B ) )
= B ) )
=> ( ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EREGULAR__CLOSED__UNION) ).
thf(1217,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ A ) )
= A )
& ( ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ B ) )
= B ) )
=> ( ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(384,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Epair_2Eprod @ TB @ TA,B: tyop_2Epair_2Eprod @ TB @ TA,C: TB > $o,D: TB > $o,E: TA > $o,F: TA > $o] :
( ( ( A = B )
& ! [G: TB,H: TA] :
( ( B
= ( c_2Epair_2E_2C @ TB @ TA @ G @ H ) )
=> ( ( C @ G )
= ( D @ G ) ) )
& ! [G: TB,H: TA] :
( ( B
= ( c_2Epair_2E_2C @ TB @ TA @ G @ H ) )
=> ( ( E @ H )
= ( F @ H ) ) ) )
=> ( ( c_2Epair_2EPROD__ALL @ TB @ TA @ C @ E @ A )
= ( c_2Epair_2EPROD__ALL @ TB @ TA @ D @ F @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2EPROD__ALL__CONG) ).
thf(1751,plain,
! [TA: $tType,TB: $tType,A: tyop_2Epair_2Eprod @ TB @ TA,B: tyop_2Epair_2Eprod @ TB @ TA,C: TB > $o,D: TB > $o,E: TA > $o,F: TA > $o] :
( ( ( A = B )
& ! [G: TB,H: TA] :
( ( B
= ( c_2Epair_2E_2C @ TB @ TA @ G @ H ) )
=> ( ( C @ G )
= ( D @ G ) ) )
& ! [G: TB,H: TA] :
( ( B
= ( c_2Epair_2E_2C @ TB @ TA @ G @ H ) )
=> ( ( E @ H )
= ( F @ H ) ) ) )
=> ( ( c_2Epair_2EPROD__ALL @ TB @ TA @ C @ E @ A )
= ( c_2Epair_2EPROD__ALL @ TB @ TA @ D @ F @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(358,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte @ A @ ( c_2Ereal_2Emax @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__MAX1) ).
thf(1666,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte @ A @ ( c_2Ereal_2Emax @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(347,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) )
= ( A
= ( c_2Epred__set_2EEMPTY @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__EMPTY) ).
thf(1619,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) )
= ( A
= ( c_2Epred__set_2EEMPTY @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(237,axiom,
! [TA: $tType,A: ( TA > $o ) > TA > $o] :
( ! [B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ B @ C )
=> ( c_2Epred__set_2ESUBSET @ TA @ ( A @ B ) @ ( A @ C ) ) )
=> ? [B: TA > $o] :
( ( A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewellorder_2ETARSKI__SET) ).
thf(1238,plain,
! [TA: $tType,A: ( TA > $o ) > TA > $o] :
( ! [B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ B @ C )
=> ( c_2Epred__set_2ESUBSET @ TA @ ( A @ B ) @ ( A @ C ) ) )
=> ? [B: TA > $o] :
( ( A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(409,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC > tyop_2EternaryComparisons_2Eordering,B: TB > TA > tyop_2EternaryComparisons_2Eordering,C: tyop_2Epair_2Eprod @ TD @ TB,D: tyop_2Epair_2Eprod @ TC @ TA,E: TD > TC > tyop_2EternaryComparisons_2Eordering,F: TB > TA > tyop_2EternaryComparisons_2Eordering,G: tyop_2Epair_2Eprod @ TD @ TB,H: tyop_2Epair_2Eprod @ TC @ TA] :
( ( ( C = G )
& ( D = H )
& ! [I: TD,J: TB,K: TC,L: TA] :
( ( ( G
= ( c_2Epair_2E_2C @ TD @ TB @ I @ J ) )
& ( H
= ( c_2Epair_2E_2C @ TC @ TA @ K @ L ) ) )
=> ( ( A @ I @ K )
= ( E @ I @ K ) ) )
& ! [I: TD,J: TB,K: TC,L: TA] :
( ( ( G
= ( c_2Epair_2E_2C @ TD @ TB @ I @ J ) )
& ( H
= ( c_2Epair_2E_2C @ TC @ TA @ K @ L ) ) )
=> ( ( B @ J @ L )
= ( F @ J @ L ) ) ) )
=> ( ( c_2EternaryComparisons_2Epair__compare @ TD @ TC @ TB @ TA @ A @ B @ C @ D )
= ( c_2EternaryComparisons_2Epair__compare @ TD @ TC @ TB @ TA @ E @ F @ G @ H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecomparison_2Epair__cmp__cong) ).
thf(1883,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC > tyop_2EternaryComparisons_2Eordering,B: TB > TA > tyop_2EternaryComparisons_2Eordering,C: tyop_2Epair_2Eprod @ TD @ TB,D: tyop_2Epair_2Eprod @ TC @ TA,E: TD > TC > tyop_2EternaryComparisons_2Eordering,F: TB > TA > tyop_2EternaryComparisons_2Eordering,G: tyop_2Epair_2Eprod @ TD @ TB,H: tyop_2Epair_2Eprod @ TC @ TA] :
( ( ( C = G )
& ( D = H )
& ! [I: TD,J: TB,K: TC,L: TA] :
( ( ( G
= ( c_2Epair_2E_2C @ TD @ TB @ I @ J ) )
& ( H
= ( c_2Epair_2E_2C @ TC @ TA @ K @ L ) ) )
=> ( ( A @ I @ K )
= ( E @ I @ K ) ) )
& ! [I: TD,J: TB,K: TC,L: TA] :
( ( ( G
= ( c_2Epair_2E_2C @ TD @ TB @ I @ J ) )
& ( H
= ( c_2Epair_2E_2C @ TC @ TA @ K @ L ) ) )
=> ( ( B @ J @ L )
= ( F @ J @ L ) ) ) )
=> ( ( c_2EternaryComparisons_2Epair__compare @ TD @ TC @ TB @ TA @ A @ B @ C @ D )
= ( c_2EternaryComparisons_2Epair__compare @ TD @ TC @ TB @ TA @ E @ F @ G @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(234,axiom,
! [TA: $tType,A: ( tyop_2Epair_2Eprod @ TA @ TA ) > $o] :
( ( ( c_2Ewellorder_2Eposet @ TA @ A )
& ? [B: TA] : ( c_2Ewellorder_2Efl @ TA @ A @ B )
& ! [B: TA > $o] :
( ( c_2Ewellorder_2EChain @ TA @ A @ B )
=> ? [C: TA] :
( ( c_2Ewellorder_2Efl @ TA @ A @ C )
& ! [D: TA] :
( ( B @ D )
=> ( A @ ( c_2Epair_2E_2C @ TA @ TA @ D @ C ) ) ) ) ) )
=> ? [B: TA] :
( ( c_2Ewellorder_2Efl @ TA @ A @ B )
& ! [C: TA] :
( ( A @ ( c_2Epair_2E_2C @ TA @ TA @ B @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewellorder_2EZL) ).
thf(1223,plain,
! [TA: $tType,A: ( tyop_2Epair_2Eprod @ TA @ TA ) > $o] :
( ( ( c_2Ewellorder_2Eposet @ TA @ A )
& ? [B: TA] : ( c_2Ewellorder_2Efl @ TA @ A @ B )
& ! [B: TA > $o] :
( ( c_2Ewellorder_2EChain @ TA @ A @ B )
=> ? [C: TA] :
( ( c_2Ewellorder_2Efl @ TA @ A @ C )
& ! [D: TA] :
( ( B @ D )
=> ( A @ ( c_2Epair_2E_2C @ TA @ TA @ D @ C ) ) ) ) ) )
=> ? [B: TA] :
( ( c_2Ewellorder_2Efl @ TA @ A @ B )
& ! [C: TA] :
( ( A @ ( c_2Epair_2E_2C @ TA @ TA @ B @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(142,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Eclosure @ A )
= ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Efrontier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__UNION__FRONTIER) ).
thf(894,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Eclosure @ A )
= ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Efrontier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(290,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__add @ C @ B )
= ( c_2Erealax_2Ereal__add @ B @ C ) )
& ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__add @ C @ B ) @ A )
= ( c_2Erealax_2Ereal__add @ C @ ( c_2Erealax_2Ereal__add @ B @ A ) ) )
& ( ( c_2Erealax_2Ereal__add @ C @ ( c_2Erealax_2Ereal__add @ B @ A ) )
= ( c_2Erealax_2Ereal__add @ B @ ( c_2Erealax_2Ereal__add @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eproduct_2EREAL__ADD__AC) ).
thf(1423,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__add @ C @ B )
= ( c_2Erealax_2Ereal__add @ B @ C ) )
& ( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__add @ C @ B ) @ A )
= ( c_2Erealax_2Ereal__add @ C @ ( c_2Erealax_2Ereal__add @ B @ A ) ) )
& ( ( c_2Erealax_2Ereal__add @ C @ ( c_2Erealax_2Ereal__add @ B @ A ) )
= ( c_2Erealax_2Ereal__add @ B @ ( c_2Erealax_2Ereal__add @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(150,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ( c_2Ereal_2Ereal__lte @ ( A @ C ) @ D )
& ( c_2Ereal_2Ereal__lte @ D @ ( A @ B ) )
& ! [E: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C ) )
=> ( c_2Elim_2Econtl @ A @ E ) ) )
=> ? [E: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C )
& ( ( A @ E )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Elim_2EIVT2) ).
thf(916,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ( c_2Ereal_2Ereal__lte @ ( A @ C ) @ D )
& ( c_2Ereal_2Ereal__lte @ D @ ( A @ B ) )
& ! [E: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C ) )
=> ( c_2Elim_2Econtl @ A @ E ) ) )
=> ? [E: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C )
& ( ( A @ E )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(54,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__lt @ A @ B )
& ( c_2Erealax_2Ereal__lt @ B @ C ) )
=> ( c_2Erealax_2Ereal__lt @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erealax_2EREAL__LT__TRANS) ).
thf(566,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__lt @ A @ B )
& ( c_2Erealax_2Ereal__lt @ B @ C ) )
=> ( c_2Erealax_2Ereal__lt @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(138,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Econnected @ A )
= ( ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ B @ A )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ C @ A ) )
=> ? [D: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Econnected @ D )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ D @ A )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ B @ D )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__IFF__CONNECTABLE__POINTS) ).
thf(879,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Econnected @ A )
= ( ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ B @ A )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ C @ A ) )
=> ? [D: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Econnected @ D )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ D @ A )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ B @ D )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(326,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ A @ ( c_2Erealax_2Ereal__add @ B @ C ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__add @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__ADD__ASSOC) ).
thf(1555,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ A @ ( c_2Erealax_2Ereal__add @ B @ C ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__add @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(216,axiom,
! [TA: $tType,A: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EEMPTY__SUBSET) ).
thf(1178,plain,
! [TA: $tType,A: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(349,axiom,
! [TA: $tType] :
( ! [A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EINTER @ TA @ A @ B ) @ A )
& ! [A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EINTER @ TA @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__SUBSET) ).
thf(1624,plain,
! [TA: $tType] :
( ! [A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EINTER @ TA @ A @ B ) @ A )
& ! [A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EINTER @ TA @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(389,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal_2Emax @ B @ C ) ) )
= ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__MAX__UNION) ).
thf(1787,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal_2Emax @ B @ C ) ) )
= ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(179,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ C @ ( c_2Ereal_2Emin @ A @ B ) )
= ( ( c_2Erealax_2Ereal__lt @ C @ A )
& ( c_2Erealax_2Ereal__lt @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EREAL__LT__MIN) ).
thf(1027,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ C @ ( c_2Ereal_2Emin @ A @ B ) )
= ( ( c_2Erealax_2Ereal__lt @ C @ A )
& ( c_2Erealax_2Ereal__lt @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(103,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ A @ B )
= ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__LE) ).
thf(757,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ A @ B )
= ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(250,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ A )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Eclosure @ B ) ) )
=> ( ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Ereal__topology_2Eclosure @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__OPEN__INTER__SUPERSET) ).
thf(1281,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ A )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Eclosure @ B ) ) )
=> ( ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Ereal__topology_2Eclosure @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(352,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Emin @ A @ B )
= ( c_2Ereal_2Emin @ B @ A ) )
& ( ( c_2Ereal_2Emin @ ( c_2Ereal_2Emin @ A @ B ) @ C )
= ( c_2Ereal_2Emin @ A @ ( c_2Ereal_2Emin @ B @ C ) ) )
& ( ( c_2Ereal_2Emin @ A @ ( c_2Ereal_2Emin @ B @ C ) )
= ( c_2Ereal_2Emin @ B @ ( c_2Ereal_2Emin @ A @ C ) ) )
& ( ( c_2Ereal_2Emin @ A @ A )
= A )
& ( ( c_2Ereal_2Emin @ A @ ( c_2Ereal_2Emin @ A @ B ) )
= ( c_2Ereal_2Emin @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MIN__ACI) ).
thf(1634,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Emin @ A @ B )
= ( c_2Ereal_2Emin @ B @ A ) )
& ( ( c_2Ereal_2Emin @ ( c_2Ereal_2Emin @ A @ B ) @ C )
= ( c_2Ereal_2Emin @ A @ ( c_2Ereal_2Emin @ B @ C ) ) )
& ( ( c_2Ereal_2Emin @ A @ ( c_2Ereal_2Emin @ B @ C ) )
= ( c_2Ereal_2Emin @ B @ ( c_2Ereal_2Emin @ A @ C ) ) )
& ( ( c_2Ereal_2Emin @ A @ A )
= A )
& ( ( c_2Ereal_2Emin @ A @ ( c_2Ereal_2Emin @ A @ B ) )
= ( c_2Ereal_2Emin @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(19,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ A )
= ( c_2Epred__set_2EEMPTY @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__EQ__EMPTY) ).
thf(456,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ A )
= ( c_2Epred__set_2EEMPTY @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(163,axiom,
! [A: tyop_2Erealax_2Ereal] :
~ ( c_2Erealax_2Ereal__lt @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__REFL) ).
thf(974,plain,
! [A: tyop_2Erealax_2Ereal] :
~ ( c_2Erealax_2Ereal__lt @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(198,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( c_2Ereal_2Ereal__lte @ B @ C ) )
=> ( c_2Ereal_2Ereal__lte @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__TRANS) ).
thf(1106,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( c_2Ereal_2Ereal__lte @ B @ C ) )
=> ( c_2Ereal_2Ereal__lte @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o,C: TA > $o] :
( ? [D: TB] : ( c_2Ebool_2EIN @ TB @ D @ B )
=> ( ( ! [D: TB,E: TB] :
( ( ( c_2Ebool_2EIN @ TB @ D @ B )
& ( c_2Ebool_2EIN @ TB @ E @ B )
& ( ( A @ D )
= ( A @ E ) ) )
=> ( D = E ) ) )
= ( ? [D: TA > TB] :
( ! [E: TA] :
( ( c_2Ebool_2EIN @ TA @ E @ C )
=> ( c_2Ebool_2EIN @ TB @ ( D @ E ) @ B ) )
& ! [E: TB] :
( ( c_2Ebool_2EIN @ TB @ E @ B )
=> ( ( D @ ( A @ E ) )
= E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewellorder_2EINJECTIVE__LEFT__INVERSE__NONEMPTY) ).
thf(583,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o,C: TA > $o] :
( ? [D: TB] : ( c_2Ebool_2EIN @ TB @ D @ B )
=> ( ( ! [D: TB,E: TB] :
( ( ( c_2Ebool_2EIN @ TB @ D @ B )
& ( c_2Ebool_2EIN @ TB @ E @ B )
& ( ( A @ D )
= ( A @ E ) ) )
=> ( D = E ) ) )
= ( ? [D: TA > TB] :
( ! [E: TA] :
( ( c_2Ebool_2EIN @ TA @ E @ C )
=> ( c_2Ebool_2EIN @ TB @ ( D @ E ) @ B ) )
& ! [E: TB] :
( ( c_2Ebool_2EIN @ TB @ E @ B )
=> ( ( D @ ( A @ E ) )
= E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(124,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__EMPTY) ).
thf(830,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(50,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal] :
( ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A @ E )
=> ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C )
@ ^ [F: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__mul @ D @ ( A @ F ) )
@ ( c_2Erealax_2Ereal__mul @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EDINT__CMUL) ).
thf(551,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal] :
( ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A @ E )
=> ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C )
@ ^ [F: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__mul @ D @ ( A @ F ) )
@ ( c_2Erealax_2Ereal__mul @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(203,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal_2Emax @ B @ C ) ) )
= ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECBALL__MAX__UNION) ).
thf(1128,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal_2Emax @ B @ C ) ) )
= ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(270,axiom,
( ( c_2Ereal__topology_2Einterior @ ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__EMPTY) ).
thf(1360,plain,
( ( c_2Ereal__topology_2Einterior @ ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o,C: TA > $o] :
( ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
=> ? [E: TB] :
( ( A @ E )
= D ) )
& ! [D: TB] :
( ( c_2Ebool_2EIN @ TA @ ( A @ D ) @ C )
= ( c_2Ebool_2EIN @ TB @ D @ B ) ) )
=> ( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ B )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESURJECTIVE__IMAGE__EQ) ).
thf(697,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o,C: TA > $o] :
( ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
=> ? [E: TB] :
( ( A @ E )
= D ) )
& ! [D: TB] :
( ( c_2Ebool_2EIN @ TA @ ( A @ D ) @ C )
= ( c_2Ebool_2EIN @ TB @ D @ B ) ) )
=> ( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(136,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB > $o] :
( ( c_2Ebool_2EIN @ TB @ A @ B )
=> ! [C: TB > TA] : ( c_2Ebool_2EIN @ TA @ ( C @ A ) @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__IN) ).
thf(874,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB > $o] :
( ( c_2Ebool_2EIN @ TB @ A @ B )
=> ! [C: TB > TA] : ( c_2Ebool_2EIN @ TA @ ( C @ A ) @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(398,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal__topology_2Ebetween @ A @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) )
& ( c_2Ereal__topology_2Ebetween @ B @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBETWEEN__ANTISYM) ).
thf(1851,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal__topology_2Ebetween @ A @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) )
& ( c_2Ereal__topology_2Ebetween @ B @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(69,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
=> ( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EINTER @ TA @ B @ C ) )
= ( c_2Epred__set_2EDIFF @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__INTER__SUBSET) ).
thf(615,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
=> ( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EINTER @ TA @ B @ C ) )
= ( c_2Epred__set_2EDIFF @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(272,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ A @ ( c_2Erealax_2Ereal__add @ B @ C ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__add @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erealax_2EREAL__ADD__ASSOC) ).
thf(1375,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ A @ ( c_2Erealax_2Ereal__add @ B @ C ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__add @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(189,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ? [D: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C )
& ( A @ D ) )
=> ? [D: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C )
& ! [E: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ E @ D )
= ( ? [F: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ F )
& ( c_2Ereal_2Ereal__lte @ F @ C )
& ( A @ F )
& ( c_2Erealax_2Ereal__lt @ E @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2ESUP__INTERVAL) ).
thf(1064,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ? [D: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C )
& ( A @ D ) )
=> ? [D: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C )
& ! [E: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ E @ D )
= ( ? [F: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ F )
& ( c_2Ereal_2Ereal__lte @ F @ C )
& ( A @ F )
& ( c_2Erealax_2Ereal__lt @ E @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(360,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EINTER @ TA @ B @ C ) )
= ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__INTER) ).
thf(1672,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EINTER @ TA @ B @ C ) )
= ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(322,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EClosed @ A )
| ( c_2Ereal__topology_2EClosed @ B ) )
=> ( ( ( c_2Ereal__topology_2Einterior @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( ( ( c_2Ereal__topology_2Einterior @ A )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( ( c_2Ereal__topology_2Einterior @ B )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__UNION__EQ__EMPTY) ).
thf(1540,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EClosed @ A )
| ( c_2Ereal__topology_2EClosed @ B ) )
=> ( ( ( c_2Ereal__topology_2Einterior @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( ( ( c_2Ereal__topology_2Einterior @ A )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( ( c_2Ereal__topology_2Einterior @ B )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(374,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC > $o,B: TB > TA > $o,C: TD,D: TB,E: TC,F: TA] :
( ( c_2Etransfer_2EPAIR__REL @ TD @ TC @ TB @ TA @ A @ B @ ( c_2Epair_2E_2C @ TD @ TB @ C @ D ) @ ( c_2Epair_2E_2C @ TC @ TA @ E @ F ) )
= ( ( A @ C @ E )
& ( B @ D @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Etransfer_2EPAIR__REL__def) ).
thf(1719,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC > $o,B: TB > TA > $o,C: TD,D: TB,E: TC,F: TA] :
( ( c_2Etransfer_2EPAIR__REL @ TD @ TC @ TB @ TA @ A @ B @ ( c_2Epair_2E_2C @ TD @ TB @ C @ D ) @ ( c_2Epair_2E_2C @ TC @ TA @ E @ F ) )
= ( ( A @ C @ E )
& ( B @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(130,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Epred__set_2EUNION @ TA @ A @ B @ C )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
| ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__applied) ).
thf(857,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Epred__set_2EUNION @ TA @ A @ B @ C )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
| ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(337,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ A @ ( c_2Ereal_2Emin @ B @ C ) )
= ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( c_2Ereal_2Ereal__lte @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__MIN) ).
thf(1592,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ A @ ( c_2Ereal_2Emin @ B @ C ) )
= ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( c_2Ereal_2Ereal__lte @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(101,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ B @ A )
= ( ~ ( c_2Ereal_2Ereal__lte @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2Ereal__lt) ).
thf(742,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ B @ A )
= ( ~ ( c_2Ereal_2Ereal__lte @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(310,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
= ( ( c_2Epred__set_2EINTER @ TA @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__INTER__ABSORPTION) ).
thf(1498,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
= ( ( c_2Epred__set_2EINTER @ TA @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(335,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Einterior @ A )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( ! [B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ B )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ B @ A ) )
=> ( B
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__EQ__EMPTY) ).
thf(1587,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Einterior @ A )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( ! [B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ B )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ B @ A ) )
=> ( B
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(24,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal,F: tyop_2Erealax_2Ereal] :
( ( ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A @ E )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B @ F ) )
=> ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D )
@ ^ [G: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add @ ( A @ G ) @ ( B @ G ) )
@ ( c_2Erealax_2Ereal__add @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EDINT__ADD) ).
thf(471,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal,F: tyop_2Erealax_2Ereal] :
( ( ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A @ E )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B @ F ) )
=> ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D )
@ ^ [G: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add @ ( A @ G ) @ ( B @ G ) )
@ ( c_2Erealax_2Ereal__add @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(362,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Emin @ B @ C ) @ A )
= ( ( c_2Ereal_2Ereal__lte @ B @ A )
| ( c_2Ereal_2Ereal__lte @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MIN__LE) ).
thf(1683,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Emin @ B @ C ) @ A )
= ( ( c_2Ereal_2Ereal__lte @ B @ A )
| ( c_2Ereal_2Ereal__lte @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(31,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Einterior @ ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Einterior @ A ) @ ( c_2Ereal__topology_2Eclosure @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__DIFF) ).
thf(488,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Einterior @ ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Einterior @ A ) @ ( c_2Ereal__topology_2Eclosure @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(218,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Einterior @ A )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( ! [B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ B )
& ( B
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) )
=> ( ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ B @ A )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__EQ__EMPTY__ALT) ).
thf(1182,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Einterior @ A )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( ! [B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ B )
& ( B
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) )
=> ( ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ B @ A )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(45,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Econnected @ A )
=> ( c_2Ereal__topology_2Econnected @ ( c_2Ereal__topology_2Eclosure @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__CLOSURE) ).
thf(537,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Econnected @ A )
=> ( c_2Ereal__topology_2Econnected @ ( c_2Ereal__topology_2Eclosure @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(26,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EClosed @ A )
& ( c_2Ereal__topology_2EOpen @ B ) )
=> ( c_2Ereal__topology_2EClosed @ ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSED__DIFF) ).
thf(476,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EClosed @ A )
& ( c_2Ereal__topology_2EOpen @ B ) )
=> ( c_2Ereal__topology_2EClosed @ ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(394,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B )
@ ^ [D: tyop_2Erealax_2Ereal] : C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EINTEGRABLE__CONST) ).
thf(1842,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B )
@ ^ [D: tyop_2Erealax_2Ereal] : C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(334,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Eclosure @ A ) )
= ( c_2Ereal__topology_2Eclosure @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__CLOSURE) ).
thf(1584,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Eclosure @ A ) )
= ( c_2Ereal__topology_2Eclosure @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(231,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Econnected @ A )
& ( c_2Ereal__topology_2Econnected @ B )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ B )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) )
=> ( c_2Ereal__topology_2Econnected @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__UNION__STRONG) ).
thf(1214,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Econnected @ A )
& ( c_2Ereal__topology_2Econnected @ B )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ B )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) )
=> ( c_2Ereal__topology_2Econnected @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(92,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( A = B )
| ( c_2Erealax_2Ereal__lt @ A @ B )
| ( c_2Erealax_2Ereal__lt @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__TOTAL) ).
thf(706,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( A = B )
| ( c_2Erealax_2Ereal__lt @ A @ B )
| ( c_2Erealax_2Ereal__lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(175,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EClosed @ A )
=> ( ( c_2Ereal__topology_2Eclosure @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__CLOSED) ).
thf(1016,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EClosed @ A )
=> ( ( c_2Ereal__topology_2Eclosure @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(228,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__add @ A @ C ) @ ( c_2Erealax_2Ereal__add @ B @ D ) ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EDIST__TRIANGLE__ADD) ).
thf(1207,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__add @ A @ C ) @ ( c_2Erealax_2Ereal__add @ B @ D ) ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(259,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Einterior @ A ) @ ( c_2Ereal__topology_2Einterior @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESUBSET__INTERIOR) ).
thf(1324,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Einterior @ A ) @ ( c_2Ereal__topology_2Einterior @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(244,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o] :
( ( ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( A @ B @ C )
= ( A @ C @ B ) )
& ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ C )
=> ( A @ B @ C ) ) )
=> ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] : ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EREAL__WLOG__LE) ).
thf(1263,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o] :
( ( ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( A @ B @ C )
= ( A @ C @ B ) )
& ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ C )
=> ( A @ B @ C ) ) )
=> ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] : ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(392,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Ebetween @ A @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
& ( c_2Ereal__topology_2Ebetween @ B @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
& ( c_2Ereal__topology_2Ebetween @ A @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBETWEEN__REFL) ).
thf(1831,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Ebetween @ A @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
& ( c_2Ereal__topology_2Ebetween @ B @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
& ( c_2Ereal__topology_2Ebetween @ A @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(359,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ A )
=> ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Einterior @ B ) )
= ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__MAXIMAL__EQ) ).
thf(1668,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ A )
=> ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Einterior @ B ) )
= ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(325,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Einterior @ A ) )
= ( c_2Ereal__topology_2Einterior @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__INTERIOR) ).
thf(1552,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Einterior @ A ) )
= ( c_2Ereal__topology_2Einterior @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(222,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Esphere @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESPHERE__SUBSET__CBALL) ).
thf(1192,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Esphere @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(97,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EINTER @ TA @ B @ A ) )
= ( c_2Epred__set_2EDIFF @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__INTER2) ).
thf(721,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EINTER @ TA @ B @ A ) )
= ( c_2Epred__set_2EDIFF @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(406,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__BALL) ).
thf(1874,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(110,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ! [D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C ) )
=> ( c_2Elim_2Econtl @ A @ D ) ) )
=> ? [D: tyop_2Erealax_2Ereal] :
( ! [E: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C ) )
=> ( c_2Ereal_2Ereal__lte @ ( A @ E ) @ D ) )
& ! [E: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ E @ D )
=> ? [F: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ F )
& ( c_2Ereal_2Ereal__lte @ F @ C )
& ( c_2Erealax_2Ereal__lt @ E @ ( A @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Elim_2ECONT__HASSUP) ).
thf(779,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ! [D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C ) )
=> ( c_2Elim_2Econtl @ A @ D ) ) )
=> ? [D: tyop_2Erealax_2Ereal] :
( ! [E: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C ) )
=> ( c_2Ereal_2Ereal__lte @ ( A @ E ) @ D ) )
& ! [E: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ E @ D )
=> ? [F: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ F )
& ( c_2Ereal_2Ereal__lte @ F @ C )
& ( c_2Erealax_2Ereal__lt @ E @ ( A @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(317,axiom,
! [A: tyop_2Erealax_2Ereal > $o] : ( c_2Ereal__topology_2EOpen @ ( c_2Ereal__topology_2Einterior @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__INTERIOR) ).
thf(1525,plain,
! [A: tyop_2Erealax_2Ereal > $o] : ( c_2Ereal__topology_2EOpen @ ( c_2Ereal__topology_2Einterior @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(304,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ A @ C ) @ ( c_2Erealax_2Ereal__add @ B @ C ) )
= ( c_2Ereal_2Ereal__lte @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__RADD) ).
thf(1478,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ A @ C ) @ ( c_2Erealax_2Ereal__add @ B @ C ) )
= ( c_2Ereal_2Ereal__lte @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(240,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ C )
=> ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ A @ B ) @ ( c_2Erealax_2Ereal__add @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__LADD__IMP) ).
thf(1249,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ C )
=> ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ A @ B ) @ ( c_2Erealax_2Ereal__add @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(204,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal] :
( ( ! [F: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ F )
& ( c_2Ereal_2Ereal__lte @ F @ D )
& ( F != E ) )
=> ( ( A @ F )
= ( B @ F ) ) )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A ) )
=> ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EINTEGRABLE__POINT__SPIKE) ).
thf(1131,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal] :
( ( ! [F: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ F )
& ( c_2Ereal_2Ereal__lte @ F @ D )
& ( F != E ) )
=> ( ( A @ F )
= ( B @ F ) ) )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A ) )
=> ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(78,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ? [B: tyop_2Erealax_2Ereal] : ( A @ B )
& ? [B: tyop_2Erealax_2Ereal] :
! [C: tyop_2Erealax_2Ereal] :
( ( A @ C )
=> ( c_2Ereal_2Ereal__lte @ C @ B ) ) )
= ( ? [B: tyop_2Erealax_2Ereal] : ( A @ B )
& ? [B: tyop_2Erealax_2Ereal] :
! [C: tyop_2Erealax_2Ereal] :
( ( A @ C )
=> ( c_2Erealax_2Ereal__lt @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2ESETOK__LE__LT) ).
thf(654,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ? [B: tyop_2Erealax_2Ereal] : ( A @ B )
& ? [B: tyop_2Erealax_2Ereal] :
! [C: tyop_2Erealax_2Ereal] :
( ( A @ C )
=> ( c_2Ereal_2Ereal__lte @ C @ B ) ) )
= ( ? [B: tyop_2Erealax_2Ereal] : ( A @ B )
& ? [B: tyop_2Erealax_2Ereal] :
! [C: tyop_2Erealax_2Ereal] :
( ( A @ C )
=> ( c_2Erealax_2Ereal__lt @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(36,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Elim_2Econtl @ A @ C )
& ( c_2Elim_2Econtl @ B @ C ) )
=> ( c_2Elim_2Econtl
@ ^ [D: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add @ ( A @ D ) @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Elim_2ECONT__ADD) ).
thf(503,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Elim_2Econtl @ A @ C )
& ( c_2Elim_2Econtl @ B @ C ) )
=> ( c_2Elim_2Econtl
@ ^ [D: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add @ ( A @ D ) @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(66,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( ~ ( c_2Erealax_2Ereal__lt @ A @ B ) )
= ( c_2Ereal_2Ereal__lte @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__NOT__LT) ).
thf(605,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( ~ ( c_2Erealax_2Ereal__lt @ A @ B ) )
= ( c_2Ereal_2Ereal__lte @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(291,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Emin @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MIN__LE2) ).
thf(1434,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Emin @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(226,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A ) )
=> ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C )
@ ^ [E: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__mul @ D @ ( A @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EINTEGRABLE__CMUL) ).
thf(1202,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A ) )
=> ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C )
@ ^ [E: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__mul @ D @ ( A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(155,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Epred__set_2EGSPEC @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal
@ ^ [C: tyop_2Erealax_2Ereal] : ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ $o @ C @ ( c_2Erealax_2Ereal__lt @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2Eball) ).
thf(938,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Epred__set_2EGSPEC @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal
@ ^ [C: tyop_2Erealax_2Ereal] : ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ $o @ C @ ( c_2Erealax_2Ereal__lt @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(73,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ B @ A )
=> ( ( ( c_2Epred__set_2EUNION @ TA @ B @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) )
= A )
& ( ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__DIFF) ).
thf(633,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ B @ A )
=> ( ( ( c_2Epred__set_2EUNION @ TA @ B @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) )
= A )
& ( ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(114,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ A @ B )
=> ( c_2Ereal_2Ereal__lte @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__IMP__LE) ).
thf(805,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ A @ B )
=> ( c_2Ereal_2Ereal__lte @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(38,axiom,
! [A: ( tyop_2Erealax_2Ereal > $o ) > $o] :
( ! [B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ebool_2EIN @ ( tyop_2Erealax_2Ereal > $o ) @ B @ A )
=> ( c_2Ereal__topology_2EClosed @ B ) )
=> ( c_2Ereal__topology_2EClosed @ ( c_2Epred__set_2EBIGINTER @ tyop_2Erealax_2Ereal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSED__BIGINTER) ).
thf(508,plain,
! [A: ( tyop_2Erealax_2Ereal > $o ) > $o] :
( ! [B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ebool_2EIN @ ( tyop_2Erealax_2Ereal > $o ) @ B @ A )
=> ( c_2Ereal__topology_2EClosed @ B ) )
=> ( c_2Ereal__topology_2EClosed @ ( c_2Epred__set_2EBIGINTER @ tyop_2Erealax_2Ereal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(151,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B )
& ( c_2Ereal__topology_2EClosed @ B )
& ! [C: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ C )
& ( c_2Ereal__topology_2EClosed @ C ) )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ B @ C ) ) )
=> ( ( c_2Ereal__topology_2Eclosure @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__UNIQUE) ).
thf(921,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B )
& ( c_2Ereal__topology_2EClosed @ B )
& ! [C: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ C )
& ( c_2Ereal__topology_2EClosed @ C ) )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ B @ C ) ) )
=> ( ( c_2Ereal__topology_2Eclosure @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(79,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o,C: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ B @ C )
& ( c_2Ereal__topology_2EOpen @ A )
& ( c_2Ereal__topology_2EClosed @ B )
& ( c_2Ereal__topology_2Econnected @ C )
& ( c_2Ereal__topology_2Econnected @ ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ B @ A ) ) )
=> ( c_2Ereal__topology_2Econnected @ ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__DIFF__OPEN__FROM__CLOSED) ).
thf(657,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o,C: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ B @ C )
& ( c_2Ereal__topology_2EOpen @ A )
& ( c_2Ereal__topology_2EClosed @ B )
& ( c_2Ereal__topology_2Econnected @ C )
& ( c_2Ereal__topology_2Econnected @ ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ B @ A ) ) )
=> ( c_2Ereal__topology_2Econnected @ ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(357,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ A @ ( c_2Ereal_2Emax @ B @ C ) )
= ( ( c_2Ereal_2Ereal__lte @ A @ B )
| ( c_2Ereal_2Ereal__lte @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__MAX) ).
thf(1663,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ A @ ( c_2Ereal_2Emax @ B @ C ) )
= ( ( c_2Ereal_2Ereal__lte @ A @ B )
| ( c_2Ereal_2Ereal__lte @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(346,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ C @ ( c_2Erealax_2Ereal__add @ B @ A ) )
= ( c_2Erealax_2Ereal__add @ B @ ( c_2Erealax_2Ereal__add @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er219) ).
thf(1616,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ C @ ( c_2Erealax_2Ereal__add @ B @ A ) )
= ( c_2Erealax_2Ereal__add @ B @ ( c_2Erealax_2Ereal__add @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(43,axiom,
c_2Ereal__topology_2EClosed @ ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSED__EMPTY) ).
thf(530,plain,
c_2Ereal__topology_2EClosed @ ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(379,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Ebetween @ ( c_2Ereal__topology_2Emidpoint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
& ( c_2Ereal__topology_2Ebetween @ ( c_2Ereal__topology_2Emidpoint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBETWEEN__MIDPOINT) ).
thf(1732,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Ebetween @ ( c_2Ereal__topology_2Emidpoint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
& ( c_2Ereal__topology_2Ebetween @ ( c_2Ereal__topology_2Emidpoint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(300,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Esphere @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__add @ A @ B ) @ C ) )
= ( c_2Epred__set_2EIMAGE @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__add @ A ) @ ( c_2Ereal__topology_2Esphere @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESPHERE__TRANSLATION) ).
thf(1466,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Esphere @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__add @ A @ B ) @ C ) )
= ( c_2Epred__set_2EIMAGE @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__add @ A ) @ ( c_2Ereal__topology_2Esphere @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(53,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal] :
( ? [C: tyop_2Erealax_2Ereal] :
! [D: tyop_2Erealax_2Ereal] :
( ( A @ D )
=> ( c_2Erealax_2Ereal__lt @ D @ C ) )
=> ? [C: tyop_2Erealax_2Ereal] :
! [D: tyop_2Erealax_2Ereal] :
( ( ^ [E: tyop_2Erealax_2Ereal] : ( A @ ( c_2Erealax_2Ereal__add @ E @ B ) )
@ D )
=> ( c_2Erealax_2Ereal__lt @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2ESUP__LEMMA3) ).
thf(558,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal] :
( ? [C: tyop_2Erealax_2Ereal] :
! [D: tyop_2Erealax_2Ereal] :
( ( A @ D )
=> ( c_2Erealax_2Ereal__lt @ D @ C ) )
=> ? [C: tyop_2Erealax_2Ereal] :
! [D: tyop_2Erealax_2Ereal] :
( ( A @ ( c_2Erealax_2Ereal__add @ D @ B ) )
=> ( c_2Erealax_2Ereal__lt @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(159,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
& ~ ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__DIFF) ).
thf(953,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
& ~ ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(219,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__add @ A @ B )
= ( c_2Erealax_2Ereal__add @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__EQ__LADD) ).
thf(1185,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__add @ A @ B )
= ( c_2Erealax_2Ereal__add @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o,C: TB > TA,D: TB > $o] :
( ( ( B = D )
& ! [E: TB] :
( ( c_2Ebool_2EIN @ TB @ E @ D )
=> ( ( A @ E )
= ( C @ E ) ) ) )
=> ( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ B )
= ( c_2Epred__set_2EIMAGE @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__CONG) ).
thf(794,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o,C: TB > TA,D: TB > $o] :
( ( ( B = D )
& ! [E: TB] :
( ( c_2Ebool_2EIN @ TB @ E @ D )
=> ( ( A @ E )
= ( C @ E ) ) ) )
=> ( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ B )
= ( c_2Epred__set_2EIMAGE @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(59,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ A @ B )
| ( c_2Ereal_2Ereal__lte @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LTE__TOTAL) ).
thf(586,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ A @ B )
| ( c_2Ereal_2Ereal__lte @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(96,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
~ ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( c_2Erealax_2Ereal__lt @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LTE__ANTISYM) ).
thf(718,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
~ ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( c_2Erealax_2Ereal__lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(140,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o] :
( ( ! [C: TB > $o,D: TB > $o] :
( ( ( c_2Epred__set_2ESUBSET @ TB @ C @ B )
& ( c_2Epred__set_2ESUBSET @ TB @ D @ B )
& ( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ C )
= ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ D ) ) )
=> ( C = D ) ) )
= ( ! [C: TB,D: TB] :
( ( ( c_2Ebool_2EIN @ TB @ C @ B )
& ( c_2Ebool_2EIN @ TB @ D @ B )
& ( ( A @ C )
= ( A @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EINJECTIVE__ON__IMAGE) ).
thf(888,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o] :
( ( ! [C: TB > $o,D: TB > $o] :
( ( ( c_2Epred__set_2ESUBSET @ TB @ C @ B )
& ( c_2Epred__set_2ESUBSET @ TB @ D @ B )
& ( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ C )
= ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ D ) ) )
=> ( C = D ) ) )
= ( ! [C: TB,D: TB] :
( ( ( c_2Ebool_2EIN @ TB @ C @ B )
& ( c_2Ebool_2EIN @ TB @ D @ B )
& ( ( A @ C )
= ( A @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(1,conjecture,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal__topology_2Ebounded__def @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__BALL) ).
thf(2,negated_conjecture,
~ ! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal__topology_2Ebounded__def @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(412,plain,
~ ! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal__topology_2Ebounded__def @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(377,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Emidpoint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Ereal__topology_2Emidpoint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EMIDPOINT__SYM) ).
thf(1727,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Emidpoint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Ereal__topology_2Emidpoint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB > TA,C: TA > $o] :
( ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
=> ? [E: TB] :
( ( c_2Ebool_2EIN @ TB @ E @ A )
& ( ( B @ E )
= D ) ) ) )
= ( ? [D: TA > TB] :
! [E: TA] :
( ( c_2Ebool_2EIN @ TA @ E @ C )
=> ( ( c_2Ebool_2EIN @ TB @ ( D @ E ) @ A )
& ( ( B @ ( D @ E ) )
= E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ESURJECTIVE__ON__RIGHT__INVERSE) ).
thf(425,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB > TA,C: TA > $o] :
( ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
=> ? [E: TB] :
( ( c_2Ebool_2EIN @ TB @ E @ A )
& ( ( B @ E )
= D ) ) ) )
= ( ? [D: TA > TB] :
! [E: TA] :
( ( c_2Ebool_2EIN @ TA @ E @ C )
=> ( ( c_2Ebool_2EIN @ TB @ ( D @ E ) @ A )
& ( ( B @ ( D @ E ) )
= E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(122,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EGSPEC @ TA @ TA
@ ^ [B: TA] : ( c_2Epair_2E_2C @ TA @ $o @ B @ ( c_2Ebool_2EIN @ TA @ B @ A ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EGSPEC__ID) ).
thf(824,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EGSPEC @ TA @ TA
@ ^ [B: TA] : ( c_2Epair_2E_2C @ TA @ $o @ B @ ( c_2Ebool_2EIN @ TA @ B @ A ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(102,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o] :
( ( ! [B: tyop_2Erealax_2Ereal] : ( A @ B @ B )
& ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( A @ B @ C )
= ( A @ C @ B ) )
& ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ B @ C )
=> ( A @ B @ C ) ) )
=> ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] : ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EREAL__WLOG__LT) ).
thf(745,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o] :
( ( ! [B: tyop_2Erealax_2Ereal] : ( A @ B @ B )
& ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( A @ B @ C )
= ( A @ C @ B ) )
& ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ B @ C )
=> ( A @ B @ C ) ) )
=> ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] : ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(338,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ A @ B )
= ( c_2Erealax_2Ereal__add @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__ADD__SYM) ).
thf(1595,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ A @ B )
= ( c_2Erealax_2Ereal__add @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(57,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ! [D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C ) )
=> ( c_2Elim_2Econtl @ A @ D ) ) )
=> ? [D: tyop_2Erealax_2Ereal] :
( ! [E: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C ) )
=> ( c_2Ereal_2Ereal__lte @ ( A @ E ) @ D ) )
& ? [E: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C )
& ( ( A @ E )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Elim_2ECONT__ATTAINS) ).
thf(573,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ! [D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C ) )
=> ( c_2Elim_2Econtl @ A @ D ) ) )
=> ? [D: tyop_2Erealax_2Ereal] :
( ! [E: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C ) )
=> ( c_2Ereal_2Ereal__lte @ ( A @ E ) @ D ) )
& ? [E: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C )
& ( ( A @ E )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(351,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Emax @ ( c_2Erealax_2Ereal__add @ B @ A ) @ ( c_2Erealax_2Ereal__add @ C @ A ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Emax @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MAX__ADD) ).
thf(1631,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Emax @ ( c_2Erealax_2Ereal__add @ B @ A ) @ ( c_2Erealax_2Ereal__add @ C @ A ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Emax @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(241,axiom,
! [TA: $tType] :
( ! [A: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A )
= ( c_2Epred__set_2EEMPTY @ TA ) )
& ! [A: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) )
= ( c_2Epred__set_2EEMPTY @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__EMPTY) ).
thf(1251,plain,
! [TA: $tType] :
( ! [A: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A )
= ( c_2Epred__set_2EEMPTY @ TA ) )
& ! [A: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) )
= ( c_2Epred__set_2EEMPTY @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(70,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ A @ C ) @ ( c_2Erealax_2Ereal__add @ B @ C ) )
= ( c_2Erealax_2Ereal__lt @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__RADD) ).
thf(618,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ A @ C ) @ ( c_2Erealax_2Ereal__add @ B @ C ) )
= ( c_2Erealax_2Ereal__lt @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(210,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ B )
=> ( ( c_2Ereal_2Emax @ A @ B )
= B ) )
& ( ( c_2Ereal_2Ereal__lte @ B @ A )
=> ( ( c_2Ereal_2Emax @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MAX__ALT) ).
thf(1154,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ B )
=> ( ( c_2Ereal_2Emax @ A @ B )
= B ) )
& ( ( c_2Ereal_2Ereal__lte @ B @ A )
=> ( ( c_2Ereal_2Emax @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(120,axiom,
! [TA: $tType,A: ( TA > $o ) > $o,B: ( TA > $o ) > $o] :
( ( c_2Epred__set_2EBIGINTER @ TA @ ( c_2Epred__set_2EUNION @ ( TA > $o ) @ A @ B ) )
= ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EBIGINTER @ TA @ A ) @ ( c_2Epred__set_2EBIGINTER @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EBIGINTER__UNION) ).
thf(819,plain,
! [TA: $tType,A: ( TA > $o ) > $o,B: ( TA > $o ) > $o] :
( ( c_2Epred__set_2EBIGINTER @ TA @ ( c_2Epred__set_2EUNION @ ( TA > $o ) @ A @ B ) )
= ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EBIGINTER @ TA @ A ) @ ( c_2Epred__set_2EBIGINTER @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(7,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__lt @ A @ B )
& ( c_2Ereal_2Ereal__lte @ C @ D ) )
=> ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ A @ C ) @ ( c_2Erealax_2Ereal__add @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LTE__ADD2) ).
thf(423,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__lt @ A @ B )
& ( c_2Ereal_2Ereal__lte @ C @ D ) )
=> ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ A @ C ) @ ( c_2Erealax_2Ereal__add @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(89,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) )
= ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__UNION) ).
thf(694,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) )
= ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TA,D: TB > $o] :
( ( ( D @ B )
& ( C
= ( A @ B ) ) )
=> ( c_2Ebool_2EIN @ TA @ C
@ ( c_2Epred__set_2EGSPEC @ TA @ TB
@ ^ [E: TB] : ( c_2Epair_2E_2C @ TA @ $o @ ( A @ E ) @ ( D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__GSPEC) ).
thf(772,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TA,D: TB > $o] :
( ( ( D @ B )
& ( C
= ( A @ B ) ) )
=> ( c_2Ebool_2EIN @ TA @ C
@ ( c_2Epred__set_2EGSPEC @ TA @ TB
@ ^ [E: TB] : ( c_2Epair_2E_2C @ TA @ $o @ ( A @ E ) @ ( D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(277,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ! [B: TA > $o] :
? [C: TB > $o] :
( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ C )
= B ) )
= ( ! [B: TA] :
? [C: TB] :
( ( A @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ESURJECTIVE__IMAGE) ).
thf(1388,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ! [B: TA > $o] :
? [C: TB > $o] :
( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ C )
= B ) )
= ( ! [B: TA] :
? [C: TB] :
( ( A @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(320,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ A ) @ ( c_2Ereal__topology_2Efrontier @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__INTER__SUBSET) ).
thf(1535,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ A ) @ ( c_2Ereal__topology_2Efrontier @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(345,axiom,
c_2Ereal__topology_2EOpen @ ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__EMPTY) ).
thf(1615,plain,
c_2Ereal__topology_2EOpen @ ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(388,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( c_2Epair_2E_2C @ TB @ TA @ B @ A )
= ( c_2Epair_2E_2C @ TB @ TA @ D @ C ) )
= ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2EPAIR__EQ) ).
thf(1784,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( c_2Epair_2E_2C @ TB @ TA @ B @ A )
= ( c_2Epair_2E_2C @ TB @ TA @ D @ C ) )
= ( ( B = D )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(75,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EClosed @ A )
& ( ( c_2Ereal__topology_2Einterior @ A )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) )
= ( ? [B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ B )
& ( A
= ( c_2Ereal__topology_2Efrontier @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__CLOSED__EQ__EMPTY__AS__FRONTIER) ).
thf(641,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EClosed @ A )
& ( ( c_2Ereal__topology_2Einterior @ A )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) )
= ( ? [B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ B )
& ( A
= ( c_2Ereal__topology_2Efrontier @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(15,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Ereal_2Emax @ A @ B ) @ C )
= ( ( c_2Erealax_2Ereal__lt @ A @ C )
& ( c_2Erealax_2Ereal__lt @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MAX__LT) ).
thf(445,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ ( c_2Ereal_2Emax @ A @ B ) @ C )
= ( ( c_2Erealax_2Ereal__lt @ A @ C )
& ( c_2Erealax_2Ereal__lt @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(370,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( tyop_2Epair_2Eprod @ TC @ TB ) > TA,B: TC,C: TB] :
( ( c_2Epair_2ECURRY @ TC @ TB @ TA @ A @ B @ C )
= ( A @ ( c_2Epair_2E_2C @ TC @ TB @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2ECURRY__DEF) ).
thf(1707,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( tyop_2Epair_2Eprod @ TC @ TB ) > TA,B: TC,C: TB] :
( ( c_2Epair_2ECURRY @ TC @ TB @ TA @ A @ B @ C )
= ( A @ ( c_2Epair_2E_2C @ TC @ TB @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(255,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ A )
=> ( ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Eclosure @ B ) ) )
= ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__OPEN__INTER__CLOSURE) ).
thf(1312,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ A )
=> ( ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Eclosure @ B ) ) )
= ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(385,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal__topology_2Ebetween @ A @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) )
& ( c_2Ereal__topology_2Ebetween @ D @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) )
=> ( c_2Ereal__topology_2Ebetween @ D @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBETWEEN__TRANS) ).
thf(1765,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal__topology_2Ebetween @ A @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) )
& ( c_2Ereal__topology_2Ebetween @ D @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) )
=> ( c_2Ereal__topology_2Ebetween @ D @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(242,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2EUNION @ TA @ A @ B )
= ( c_2Epred__set_2EEMPTY @ TA ) )
= ( ( A
= ( c_2Epred__set_2EEMPTY @ TA ) )
& ( B
= ( c_2Epred__set_2EEMPTY @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EEMPTY__UNION) ).
thf(1258,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2EUNION @ TA @ A @ B )
= ( c_2Epred__set_2EEMPTY @ TA ) )
= ( ( A
= ( c_2Epred__set_2EEMPTY @ TA ) )
& ( B
= ( c_2Epred__set_2EEMPTY @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(158,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ A )
| ( c_2Ereal__topology_2EClosed @ A ) )
=> ( ( c_2Ereal__topology_2Efrontier @ ( c_2Ereal__topology_2Efrontier @ A ) )
= ( c_2Ereal__topology_2Efrontier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__FRONTIER) ).
thf(947,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ A )
| ( c_2Ereal__topology_2EClosed @ A ) )
=> ( ( c_2Ereal__topology_2Efrontier @ ( c_2Ereal__topology_2Efrontier @ A ) )
= ( c_2Ereal__topology_2Efrontier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(361,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ B )
=> ( ( c_2Ereal_2Emin @ A @ B )
= A ) )
& ( ( c_2Ereal_2Ereal__lte @ B @ A )
=> ( ( c_2Ereal_2Emin @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MIN__ALT) ).
thf(1675,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ B )
=> ( ( c_2Ereal_2Emin @ A @ B )
= A ) )
& ( ( c_2Ereal_2Ereal__lte @ B @ A )
=> ( ( c_2Ereal_2Emin @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(84,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
= ( ! [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ A )
=> ( c_2Ebool_2EIN @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__DEF) ).
thf(672,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
= ( ! [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ A )
=> ( c_2Ebool_2EIN @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(223,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EIMAGE @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__ID) ).
thf(1194,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EIMAGE @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(229,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ A )
& ( c_2Ereal__topology_2EOpen @ B ) )
=> ( c_2Ereal__topology_2EOpen @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__UNION) ).
thf(1209,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ A )
& ( c_2Ereal__topology_2EOpen @ B ) )
=> ( c_2Ereal__topology_2EOpen @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(87,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ! [D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C ) )
=> ( c_2Elim_2Econtl @ A @ D ) ) )
=> ? [D: tyop_2Erealax_2Ereal] :
( ! [E: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C ) )
=> ( c_2Ereal_2Ereal__lte @ D @ ( A @ E ) ) )
& ? [E: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C )
& ( ( A @ E )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Elim_2ECONT__ATTAINS2) ).
thf(681,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ! [D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C ) )
=> ( c_2Elim_2Econtl @ A @ D ) ) )
=> ? [D: tyop_2Erealax_2Ereal] :
( ! [E: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C ) )
=> ( c_2Ereal_2Ereal__lte @ D @ ( A @ E ) ) )
& ? [E: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C )
& ( ( A @ E )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(100,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal] :
( ( ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A @ E )
& ! [F: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ F )
& ( c_2Ereal_2Ereal__lte @ F @ D ) )
=> ( ( A @ F )
= ( B @ F ) ) ) )
=> ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EINTEGRAL__EQ) ).
thf(736,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal] :
( ( ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A @ E )
& ! [F: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ F )
& ( c_2Ereal_2Ereal__lte @ F @ D ) )
=> ( ( A @ F )
= ( B @ F ) ) ) )
=> ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(307,axiom,
! [A: ( tyop_2Erealax_2Ereal > $o ) > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EBIGINTER @ tyop_2Erealax_2Ereal @ A ) ) @ ( c_2Epred__set_2EBIGINTER @ tyop_2Erealax_2Ereal @ ( c_2Epred__set_2EIMAGE @ ( tyop_2Erealax_2Ereal > $o ) @ ( tyop_2Erealax_2Ereal > $o ) @ c_2Ereal__topology_2Eclosure @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__BIGINTER__SUBSET) ).
thf(1492,plain,
! [A: ( tyop_2Erealax_2Ereal > $o ) > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EBIGINTER @ tyop_2Erealax_2Ereal @ A ) ) @ ( c_2Epred__set_2EBIGINTER @ tyop_2Erealax_2Ereal @ ( c_2Epred__set_2EIMAGE @ ( tyop_2Erealax_2Ereal > $o ) @ ( tyop_2Erealax_2Ereal > $o ) @ c_2Ereal__topology_2Eclosure @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(17,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( c_2Erealax_2Ereal__lt @ B @ C ) )
=> ( c_2Erealax_2Ereal__lt @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LET__TRANS) ).
thf(451,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( c_2Erealax_2Ereal__lt @ B @ C ) )
=> ( c_2Erealax_2Ereal__lt @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(375,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__add @ A @ B ) @ C ) )
= ( c_2Epred__set_2EIMAGE @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__add @ A ) @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__TRANSLATION) ).
thf(1722,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__add @ A @ B ) @ C ) )
= ( c_2Epred__set_2EIMAGE @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__add @ A ) @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(11,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A
@ ( c_2Epred__set_2EGSPEC @ TA @ TA
@ ^ [C: TA] : ( c_2Epair_2E_2C @ TA @ $o @ C @ ( B @ C ) ) ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__GSPEC__IFF) ).
thf(434,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A
@ ( c_2Epred__set_2EGSPEC @ TA @ TA
@ ^ [C: TA] : ( c_2Epair_2E_2C @ TA @ $o @ C @ ( B @ C ) ) ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(331,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB > TA] :
( ( ( c_2Epred__set_2EIMAGE @ TB @ TA @ B @ A )
= ( c_2Epred__set_2EEMPTY @ TA ) )
= ( A
= ( c_2Epred__set_2EEMPTY @ TB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__EQ__EMPTY) ).
thf(1574,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB > TA] :
( ( ( c_2Epred__set_2EIMAGE @ TB @ TA @ B @ A )
= ( c_2Epred__set_2EEMPTY @ TA ) )
= ( A
= ( c_2Epred__set_2EEMPTY @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(5,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ B @ C )
=> ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ A @ B ) @ ( c_2Erealax_2Ereal__add @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__IADD) ).
thf(419,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ B @ C )
=> ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ A @ B ) @ ( c_2Erealax_2Ereal__add @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(330,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o,C: TB > $o] :
( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ ( c_2Epred__set_2EUNION @ TB @ B @ C ) )
= ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ B ) @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__UNION) ).
thf(1571,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o,C: TB > $o] :
( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ ( c_2Epred__set_2EUNION @ TB @ B @ C ) )
= ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ B ) @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(64,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A )
= ( c_2Epred__set_2EEMPTY @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EEMPTY__DIFF) ).
thf(599,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A )
= ( c_2Epred__set_2EEMPTY @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(293,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ C )
= ( ( c_2Epred__set_2ESUBSET @ TA @ A @ C )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__SUBSET) ).
thf(1439,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ C )
= ( ( c_2Epred__set_2ESUBSET @ TA @ A @ C )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(132,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( ~ ( c_2Ereal_2Ereal__lte @ A @ B ) )
= ( c_2Erealax_2Ereal__lt @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__NOT__LE) ).
thf(863,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( ~ ( c_2Ereal_2Ereal__lte @ A @ B ) )
= ( c_2Erealax_2Ereal__lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(215,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Esphere @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__UNION__SPHERE) ).
thf(1175,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Esphere @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(407,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA > $o,D: TB > $o] :
( ( c_2Epair_2EPROD__ALL @ TB @ TA @ D @ C @ ( c_2Epair_2E_2C @ TB @ TA @ B @ A ) )
= ( ( D @ B )
& ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2EPROD__ALL__THM) ).
thf(1877,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA > $o,D: TB > $o] :
( ( c_2Epair_2EPROD__ALL @ TB @ TA @ D @ C @ ( c_2Epair_2E_2C @ TB @ TA @ B @ A ) )
= ( ( D @ B )
& ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(33,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ A )
= ( c_2Ereal__topology_2EClosed @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__SUBSET__EQ) ).
thf(494,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ A )
= ( c_2Ereal__topology_2EClosed @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(264,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ A ) )
= A )
& ( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ B ) )
= B ) )
=> ( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EREGULAR__OPEN__INTER) ).
thf(1339,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ A ) )
= A )
& ( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ B ) )
= B ) )
=> ( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(119,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) @ C @ D )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) @ C @ E ) )
=> ( D = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Etransc_2EDINT__UNIQ) ).
thf(816,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) @ C @ D )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) @ C @ E ) )
=> ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(62,axiom,
! [TA: $tType,A: TA > $o,B: ( TA > $o ) > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EBIGINTER @ TA @ B ) )
= ( ! [C: TA > $o] :
( ( c_2Ebool_2EIN @ ( TA > $o ) @ C @ B )
=> ( c_2Epred__set_2ESUBSET @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Emeasure_2ESUBSET__BIGINTER) ).
thf(594,plain,
! [TA: $tType,A: TA > $o,B: ( TA > $o ) > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EBIGINTER @ TA @ B ) )
= ( ! [C: TA > $o] :
( ( c_2Ebool_2EIN @ ( TA > $o ) @ C @ B )
=> ( c_2Epred__set_2ESUBSET @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(211,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( A = B )
=> ( c_2Ereal_2Ereal__lte @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__EQ__IMP__LE) ).
thf(1162,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( A = B )
=> ( c_2Ereal_2Ereal__lte @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > TA,C: TB > $o] :
( ( ! [D: TB] :
( ( c_2Ebool_2EIN @ TB @ D @ C )
=> ( ( A @ ( B @ D ) )
= D ) ) )
= ( ! [D: TA,E: TB] :
( ( ( c_2Ebool_2EIN @ TB @ E @ C )
& ( D
= ( B @ E ) ) )
=> ( ( A @ D )
= E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewellorder_2EFLATTEN__LEMMA) ).
thf(621,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > TA,C: TB > $o] :
( ( ! [D: TB] :
( ( c_2Ebool_2EIN @ TB @ D @ C )
=> ( ( A @ ( B @ D ) )
= D ) ) )
= ( ! [D: TA,E: TB] :
( ( ( c_2Ebool_2EIN @ TB @ E @ C )
& ( D
= ( B @ E ) ) )
=> ( ( A @ D )
= E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(29,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( c_2Erealax_2Ereal__lt @ C @ D ) )
=> ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ A @ C ) @ ( c_2Erealax_2Ereal__add @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LET__ADD2) ).
thf(483,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ B )
& ( c_2Erealax_2Ereal__lt @ C @ D ) )
=> ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ A @ C ) @ ( c_2Erealax_2Ereal__add @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(40,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ! [D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C ) )
=> ( c_2Elim_2Econtl @ A @ D ) ) )
=> ? [D: tyop_2Erealax_2Ereal] :
! [E: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C ) )
=> ( c_2Ereal_2Ereal__lte @ ( A @ E ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Elim_2ECONT__BOUNDED) ).
thf(520,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ! [D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C ) )
=> ( c_2Elim_2Econtl @ A @ D ) ) )
=> ? [D: tyop_2Erealax_2Ereal] :
! [E: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C ) )
=> ( c_2Ereal_2Ereal__lte @ ( A @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(177,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Elim_2Econtl @ A @ C )
& ( c_2Elim_2Econtl @ B @ ( A @ C ) ) )
=> ( c_2Elim_2Econtl
@ ^ [D: tyop_2Erealax_2Ereal] : ( B @ ( A @ D ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Elim_2ECONT__COMPOSE) ).
thf(1022,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Elim_2Econtl @ A @ C )
& ( c_2Elim_2Econtl @ B @ ( A @ C ) ) )
=> ( c_2Elim_2Econtl
@ ^ [D: tyop_2Erealax_2Ereal] : ( B @ ( A @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(364,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Epair_2Eprod @ TB @ TA,B: tyop_2Epair_2Eprod @ TB @ TA,C: TA > TA > $o,D: TA > TA > $o,E: TB > TB > $o,F: TB > TB > $o] :
( ( ! [G: TB,H: TB] :
( ( F @ G @ H )
=> ( E @ G @ H ) )
& ! [G: TA,H: TA] :
( ( D @ G @ H )
=> ( C @ G @ H ) ) )
=> ( ( c_2Epair_2ELEX @ TB @ TA @ F @ D @ B @ A )
=> ( c_2Epair_2ELEX @ TB @ TA @ E @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2ELEX__MONO) ).
thf(1688,plain,
! [TA: $tType,TB: $tType,A: tyop_2Epair_2Eprod @ TB @ TA,B: tyop_2Epair_2Eprod @ TB @ TA,C: TA > TA > $o,D: TA > TA > $o,E: TB > TB > $o,F: TB > TB > $o] :
( ( ! [G: TB,H: TB] :
( ( F @ G @ H )
=> ( E @ G @ H ) )
& ! [G: TA,H: TA] :
( ( D @ G @ H )
=> ( C @ G @ H ) ) )
=> ( ( c_2Epair_2ELEX @ TB @ TA @ F @ D @ B @ A )
=> ( c_2Epair_2ELEX @ TB @ TA @ E @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(107,axiom,
! [A: tyop_2Erealax_2Ereal] :
~ ( c_2Erealax_2Ereal__lt @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erealax_2EREAL__LT__REFL) ).
thf(769,plain,
! [A: tyop_2Erealax_2Ereal] :
~ ( c_2Erealax_2Ereal__lt @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(298,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal] :
( ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ B @ ( c_2Ereal__topology_2Eclosure @ A ) )
= ( ! [C: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ B @ C )
& ( c_2Ereal__topology_2EOpen @ C ) )
=> ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ C )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__NONEMPTY__OPEN__INTER) ).
thf(1460,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal] :
( ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ B @ ( c_2Ereal__topology_2Eclosure @ A ) )
= ( ! [C: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ B @ C )
& ( c_2Ereal__topology_2EOpen @ C ) )
=> ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ C )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(21,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Efrontier @ A ) )
= ( c_2Ereal__topology_2Einterior @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESET__DIFF__FRONTIER) ).
thf(462,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Efrontier @ A ) )
= ( c_2Ereal__topology_2Einterior @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(153,axiom,
! [TA: $tType] :
( ( c_2Ebool_2EIN @ TA )
= ( ^ [A: TA,B: TA > $o] : ( B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIN__DEF) ).
thf(932,plain,
! [TA: $tType] :
( ( c_2Ebool_2EIN @ TA )
= ( ^ [A: TA,B: TA > $o] : ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(188,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ A @ ( c_2Erealax_2Ereal__add @ B @ C ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ A @ B ) @ ( c_2Erealax_2Ereal__mul @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erealax_2EREAL__LDISTRIB) ).
thf(1061,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ A @ ( c_2Erealax_2Ereal__add @ B @ C ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ A @ B ) @ ( c_2Erealax_2Ereal__mul @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(166,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Efrontier @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Ereal__topology_2Esphere @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__CBALL) ).
thf(983,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Efrontier @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Ereal__topology_2Esphere @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(280,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( ( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ A ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ B ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ENOWHERE__DENSE__UNION) ).
thf(1396,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( ( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ A ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ B ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(367,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Ebetween @ C @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Ereal__topology_2Ebetween @ C @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBETWEEN__SYM) ).
thf(1699,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Ebetween @ C @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Ereal__topology_2Ebetween @ C @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(161,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A )
=> ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A @ ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EINTEGRABLE__DINT) ).
thf(959,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A )
=> ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A @ ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(123,axiom,
! [TA: $tType,A: TA,B: ( TA > $o ) > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ ( c_2Epred__set_2EBIGINTER @ TA @ B ) )
= ( ! [C: TA > $o] :
( ( c_2Ebool_2EIN @ ( TA > $o ) @ C @ B )
=> ( c_2Ebool_2EIN @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__BIGINTER) ).
thf(827,plain,
! [TA: $tType,A: TA,B: ( TA > $o ) > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ ( c_2Epred__set_2EBIGINTER @ TA @ B ) )
= ( ! [C: TA > $o] :
( ( c_2Ebool_2EIN @ ( TA > $o ) @ C @ B )
=> ( c_2Ebool_2EIN @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(186,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o,C: TA > $o] :
( ( ! [D: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ D @ C )
=> ? [E: TB > $o] :
( ( c_2Epred__set_2ESUBSET @ TB @ E @ B )
& ( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ E )
= D ) ) ) )
= ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
=> ? [E: TB] :
( ( c_2Ebool_2EIN @ TB @ E @ B )
& ( ( A @ E )
= D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ESURJECTIVE__ON__IMAGE) ).
thf(1044,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o,C: TA > $o] :
( ( ! [D: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ D @ C )
=> ? [E: TB > $o] :
( ( c_2Epred__set_2ESUBSET @ TB @ E @ B )
& ( ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ E )
= D ) ) ) )
= ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
=> ? [E: TB] :
( ( c_2Ebool_2EIN @ TB @ E @ B )
& ( ( A @ E )
= D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(134,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > TB,C: TA > $o] :
( ( ! [D: TB] :
( ( c_2Ebool_2EIN @ TB @ D @ ( c_2Epred__set_2EIMAGE @ TA @ TB @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
=> ( A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EFORALL__IN__IMAGE) ).
thf(868,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > TB,C: TA > $o] :
( ( ! [D: TB] :
( ( c_2Ebool_2EIN @ TB @ D @ ( c_2Epred__set_2EIMAGE @ TA @ TB @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
=> ( A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(67,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ A @ B )
=> ? [C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ A @ C )
& ( c_2Erealax_2Ereal__lt @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MEAN) ).
thf(608,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ A @ B )
=> ? [C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ A @ C )
& ( c_2Erealax_2Ereal__lt @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(167,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EClosed @ A )
& ( c_2Ereal__topology_2EClosed @ B ) )
=> ( c_2Ereal__topology_2EClosed @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSED__UNION) ).
thf(986,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EClosed @ A )
& ( c_2Ereal__topology_2EClosed @ B ) )
=> ( c_2Ereal__topology_2EClosed @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(201,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ D )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B ) )
=> ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D )
@ ^ [E: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add @ ( A @ E ) @ ( B @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EINTEGRABLE__ADD) ).
thf(1113,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ D )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B ) )
=> ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D )
@ ^ [E: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add @ ( A @ E ) @ ( B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(309,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal,F: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ( c_2Ereal_2Ereal__lte @ C @ D )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A @ E )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A @ F ) )
=> ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ D ) @ A @ ( c_2Erealax_2Ereal__add @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EDINT__COMBINE) ).
thf(1496,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal,F: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ( c_2Ereal_2Ereal__lte @ C @ D )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A @ E )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A @ F ) )
=> ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ D ) @ A @ ( c_2Erealax_2Ereal__add @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(197,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ A )
=> ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Einterior @ B ) )
= ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__SUBSET__INTERIOR) ).
thf(1102,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ A )
=> ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Einterior @ B ) )
= ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(37,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ A @ ( c_2Erealax_2Ereal__mul @ B @ C ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__mul @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MUL__ASSOC) ).
thf(505,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ A @ ( c_2Erealax_2Ereal__mul @ B @ C ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__mul @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB > $o,C: TB > TA] :
( ( c_2Ebool_2EIN @ TA @ A @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ C @ B ) )
= ( ? [D: TB] :
( ( A
= ( C @ D ) )
& ( c_2Ebool_2EIN @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__IMAGE) ).
thf(431,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB > $o,C: TB > TA] :
( ( c_2Ebool_2EIN @ TA @ A @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ C @ B ) )
= ( ? [D: TB] :
( ( A
= ( C @ D ) )
& ( c_2Ebool_2EIN @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(365,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Epair_2Eprod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( c_2Epair_2E_2C @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2Epair__CASES) ).
thf(1694,plain,
! [TA: $tType,TB: $tType,A: tyop_2Epair_2Eprod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( c_2Epair_2E_2C @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(85,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ B @ A )
=> ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EDINT__WRONG) ).
thf(675,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ B @ A )
=> ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(212,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__IDEMPOT) ).
thf(1166,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(49,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Efrontier @ ( c_2Ereal__topology_2Efrontier @ ( c_2Ereal__topology_2Efrontier @ A ) ) )
= ( c_2Ereal__topology_2Efrontier @ ( c_2Ereal__topology_2Efrontier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__FRONTIER__FRONTIER) ).
thf(548,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Efrontier @ ( c_2Ereal__topology_2Efrontier @ ( c_2Ereal__topology_2Efrontier @ A ) ) )
= ( c_2Ereal__topology_2Efrontier @ ( c_2Ereal__topology_2Efrontier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(248,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB > $o] :
( ( c_2Epred__set_2ESUBSET @ TB @ A @ B )
=> ! [C: TB > TA] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ C @ A ) @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__SUBSET) ).
thf(1277,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB > $o] :
( ( c_2Epred__set_2ESUBSET @ TB @ A @ B )
=> ! [C: TB > TA] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ C @ A ) @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(193,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
=> ( ( c_2Epred__set_2EINTER @ TA @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__INTER1) ).
thf(1081,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
=> ( ( c_2Epred__set_2EINTER @ TA @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(302,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ A )
=> ( ( c_2Ereal__topology_2Einterior @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__OPEN) ).
thf(1472,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ A )
=> ( ( c_2Ereal__topology_2Einterior @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(207,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > $o,C: TB > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ B @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ C ) )
= ( ? [D: TB > $o] :
( ( c_2Epred__set_2ESUBSET @ TB @ D @ C )
& ( B
= ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESUBSET__IMAGE) ).
thf(1145,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > $o,C: TB > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ B @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ C ) )
= ( ? [D: TB > $o] :
( ( c_2Epred__set_2ESUBSET @ TB @ D @ C )
& ( B
= ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(51,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__add @ A @ B ) @ C )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ A @ C ) @ ( c_2Erealax_2Ereal__mul @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__ADD__RDISTRIB) ).
thf(553,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__add @ A @ B ) @ C )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ A @ C ) @ ( c_2Erealax_2Ereal__mul @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(25,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2EDIFF @ TA @ A @ B )
= ( c_2Epred__set_2EEMPTY @ TA ) )
= ( c_2Epred__set_2ESUBSET @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__DIFF__EMPTY) ).
thf(473,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2EDIFF @ TA @ A @ B )
= ( c_2Epred__set_2EEMPTY @ TA ) )
= ( c_2Epred__set_2ESUBSET @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(191,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ A @ B )
| ( c_2Erealax_2Ereal__lt @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LET__TOTAL) ).
thf(1076,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ A @ B )
| ( c_2Erealax_2Ereal__lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(44,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ A )
= ( c_2Epred__set_2EDIFF @ TA @ B @ A ) )
& ( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ B )
= ( c_2Epred__set_2EDIFF @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__SAME__UNION) ).
thf(531,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ A )
= ( c_2Epred__set_2EDIFF @ TA @ B @ A ) )
& ( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ B )
= ( c_2Epred__set_2EDIFF @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(157,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o] :
( ( c_2Epred__set_2EGSPEC @ TA @ TB
@ ^ [C: TB] : ( c_2Epair_2E_2C @ TA @ $o @ ( A @ C ) @ ( B @ C ) ) )
= ( c_2Epred__set_2EIMAGE @ TB @ TA @ A
@ ( c_2Epred__set_2EGSPEC @ TB @ TB
@ ^ [C: TB] : ( c_2Epair_2E_2C @ TB @ $o @ C @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESIMPLE__IMAGE__GEN) ).
thf(944,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o] :
( ( c_2Epred__set_2EGSPEC @ TA @ TB
@ ^ [C: TB] : ( c_2Epair_2E_2C @ TA @ $o @ ( A @ C ) @ ( B @ C ) ) )
= ( c_2Epred__set_2EIMAGE @ TB @ TA @ A
@ ( c_2Epred__set_2EGSPEC @ TB @ TB
@ ^ [C: TB] : ( c_2Epair_2E_2C @ TB @ $o @ C @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(117,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__SUBSET) ).
thf(812,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(314,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o,C: TB > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ ( c_2Epred__set_2EINTER @ TB @ B @ C ) ) @ ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ B ) @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__INTER) ).
thf(1509,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o,C: TB > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ ( c_2Epred__set_2EINTER @ TB @ B @ C ) ) @ ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ B ) @ ( c_2Epred__set_2EIMAGE @ TB @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(41,axiom,
! [A: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ ( c_2Ereal__topology_2Efrontier @ A ) ) @ ( c_2Ereal__topology_2Efrontier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__FRONTIER__SUBSET) ).
thf(525,plain,
! [A: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ ( c_2Ereal__topology_2Efrontier @ A ) ) @ ( c_2Ereal__topology_2Efrontier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(94,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Ereal__topology_2Esphere @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECBALL__DIFF__BALL) ).
thf(712,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Ereal__topology_2Esphere @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(339,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ A ) ) ) )
= ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__INTERIOR__IDEMP) ).
thf(1598,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ A ) ) ) )
= ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(190,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ A )
| ( c_2Ereal__topology_2EClosed @ A ) )
=> ( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Efrontier @ A ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__FRONTIER__EMPTY) ).
thf(1070,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ A )
| ( c_2Ereal__topology_2EClosed @ A ) )
=> ( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Efrontier @ A ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(3,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ D )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A ) )
=> ( ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D )
@ ^ [E: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__mul @ B @ ( A @ E ) ) )
= ( c_2Erealax_2Ereal__mul @ B @ ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EINTEGRAL__CMUL) ).
thf(414,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ D )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A ) )
=> ( ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D )
@ ^ [E: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__mul @ B @ ( A @ E ) ) )
= ( c_2Erealax_2Ereal__mul @ B @ ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(170,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o] :
( ( ! [B: tyop_2Erealax_2Ereal] : ( A @ B @ B )
& ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( A @ B @ C )
= ( A @ C @ B ) )
& ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ B @ C )
=> ( A @ B @ C ) ) )
=> ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] : ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eiterate_2EREAL__WLOG__LT) ).
thf(993,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal > $o] :
( ( ! [B: tyop_2Erealax_2Ereal] : ( A @ B @ B )
& ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( A @ B @ C )
= ( A @ C @ B ) )
& ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ B @ C )
=> ( A @ B @ C ) ) )
=> ! [B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] : ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(109,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ A )
= ( c_2Ebool_2EIN @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EEXTENSION) ).
thf(776,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ A )
= ( c_2Ebool_2EIN @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(383,axiom,
! [TA: $tType,TB: $tType,A: ( tyop_2Epair_2Eprod @ TB @ TA ) > $o] :
( ( ? [B: tyop_2Epair_2Eprod @ TB @ TA] : ( A @ B ) )
= ( ? [B: TB,C: TA] : ( A @ ( c_2Epair_2E_2C @ TB @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2EEXISTS__PROD) ).
thf(1748,plain,
! [TA: $tType,TB: $tType,A: ( tyop_2Epair_2Eprod @ TB @ TA ) > $o] :
( ( ? [B: tyop_2Epair_2Eprod @ TB @ TA] : ( A @ B ) )
= ( ? [B: TB,C: TA] : ( A @ ( c_2Epair_2E_2C @ TB @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(111,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Esphere @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECBALL__DIFF__SPHERE) ).
thf(791,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Esphere @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(220,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EDIST__TRIANGLE__ALT) ).
thf(1188,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) ) @ ( c_2Erealax_2Ereal__add @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(183,axiom,
! [A: tyop_2Erealax_2Ereal > $o] : ( c_2Ereal__topology_2EClosed @ ( c_2Ereal__topology_2Efrontier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__CLOSED) ).
thf(1038,plain,
! [A: tyop_2Erealax_2Ereal > $o] : ( c_2Ereal__topology_2EClosed @ ( c_2Ereal__topology_2Efrontier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(404,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal__topology_2Ebetween @ A @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) )
& ( c_2Ereal__topology_2Ebetween @ D @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
=> ( c_2Ereal__topology_2Ebetween @ A @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBETWEEN__TRANS__2) ).
thf(1869,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal__topology_2Ebetween @ A @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) )
& ( c_2Ereal__topology_2Ebetween @ D @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
=> ( c_2Ereal__topology_2Ebetween @ A @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(128,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA > $o] :
( ( ! [C: TB,D: TB] :
( ( A @ C @ D )
=> ( A @ D @ C ) )
& ! [C: TA,D: TB,E: TB] :
( ( ( A @ D @ E )
& ( c_2Ebool_2EIN @ TA @ C @ ( B @ D ) ) )
=> ( c_2Ebool_2EIN @ TA @ C @ ( B @ E ) ) ) )
=> ! [C: TB,D: TB] :
( ( A @ C @ D )
=> ( ( B @ C )
= ( B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewellorder_2Eseteq__wlog) ).
thf(840,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA > $o] :
( ( ! [C: TB,D: TB] :
( ( A @ C @ D )
=> ( A @ D @ C ) )
& ! [C: TA,D: TB,E: TB] :
( ( ( A @ D @ E )
& ( c_2Ebool_2EIN @ TA @ C @ ( B @ D ) ) )
=> ( c_2Ebool_2EIN @ TA @ C @ ( B @ E ) ) ) )
=> ! [C: TB,D: TB] :
( ( A @ C @ D )
=> ( ( B @ C )
= ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(236,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ A @ B )
= ( c_2Erealax_2Ereal__add @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erealax_2EREAL__ADD__SYM) ).
thf(1235,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ A @ B )
= ( c_2Erealax_2Ereal__add @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(380,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal_2Emin @ B @ C ) ) )
= ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__MIN__INTER) ).
thf(1738,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal_2Emin @ B @ C ) ) )
= ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(263,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ C @ ( c_2Erealax_2Ereal__add @ B @ A ) )
= ( c_2Erealax_2Ereal__add @ B @ ( c_2Erealax_2Ereal__add @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er220) ).
thf(1336,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ C @ ( c_2Erealax_2Ereal__add @ B @ A ) )
= ( c_2Erealax_2Ereal__add @ B @ ( c_2Erealax_2Ereal__add @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(233,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ A @ B )
= ( ? [C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ A @ C )
& ( c_2Ereal_2Ereal__lte @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EREAL__LE__BETWEEN) ).
thf(1220,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ A @ B )
= ( ? [C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ A @ C )
& ( c_2Ereal_2Ereal__lte @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(390,axiom,
! [TA: $tType,A: TA > $o,B: TA > TA > $o] :
( ( c_2Eposet_2Erelation @ TA @ ( c_2Epair_2E_2C @ ( TA > $o ) @ ( TA > TA > $o ) @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eposet_2Erelation__def) ).
thf(1790,plain,
! [TA: $tType,A: TA > $o,B: TA > TA > $o] :
( ( c_2Eposet_2Erelation @ TA @ ( c_2Epair_2E_2C @ ( TA > $o ) @ ( TA > TA > $o ) @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(373,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( c_2Epair_2E_2C @ TB @ TA @ A @ B )
= ( c_2Epair_2E_2C @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2ECLOSED__PAIR__EQ) ).
thf(1716,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( c_2Epair_2E_2C @ TB @ TA @ A @ B )
= ( c_2Epair_2E_2C @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(48,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__IMP__NE) ).
thf(544,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(147,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
~ ( ( c_2Erealax_2Ereal__lt @ A @ B )
& ( c_2Erealax_2Ereal__lt @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__ANTISYM) ).
thf(907,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
~ ( ( c_2Erealax_2Ereal__lt @ A @ B )
& ( c_2Erealax_2Ereal__lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(91,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ A @ B )
= ( ? [C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ A @ C )
& ( c_2Erealax_2Ereal__lt @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eiterate_2EREAL__LT__BETWEEN) ).
thf(703,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ A @ B )
= ( ? [C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ A @ C )
& ( c_2Erealax_2Ereal__lt @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(368,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EDIST__SYM) ).
thf(1702,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(251,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Emin @ ( c_2Erealax_2Ereal__add @ B @ A ) @ ( c_2Erealax_2Ereal__add @ C @ A ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Emin @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MIN__ADD) ).
thf(1284,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Emin @ ( c_2Erealax_2Ereal__add @ B @ A ) @ ( c_2Erealax_2Ereal__add @ C @ A ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Ereal_2Emin @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(205,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ C ) )
=> ( c_2Epred__set_2ESUBSET @ TA @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__TRANS) ).
thf(1140,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ C ) )
=> ( c_2Epred__set_2ESUBSET @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(172,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__lt @ A @ B )
& ( c_2Erealax_2Ereal__lt @ C @ D ) )
=> ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ A @ C ) @ ( c_2Erealax_2Ereal__add @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__ADD2) ).
thf(1008,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__lt @ A @ B )
& ( c_2Erealax_2Ereal__lt @ C @ D ) )
=> ( c_2Erealax_2Ereal__lt @ ( c_2Erealax_2Ereal__add @ A @ C ) @ ( c_2Erealax_2Ereal__add @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(56,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ ( c_2Ereal__topology_2Eclosure @ B ) ) @ ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EDIFF__CLOSURE__SUBSET) ).
thf(571,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ ( c_2Ereal__topology_2Eclosure @ B ) ) @ ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(169,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Elim_2Econtl @ A @ C )
& ( c_2Elim_2Econtl @ B @ C ) )
=> ( c_2Elim_2Econtl
@ ^ [D: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__mul @ ( A @ D ) @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Elim_2ECONT__MUL) ).
thf(991,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Elim_2Econtl @ A @ C )
& ( c_2Elim_2Econtl @ B @ C ) )
=> ( c_2Elim_2Econtl
@ ^ [D: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__mul @ ( A @ D ) @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(283,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ A @ B )
| ( c_2Ereal_2Ereal__lte @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__TOTAL) ).
thf(1404,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ A @ B )
| ( c_2Ereal_2Ereal__lte @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(269,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ ( c_2Ereal__topology_2Eclosure @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESUBSET__CLOSURE) ).
thf(1358,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ ( c_2Ereal__topology_2Eclosure @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(312,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) )
= ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EINTER @ TA @ A @ B ) @ ( c_2Epred__set_2EINTER @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__OVER__INTER) ).
thf(1504,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) )
= ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EINTER @ TA @ A @ B ) @ ( c_2Epred__set_2EINTER @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(99,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ? [B: tyop_2Erealax_2Ereal] : ( A @ B )
& ? [B: tyop_2Erealax_2Ereal] :
! [C: tyop_2Erealax_2Ereal] :
( ( A @ C )
=> ( c_2Erealax_2Ereal__lt @ C @ B ) ) )
=> ? [B: tyop_2Erealax_2Ereal] :
! [C: tyop_2Erealax_2Ereal] :
( ( ? [D: tyop_2Erealax_2Ereal] :
( ( A @ D )
& ( c_2Erealax_2Ereal__lt @ C @ D ) ) )
= ( c_2Erealax_2Ereal__lt @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__SUP__EXISTS) ).
thf(727,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ? [B: tyop_2Erealax_2Ereal] : ( A @ B )
& ? [B: tyop_2Erealax_2Ereal] :
! [C: tyop_2Erealax_2Ereal] :
( ( A @ C )
=> ( c_2Erealax_2Ereal__lt @ C @ B ) ) )
=> ? [B: tyop_2Erealax_2Ereal] :
! [C: tyop_2Erealax_2Ereal] :
( ( ? [D: tyop_2Erealax_2Ereal] :
( ( A @ D )
& ( c_2Erealax_2Ereal__lt @ C @ D ) ) )
= ( c_2Erealax_2Ereal__lt @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(246,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ ( c_2Ereal__topology_2Eclosure @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__INTER__SUBSET) ).
thf(1272,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ ( c_2Ereal__topology_2Eclosure @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(68,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ A @ B )
= ( c_2Erealax_2Ereal__mul @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MUL__SYM) ).
thf(612,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ A @ B )
= ( c_2Erealax_2Ereal__mul @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(34,axiom,
! [TA: $tType,A: TA > $o,B: ( TA > $o ) > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EBIGINTER @ TA @ B ) )
= ( ! [C: TA > $o] :
( ( c_2Ebool_2EIN @ ( TA > $o ) @ C @ B )
=> ( c_2Epred__set_2ESUBSET @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__BIGINTER) ).
thf(497,plain,
! [TA: $tType,A: TA > $o,B: ( TA > $o ) > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EBIGINTER @ TA @ B ) )
= ( ! [C: TA > $o] :
( ( c_2Ebool_2EIN @ ( TA > $o ) @ C @ B )
=> ( c_2Epred__set_2ESUBSET @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(137,axiom,
! [TA: $tType,A: ( tyop_2Epair_2Eprod @ TA @ TA ) > $o] :
( ( c_2Ewellorder_2Eposet @ TA @ A )
= ( ! [B: TA] :
( ( c_2Ewellorder_2Efl @ TA @ A @ B )
=> ( A @ ( c_2Epair_2E_2C @ TA @ TA @ B @ B ) ) )
& ! [B: TA,C: TA,D: TA] :
( ( ( A @ ( c_2Epair_2E_2C @ TA @ TA @ B @ C ) )
& ( A @ ( c_2Epair_2E_2C @ TA @ TA @ C @ D ) ) )
=> ( A @ ( c_2Epair_2E_2C @ TA @ TA @ B @ D ) ) )
& ! [B: TA,C: TA] :
( ( ( A @ ( c_2Epair_2E_2C @ TA @ TA @ B @ C ) )
& ( A @ ( c_2Epair_2E_2C @ TA @ TA @ C @ B ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewellorder_2Eposet) ).
thf(876,plain,
! [TA: $tType,A: ( tyop_2Epair_2Eprod @ TA @ TA ) > $o] :
( ( c_2Ewellorder_2Eposet @ TA @ A )
= ( ! [B: TA] :
( ( c_2Ewellorder_2Efl @ TA @ A @ B )
=> ( A @ ( c_2Epair_2E_2C @ TA @ TA @ B @ B ) ) )
& ! [B: TA,C: TA,D: TA] :
( ( ( A @ ( c_2Epair_2E_2C @ TA @ TA @ B @ C ) )
& ( A @ ( c_2Epair_2E_2C @ TA @ TA @ C @ D ) ) )
=> ( A @ ( c_2Epair_2E_2C @ TA @ TA @ B @ D ) ) )
& ! [B: TA,C: TA] :
( ( ( A @ ( c_2Epair_2E_2C @ TA @ TA @ B @ C ) )
& ( A @ ( c_2Epair_2E_2C @ TA @ TA @ C @ B ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(393,axiom,
! [TA: $tType,TB: $tType,A: ( tyop_2Epair_2Eprod @ TB @ TA ) > $o] :
( ( ! [B: tyop_2Epair_2Eprod @ TB @ TA] : ( A @ B ) )
= ( ! [B: TB,C: TA] : ( A @ ( c_2Epair_2E_2C @ TB @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2EFORALL__PROD) ).
thf(1839,plain,
! [TA: $tType,TB: $tType,A: ( tyop_2Epair_2Eprod @ TB @ TA ) > $o] :
( ( ! [B: tyop_2Epair_2Eprod @ TB @ TA] : ( A @ B ) )
= ( ! [B: TB,C: TA] : ( A @ ( c_2Epair_2E_2C @ TB @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(217,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A ) )
=> ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ D @ E ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EINTEGRABLE__SUBINTERVAL) ).
thf(1180,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A ) )
=> ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ D @ E ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(52,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ A @ B )
=> ~ ( c_2Erealax_2Ereal__lt @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__GT) ).
thf(556,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ A @ B )
=> ~ ( c_2Erealax_2Ereal__lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(46,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ A @ ( c_2Erealax_2Ereal__mul @ B @ C ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__mul @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erealax_2EREAL__MUL__ASSOC) ).
thf(539,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ A @ ( c_2Erealax_2Ereal__mul @ B @ C ) )
= ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__mul @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(395,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TD > TC > $o,B: TB > TD > TA > $o,C: TE,D: TB,E: TD,F: TC,G: TA] :
( ( c_2Epath_2Eparallel__comp @ TE @ TD @ TC @ TB @ TA @ A @ B @ ( c_2Epair_2E_2C @ TE @ TB @ C @ D ) @ E @ ( c_2Epair_2E_2C @ TC @ TA @ F @ G ) )
= ( ( A @ C @ E @ F )
& ( B @ D @ E @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epath_2Eparallel__comp__def) ).
thf(1844,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TD > TC > $o,B: TB > TD > TA > $o,C: TE,D: TB,E: TD,F: TC,G: TA] :
( ( c_2Epath_2Eparallel__comp @ TE @ TD @ TC @ TB @ TA @ A @ B @ ( c_2Epair_2E_2C @ TE @ TB @ C @ D ) @ E @ ( c_2Epair_2E_2C @ TC @ TA @ F @ G ) )
= ( ( A @ C @ E @ F )
& ( B @ D @ E @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(316,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ B @ A )
& ( c_2Ereal__topology_2EOpen @ B )
& ! [C: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ C @ A )
& ( c_2Ereal__topology_2EOpen @ C ) )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ C @ B ) ) )
=> ( ( c_2Ereal__topology_2Einterior @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__UNIQUE) ).
thf(1517,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ B @ A )
& ( c_2Ereal__topology_2EOpen @ B )
& ! [C: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ C @ A )
& ( c_2Ereal__topology_2EOpen @ C ) )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ C @ B ) ) )
=> ( ( c_2Ereal__topology_2Einterior @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(173,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__DIFF__2) ).
thf(1010,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(403,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Ebetween @ B @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ A ) )
= ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBETWEEN__REFL__EQ) ).
thf(1866,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Ebetween @ B @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ A ) )
= ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(199,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ B @ A )
& ( c_2Ereal__topology_2EOpen @ B ) )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ B @ ( c_2Ereal__topology_2Einterior @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__MAXIMAL) ).
thf(1108,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ B @ A )
& ( c_2Ereal__topology_2EOpen @ B ) )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ B @ ( c_2Ereal__topology_2Einterior @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(289,axiom,
( ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__EMPTY) ).
thf(1421,plain,
( ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(22,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ A @ ( c_2Erealax_2Ereal__add @ B @ C ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ A @ B ) @ ( c_2Erealax_2Ereal__mul @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__ADD__LDISTRIB) ).
thf(465,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ A @ ( c_2Erealax_2Ereal__add @ B @ C ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ A @ B ) @ ( c_2Erealax_2Ereal__mul @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(256,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__add @ A @ C )
= ( c_2Erealax_2Ereal__add @ B @ C ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__EQ__RADD) ).
thf(1316,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( ( c_2Erealax_2Ereal__add @ A @ C )
= ( c_2Erealax_2Ereal__add @ B @ C ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(194,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( ( c_2Epred__set_2EUNION @ TA @ B @ C )
= ( c_2Epred__set_2EUNION @ TA @ C @ B ) )
& ( ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) @ A )
= ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) @ A ) )
& ( ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) @ A )
= ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EUNION @ TA @ C @ B ) @ A ) )
& ( ( c_2Epred__set_2EUNION @ TA @ B @ B )
= B )
& ( ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EUNION @ TA @ B @ B ) @ C )
= ( c_2Epred__set_2EUNION @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EUNION__ACI) ).
thf(1084,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( ( c_2Epred__set_2EUNION @ TA @ B @ C )
= ( c_2Epred__set_2EUNION @ TA @ C @ B ) )
& ( ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) @ A )
= ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EUNION @ TA @ C @ B ) @ A ) )
& ( ( c_2Epred__set_2EUNION @ TA @ B @ B )
= B )
& ( ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EUNION @ TA @ B @ B ) @ C )
= ( c_2Epred__set_2EUNION @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(354,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__applied) ).
thf(1654,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(286,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ A @ B ) @ ( c_2Erealax_2Ereal__add @ A @ C ) )
= ( c_2Ereal_2Ereal__lte @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__LADD) ).
thf(1412,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ ( c_2Erealax_2Ereal__add @ A @ B ) @ ( c_2Erealax_2Ereal__add @ A @ C ) )
= ( c_2Ereal_2Ereal__lte @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(387,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Ebounded__def @ ( c_2Ereal__topology_2Eclosure @ A ) )
= ( c_2Ereal__topology_2Ebounded__def @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__CLOSURE__EQ) ).
thf(1781,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Ebounded__def @ ( c_2Ereal__topology_2Eclosure @ A ) )
= ( c_2Ereal__topology_2Ebounded__def @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(141,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__add @ A @ B ) @ C )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ A @ C ) @ ( c_2Erealax_2Ereal__mul @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__RDISTRIB) ).
thf(891,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__mul @ ( c_2Erealax_2Ereal__add @ A @ B ) @ C )
= ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__mul @ A @ C ) @ ( c_2Erealax_2Ereal__mul @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(336,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ C )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESUBSET__CBALL) ).
thf(1590,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ C )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(260,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ! [D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C ) )
=> ( c_2Elim_2Econtl @ A @ D ) )
=> ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EINTEGRABLE__CONTINUOUS) ).
thf(1326,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ! [D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C ) )
=> ( c_2Elim_2Econtl @ A @ D ) )
=> ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(60,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ B @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) )
= ( c_2Erealax_2Ereal__lt @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EIN__BALL) ).
thf(588,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ B @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) )
= ( c_2Erealax_2Ereal__lt @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(162,axiom,
! [TA: $tType,A: ( TA > $o ) > $o] :
( ! [B: ( TA > $o ) > $o] :
( ( ! [C: TA > $o] :
( ( c_2Ebool_2EIN @ ( TA > $o ) @ C @ B )
=> ( A @ C ) )
& ! [C: TA > $o,D: TA > $o] :
( ( ( c_2Ebool_2EIN @ ( TA > $o ) @ C @ B )
& ( c_2Ebool_2EIN @ ( TA > $o ) @ D @ B ) )
=> ( ( c_2Epred__set_2ESUBSET @ TA @ C @ D )
| ( c_2Epred__set_2ESUBSET @ TA @ D @ C ) ) ) )
=> ? [C: TA > $o] :
( ( A @ C )
& ! [D: TA > $o] :
( ( c_2Ebool_2EIN @ ( TA > $o ) @ D @ B )
=> ( c_2Epred__set_2ESUBSET @ TA @ D @ C ) ) ) )
=> ? [B: TA > $o] :
( ( A @ B )
& ! [C: TA > $o] :
( ( ( A @ C )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewellorder_2EZL__SUBSETS) ).
thf(961,plain,
! [TA: $tType,A: ( TA > $o ) > $o] :
( ! [B: ( TA > $o ) > $o] :
( ( ! [C: TA > $o] :
( ( c_2Ebool_2EIN @ ( TA > $o ) @ C @ B )
=> ( A @ C ) )
& ! [C: TA > $o,D: TA > $o] :
( ( ( c_2Ebool_2EIN @ ( TA > $o ) @ C @ B )
& ( c_2Ebool_2EIN @ ( TA > $o ) @ D @ B ) )
=> ( ( c_2Epred__set_2ESUBSET @ TA @ C @ D )
| ( c_2Epred__set_2ESUBSET @ TA @ D @ C ) ) ) )
=> ? [C: TA > $o] :
( ( A @ C )
& ! [D: TA > $o] :
( ( c_2Ebool_2EIN @ ( TA > $o ) @ D @ B )
=> ( c_2Epred__set_2ESUBSET @ TA @ D @ C ) ) ) )
=> ? [B: TA > $o] :
( ( A @ B )
& ! [C: TA > $o] :
( ( ( A @ C )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(305,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
=> ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EEQ__SUBSET__SUBSET) ).
thf(1481,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
=> ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(77,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ A )
& ( c_2Ereal__topology_2EClosed @ B ) )
=> ( c_2Ereal__topology_2EOpen @ ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__DIFF) ).
thf(652,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2EOpen @ A )
& ( c_2Ereal__topology_2EClosed @ B ) )
=> ( c_2Ereal__topology_2EOpen @ ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(350,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A ) )
=> ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ D @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EINTEGRABLE__SUBINTERVAL__RIGHT) ).
thf(1629,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ D )
& ( c_2Ereal_2Ereal__lte @ D @ C )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A ) )
=> ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ D @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(382,axiom,
! [TA: $tType,A: ( tyop_2Epair_2Eprod @ TA @ TA ) > $o,B: TA] :
( ( c_2Ewellorder_2Efl @ TA @ A @ B )
= ( ? [C: TA] :
( ( A @ ( c_2Epair_2E_2C @ TA @ TA @ B @ C ) )
| ( A @ ( c_2Epair_2E_2C @ TA @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewellorder_2Efl) ).
thf(1745,plain,
! [TA: $tType,A: ( tyop_2Epair_2Eprod @ TA @ TA ) > $o,B: TA] :
( ( c_2Ewellorder_2Efl @ TA @ A @ B )
= ( ? [C: TA] :
( ( A @ ( c_2Epair_2E_2C @ TA @ TA @ B @ C ) )
| ( A @ ( c_2Epair_2E_2C @ TA @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(238,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Ebetween @ A @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) )
= ( ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ A ) ) @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2Ebetween) ).
thf(1244,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Ebetween @ A @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) )
= ( ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ A ) ) @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(327,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB > $o,C: TB > TA] :
( ! [D: TB,E: TB] :
( ( ( C @ D )
= ( C @ E ) )
= ( D = E ) )
=> ( ( ( c_2Epred__set_2EIMAGE @ TB @ TA @ C @ B )
= ( c_2Epred__set_2EIMAGE @ TB @ TA @ C @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__11) ).
thf(1558,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB > $o,C: TB > TA] :
( ! [D: TB,E: TB] :
( ( ( C @ D )
= ( C @ E ) )
= ( D = E ) )
=> ( ( ( c_2Epred__set_2EIMAGE @ TB @ TA @ C @ B )
= ( c_2Epred__set_2EIMAGE @ TB @ TA @ C @ A ) )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(180,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ ( c_2Epred__set_2EINTER @ TA @ A @ B ) )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
& ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__INTER) ).
thf(1030,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ ( c_2Epred__set_2EINTER @ TA @ A @ B ) )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
& ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(55,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EClosed @ A )
=> ( ( c_2Ereal__topology_2Econnected @ A )
= ( ~ ? [B: tyop_2Erealax_2Ereal > $o,C: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EClosed @ B )
& ( c_2Ereal__topology_2EClosed @ C )
& ( B
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( C
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ B @ C )
= A )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ B @ C )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__CLOSED__SET) ).
thf(568,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EClosed @ A )
=> ( ( c_2Ereal__topology_2Econnected @ A )
= ( ~ ? [B: tyop_2Erealax_2Ereal > $o,C: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EClosed @ B )
& ( c_2Ereal__topology_2EClosed @ C )
& ( B
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( C
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ B @ C )
= A )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ B @ C )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(83,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal,F: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ D )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A @ E )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B @ F )
& ! [G: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ G )
& ( c_2Ereal_2Ereal__lte @ G @ D ) )
=> ( c_2Ereal_2Ereal__lte @ ( A @ G ) @ ( B @ G ) ) ) )
=> ( c_2Ereal_2Ereal__lte @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EDINT__LE) ).
thf(667,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal,F: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ D )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A @ E )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B @ F )
& ! [G: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ G )
& ( c_2Ereal_2Ereal__lte @ G @ D ) )
=> ( c_2Ereal_2Ereal__lte @ ( A @ G ) @ ( B @ G ) ) ) )
=> ( c_2Ereal_2Ereal__lte @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(152,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Efrontier @ A ) )
= ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ A ) ) @ ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__FRONTIER) ).
thf(929,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Efrontier @ A ) )
= ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Eclosure @ A ) ) @ ( c_2Ereal__topology_2Eclosure @ ( c_2Ereal__topology_2Einterior @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(27,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( c_2Elim_2Econtl
@ ^ [C: tyop_2Erealax_2Ereal] : A
@ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Elim_2ECONT__CONST) ).
thf(478,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( c_2Elim_2Econtl
@ ^ [C: tyop_2Erealax_2Ereal] : A
@ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(144,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ B @ ( c_2Ereal__topology_2Esphere @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) )
= ( ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EIN__SPHERE) ).
thf(899,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ B @ ( c_2Ereal__topology_2Esphere @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) )
= ( ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(342,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ B @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) )
= ( c_2Ereal_2Ereal__lte @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EIN__CBALL) ).
thf(1607,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ B @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) )
= ( c_2Ereal_2Ereal__lte @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(105,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ A ) @ A )
= ( c_2Ereal__topology_2EClosed @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__SUBSET__EQ) ).
thf(763,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ A ) @ A )
= ( c_2Ereal__topology_2EClosed @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(295,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Epred__set_2EGSPEC @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal
@ ^ [C: tyop_2Erealax_2Ereal] : ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ $o @ C @ ( c_2Ereal_2Ereal__lte @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2Ecball) ).
thf(1444,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Epred__set_2EGSPEC @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal
@ ^ [C: tyop_2Erealax_2Ereal] : ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ $o @ C @ ( c_2Ereal_2Ereal__lte @ ( c_2Ereal__topology_2EDist @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(294,axiom,
! [A: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Eclosure @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__SUBSET) ).
thf(1442,plain,
! [A: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Eclosure @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(266,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ A )
=> ( ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Eclosure @ B ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__INTER__CLOSURE__EQ__EMPTY) ).
thf(1348,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ A )
=> ( ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Eclosure @ B ) )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
= ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(376,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ C )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESUBSET__BALL) ).
thf(1725,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ C )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(125,axiom,
! [A: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ ( c_2Ereal__topology_2Eclosure @ A ) ) @ ( c_2Ereal__topology_2Efrontier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__CLOSURE__SUBSET) ).
thf(833,plain,
! [A: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ ( c_2Ereal__topology_2Eclosure @ A ) ) @ ( c_2Ereal__topology_2Efrontier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(323,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Esphere @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESPHERE__UNION__BALL) ).
thf(1546,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Esphere @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(274,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
=> ( ( c_2Epred__set_2EINTER @ TA @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__INTER2) ).
thf(1380,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
=> ( ( c_2Epred__set_2EINTER @ TA @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(129,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ A )
= ( ! [B: tyop_2Erealax_2Ereal] :
( ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ B @ A )
=> ? [C: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ C )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ B @ C )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__SUB__OPEN) ).
thf(854,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ A )
= ( ! [B: tyop_2Erealax_2Ereal] :
( ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ B @ A )
=> ? [C: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ C )
& ( c_2Ebool_2EIN @ tyop_2Erealax_2Ereal @ B @ C )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(195,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Econnected @ A )
= ( ~ ? [B: tyop_2Erealax_2Ereal > $o,C: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ B )
& ( c_2Ereal__topology_2EOpen @ C )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ B @ C ) )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ B @ C ) @ A )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ B @ A )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ C @ A )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2Econnected) ).
thf(1097,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Econnected @ A )
= ( ~ ? [B: tyop_2Erealax_2Ereal > $o,C: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ B )
& ( c_2Ereal__topology_2EOpen @ C )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ B @ C ) )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ B @ C ) @ A )
= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ B @ A )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ C @ A )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(126,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( c_2Ebool_2EIN @ TA @ B @ A )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESPECIFICATION) ).
thf(835,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( c_2Ebool_2EIN @ TA @ B @ A )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(318,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: TB,F: TA] :
( ( ( c_2Ereal_2Ereal__lte @ C @ D )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B )
& ! [G: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ G )
& ( c_2Ereal_2Ereal__lte @ G @ D ) )
=> ( c_2Ereal_2Ereal__lte @ ( A @ G ) @ ( B @ G ) ) ) )
=> ( c_2Ereal_2Ereal__lte @ ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A ) @ ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EINTEGRAL__LE) ).
thf(1527,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ D )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B )
& ! [E: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ E )
& ( c_2Ereal_2Ereal__lte @ E @ D ) )
=> ( c_2Ereal_2Ereal__lte @ ( A @ E ) @ ( B @ E ) ) ) )
=> ( c_2Ereal_2Ereal__lte @ ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A ) @ ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(208,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ A )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Eclosure @ B ) ) @ ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__INTER__CLOSURE__SUBSET) ).
thf(1148,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2EOpen @ A )
=> ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Eclosure @ B ) ) @ ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(292,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ A @ B )
= ( c_2Erealax_2Ereal__add @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__ADD__COMM) ).
thf(1436,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ A @ B )
= ( c_2Erealax_2Ereal__add @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(355,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ B @ A )
= ( c_2Erealax_2Ereal__add @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er215) ).
thf(1657,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ B @ A )
= ( c_2Erealax_2Ereal__add @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(115,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Econnected @ A )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ A @ B )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) )
=> ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Efrontier @ B ) )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__INTER__FRONTIER) ).
thf(807,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Econnected @ A )
& ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) )
& ( ( c_2Epred__set_2EDIFF @ tyop_2Erealax_2Ereal @ A @ B )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) )
=> ( ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ ( c_2Ereal__topology_2Efrontier @ B ) )
!= ( c_2Epred__set_2EEMPTY @ tyop_2Erealax_2Ereal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(12,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__ABS) ).
thf(437,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(328,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ ( c_2Ereal__topology_2Eclosure @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__UNION) ).
thf(1561,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Ereal__topology_2Eclosure @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) )
= ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Eclosure @ A ) @ ( c_2Ereal__topology_2Eclosure @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB > $o,C: TA > $o] :
( ( c_2Ebool_2EIN @ TB @ A @ ( c_2Epred__set_2EBIGINTER @ TB @ ( c_2Epred__set_2EIMAGE @ TA @ ( TB > $o ) @ B @ C ) ) )
= ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
=> ( c_2Ebool_2EIN @ TB @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__BIGINTER__IMAGE) ).
thf(664,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB > $o,C: TA > $o] :
( ( c_2Ebool_2EIN @ TB @ A @ ( c_2Epred__set_2EBIGINTER @ TB @ ( c_2Epred__set_2EIMAGE @ TA @ ( TB > $o ) @ B @ C ) ) )
= ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
=> ( c_2Ebool_2EIN @ TB @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(343,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ D )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B ) )
=> ( ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D )
@ ^ [E: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add @ ( A @ E ) @ ( B @ E ) ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A ) @ ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EINTEGRAL__ADD) ).
thf(1610,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ D )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B ) )
=> ( ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D )
@ ^ [E: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add @ ( A @ E ) @ ( B @ E ) ) )
= ( c_2Erealax_2Ereal__add @ ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A ) @ ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(214,axiom,
! [A: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Emin @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MIN__REFL) ).
thf(1172,plain,
! [A: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Emin @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(143,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal__topology_2EClosed @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSED__CBALL) ).
thf(897,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal__topology_2EClosed @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(181,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Epred__set_2EINTER @ TA @ A @ B @ C )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
& ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__applied) ).
thf(1033,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Epred__set_2EINTER @ TA @ A @ B @ C )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
& ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(371,axiom,
! [TA: $tType,A: ( tyop_2Epair_2Eprod @ TA @ TA ) > $o,B: TA > $o] :
( ( c_2Ewellorder_2EChain @ TA @ A @ B )
= ( ! [C: TA,D: TA] :
( ( ( B @ C )
& ( B @ D ) )
=> ( ( A @ ( c_2Epair_2E_2C @ TA @ TA @ C @ D ) )
| ( A @ ( c_2Epair_2E_2C @ TA @ TA @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewellorder_2Echain) ).
thf(1710,plain,
! [TA: $tType,A: ( tyop_2Epair_2Eprod @ TA @ TA ) > $o,B: TA > $o] :
( ( c_2Ewellorder_2EChain @ TA @ A @ B )
= ( ! [C: TA,D: TA] :
( ( ( B @ C )
& ( B @ D ) )
=> ( ( A @ ( c_2Epair_2E_2C @ TA @ TA @ C @ D ) )
| ( A @ ( c_2Epair_2E_2C @ TA @ TA @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(224,axiom,
! [A: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Emax @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MAX__REFL) ).
thf(1197,plain,
! [A: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Emax @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(72,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ( c_2Ereal_2Ereal__lte @ ( A @ B ) @ D )
& ( c_2Ereal_2Ereal__lte @ D @ ( A @ C ) )
& ! [E: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C ) )
=> ( c_2Elim_2Econtl @ A @ E ) ) )
=> ? [E: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C )
& ( ( A @ E )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Elim_2EIVT) ).
thf(624,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ( c_2Ereal_2Ereal__lte @ ( A @ B ) @ D )
& ( c_2Ereal_2Ereal__lte @ D @ ( A @ C ) )
& ! [E: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C ) )
=> ( c_2Elim_2Econtl @ A @ E ) ) )
=> ? [E: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ B @ E )
& ( c_2Ereal_2Ereal__lte @ E @ C )
& ( ( A @ E )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(267,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ( c_2Ereal_2Ereal__lte @ C @ D )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ D ) @ A ) )
=> ( ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ D ) @ A )
= ( c_2Erealax_2Ereal__add @ ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A ) @ ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EINTEGRAL__COMBINE) ).
thf(1352,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ B @ C )
& ( c_2Ereal_2Ereal__lte @ C @ D )
& ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ D ) @ A ) )
=> ( ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ D ) @ A )
= ( c_2Erealax_2Ereal__add @ ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ B @ C ) @ A ) @ ( c_2Eintegral_2Eintegral @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(243,axiom,
! [A: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__REFL) ).
thf(1261,plain,
! [A: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(321,axiom,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Einterior @ A )
= A )
= ( c_2Ereal__topology_2EOpen @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__EQ) ).
thf(1537,plain,
! [A: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Einterior @ A )
= A )
= ( c_2Ereal__topology_2EOpen @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(273,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ C )
& ( c_2Ereal_2Ereal__lte @ B @ D ) )
=> ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Emin @ A @ B ) @ ( c_2Ereal_2Emin @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__IMP__MIN__LE2) ).
thf(1378,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ A @ C )
& ( c_2Ereal_2Ereal__lte @ B @ D ) )
=> ( c_2Ereal_2Ereal__lte @ ( c_2Ereal_2Emin @ A @ B ) @ ( c_2Ereal_2Emin @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(176,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A != B )
= ( ? [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ B )
= ( ~ ( c_2Ebool_2EIN @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ENOT__EQUAL__SETS) ).
thf(1019,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A != B )
= ( ? [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ B )
= ( ~ ( c_2Ebool_2EIN @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(76,axiom,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal,F: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ D )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A @ E )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B @ F )
& ! [G: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ G )
& ( c_2Ereal_2Ereal__lte @ G @ D ) )
=> ( ( A @ G )
= ( B @ G ) ) ) )
=> ( E = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EDINT__EQ) ).
thf(644,plain,
! [A: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal,D: tyop_2Erealax_2Ereal,E: tyop_2Erealax_2Ereal,F: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ D )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ A @ E )
& ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ C @ D ) @ B @ F )
& ! [G: tyop_2Erealax_2Ereal] :
( ( ( c_2Ereal_2Ereal__lte @ C @ G )
& ( c_2Ereal_2Ereal__lte @ G @ D ) )
=> ( ( A @ G )
= ( B @ G ) ) ) )
=> ( E = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(20,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal] :
( ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) @ C )
= ( ? [D: tyop_2Erealax_2Ereal] : ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2Eintegrable__def) ).
thf(459,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal] :
( ( c_2Eintegral_2Eintegrable @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) @ C )
= ( ? [D: tyop_2Erealax_2Ereal] : ( c_2Etransc_2EDint @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(121,axiom,
! [A: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ ( c_2Ereal__topology_2Einterior @ A ) ) @ ( c_2Ereal__topology_2Efrontier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__INTERIOR__SUBSET) ).
thf(822,plain,
! [A: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ ( c_2Ereal__topology_2Einterior @ A ) ) @ ( c_2Ereal__topology_2Efrontier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(372,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB,E: TA > TA > $o,F: TB > TB > $o] :
( ( c_2Epair_2ELEX @ TB @ TA @ F @ E @ ( c_2Epair_2E_2C @ TB @ TA @ D @ C ) @ ( c_2Epair_2E_2C @ TB @ TA @ B @ A ) )
= ( ( F @ D @ B )
| ( ( D = B )
& ( E @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2ELEX__DEF__THM) ).
thf(1713,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB,E: TA > TA > $o,F: TB > TB > $o] :
( ( c_2Epair_2ELEX @ TB @ TA @ F @ E @ ( c_2Epair_2E_2C @ TB @ TA @ D @ C ) @ ( c_2Epair_2E_2C @ TB @ TA @ B @ A ) )
= ( ( F @ D @ B )
| ( ( D = B )
& ( E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(408,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__CBALL) ).
thf(1880,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal__topology_2Einterior @ ( c_2Ereal__topology_2Ecball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) )
= ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(88,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ A ) @ ( c_2Ereal__topology_2Efrontier @ B ) )
= ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Efrontier @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) ) @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ A ) @ ( c_2Ereal__topology_2Efrontier @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EUNION__FRONTIER) ).
thf(691,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ A ) @ ( c_2Ereal__topology_2Efrontier @ B ) )
= ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Ereal__topology_2Efrontier @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ A @ B ) ) ) @ ( c_2Epred__set_2EINTER @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ A ) @ ( c_2Ereal__topology_2Efrontier @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(135,axiom,
! [TA: $tType,A: TA,B: ( TA > $o ) > $o] :
( ( c_2Epred__set_2EBIGINTER @ TA @ B @ A )
= ( ! [C: TA > $o] :
( ( c_2Ebool_2EIN @ ( TA > $o ) @ C @ B )
=> ( c_2Ebool_2EIN @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EBIGINTER__applied) ).
thf(871,plain,
! [TA: $tType,A: TA,B: ( TA > $o ) > $o] :
( ( c_2Epred__set_2EBIGINTER @ TA @ B @ A )
= ( ! [C: TA > $o] :
( ( c_2Ebool_2EIN @ ( TA > $o ) @ C @ B )
=> ( c_2Ebool_2EIN @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(281,axiom,
! [A: ( tyop_2Erealax_2Ereal > $o ) > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Einterior @ ( c_2Epred__set_2EBIGINTER @ tyop_2Erealax_2Ereal @ A ) ) @ ( c_2Epred__set_2EBIGINTER @ tyop_2Erealax_2Ereal @ ( c_2Epred__set_2EIMAGE @ ( tyop_2Erealax_2Ereal > $o ) @ ( tyop_2Erealax_2Ereal > $o ) @ c_2Ereal__topology_2Einterior @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__BIGINTER__SUBSET) ).
thf(1399,plain,
! [A: ( tyop_2Erealax_2Ereal > $o ) > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Einterior @ ( c_2Epred__set_2EBIGINTER @ tyop_2Erealax_2Ereal @ A ) ) @ ( c_2Epred__set_2EBIGINTER @ tyop_2Erealax_2Ereal @ ( c_2Epred__set_2EIMAGE @ ( tyop_2Erealax_2Ereal > $o ) @ ( tyop_2Erealax_2Ereal > $o ) @ c_2Ereal__topology_2Einterior @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(319,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) )
= ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__ASSOC) ).
thf(1532,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) )
= ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(131,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ A @ B )
= ( ( c_2Erealax_2Ereal__lt @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__LT) ).
thf(860,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] :
( ( c_2Ereal_2Ereal__lte @ A @ B )
= ( ( c_2Erealax_2Ereal__lt @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(261,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__add @ C @ B ) @ A )
= ( c_2Erealax_2Ereal__add @ C @ ( c_2Erealax_2Ereal__add @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er217) ).
thf(1331,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add @ ( c_2Erealax_2Ereal__add @ C @ B ) @ A )
= ( c_2Erealax_2Ereal__add @ C @ ( c_2Erealax_2Ereal__add @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(154,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ C @ ( c_2Ereal_2Emax @ A @ B ) )
= ( ( c_2Erealax_2Ereal__lt @ C @ A )
| ( c_2Erealax_2Ereal__lt @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__MAX) ).
thf(935,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal,C: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__lt @ C @ ( c_2Ereal_2Emax @ A @ B ) )
= ( ( c_2Erealax_2Ereal__lt @ C @ A )
| ( c_2Erealax_2Ereal__lt @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(397,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TA,B: TC,C: TB] :
( ( c_2Efmapal_2EAP__SND @ TC @ TB @ TA @ A @ ( c_2Epair_2E_2C @ TC @ TB @ B @ C ) )
= ( c_2Epair_2E_2C @ TC @ TA @ B @ ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Efmapal_2EAP__SND) ).
thf(1848,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TA,B: TC,C: TB] :
( ( c_2Efmapal_2EAP__SND @ TC @ TB @ TA @ A @ ( c_2Epair_2E_2C @ TC @ TB @ B @ C ) )
= ( c_2Epair_2E_2C @ TC @ TA @ B @ ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(74,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Econnected @ A )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ B @ ( c_2Ereal__topology_2Eclosure @ A ) ) )
=> ( c_2Ereal__topology_2Econnected @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__INTERMEDIATE__CLOSURE) ).
thf(639,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] :
( ( ( c_2Ereal__topology_2Econnected @ A )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ A @ B )
& ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ B @ ( c_2Ereal__topology_2Eclosure @ A ) ) )
=> ( c_2Ereal__topology_2Econnected @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB > $o,C: TB > TA] :
( ( c_2Epred__set_2EIMAGE @ TB @ TA @ C @ B @ A )
= ( ? [D: TB] :
( ( A
= ( C @ D ) )
& ( c_2Ebool_2EIN @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__applied) ).
thf(491,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB > $o,C: TB > TA] :
( ( c_2Epred__set_2EIMAGE @ TB @ TA @ C @ B @ A )
= ( ? [D: TB] :
( ( A
= ( C @ D ) )
& ( c_2Ebool_2EIN @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(410,axiom,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal__topology_2EOpen @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__BALL) ).
thf(1912,plain,
! [A: tyop_2Erealax_2Ereal,B: tyop_2Erealax_2Ereal] : ( c_2Ereal__topology_2EOpen @ ( c_2Ereal__topology_2Eball @ ( c_2Epair_2E_2C @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(139,axiom,
! [TA: $tType,A: TA > $o,B: ( TA > $o ) > $o] :
( ( ! [C: TA > $o] :
( ( c_2Ebool_2EIN @ ( TA > $o ) @ C @ B )
=> ( c_2Epred__set_2ESUBSET @ TA @ C @ A ) )
& ( B
!= ( c_2Epred__set_2EEMPTY @ ( TA > $o ) ) ) )
=> ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EBIGINTER @ TA @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EBIGINTER__SUBSET) ).
thf(882,plain,
! [TA: $tType,A: TA > $o,B: ( TA > $o ) > $o] :
( ( ! [C: TA > $o] :
( ( c_2Ebool_2EIN @ ( TA > $o ) @ C @ B )
=> ( c_2Epred__set_2ESUBSET @ TA @ C @ A ) )
& ( B
!= ( c_2Epred__set_2EEMPTY @ ( TA > $o ) ) ) )
=> ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EBIGINTER @ TA @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(299,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ B )
= ( c_2Epred__set_2EINTER @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__COMM) ).
thf(1463,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ B )
= ( c_2Epred__set_2EINTER @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(80,axiom,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ A ) @ ( c_2Ereal__topology_2Efrontier @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__UNION__SUBSET) ).
thf(659,plain,
! [A: tyop_2Erealax_2Ereal > $o,B: tyop_2Erealax_2Ereal > $o] : ( c_2Epred__set_2ESUBSET @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ A @ B ) ) @ ( c_2Epred__set_2EUNION @ tyop_2Erealax_2Ereal @ ( c_2Ereal__topology_2Efrontier @ A ) @ ( c_2Ereal__topology_2Efrontier @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(2084,plain,
$false,
inference(e,[status(thm)],[1322,1036,1501,1190,760,1767,468,941,1295,1549,1110,1686,1024,1469,977,1211,1005,1406,1290,1401,1205,440,1793,597,1041,1855,1200,1142,1269,1705,1078,500,715,814,1507,1342,913,1914,1391,709,417,1613,1475,1601,1386,1287,1660,1871,1860,838,1511,802,1279,1577,542,1409,724,902,1247,1013,1741,1115,1362,1100,1232,1847,1319,421,448,1494,1450,591,443,1040,1418,1334,485,1858,1151,1383,1581,1489,1415,905,480,1169,866,453,1622,1394,988,428,1697,527,1564,602,981,766,1447,956,1863,1651,1604,512,678,661,810,1047,1730,1274,910,1355,1217,1751,1666,1619,1238,1883,1223,894,1423,916,566,879,1555,1178,1624,1787,1027,757,1281,1634,456,974,1106,583,830,551,1128,1360,697,874,1851,615,1375,1064,1672,1540,1719,857,1592,742,1498,1587,471,1683,488,1182,537,476,1842,1584,1214,706,1016,1207,1324,1263,1831,1668,1552,1192,721,1874,779,1525,1478,1249,1131,654,503,605,1434,1202,938,633,805,508,921,657,1663,1616,530,1732,1466,558,953,1185,794,586,718,888,412,1727,425,824,745,1595,573,1631,1251,618,1154,819,423,694,772,1388,1535,1615,1784,641,445,1707,1312,1765,1258,947,1675,672,1194,1209,681,736,1492,451,1722,434,1574,419,1571,599,1439,863,1175,1877,494,1339,816,594,1162,621,483,520,1022,1688,769,1460,462,932,1061,983,1396,1699,959,827,1044,868,608,986,1113,1496,1102,505,431,1694,675,1166,548,1277,1081,1472,1145,553,473,1076,531,944,812,1509,525,712,1598,1070,414,993,776,1748,791,1188,1038,1869,840,1235,1738,1336,1220,1790,1716,544,907,703,1702,1284,1140,1008,571,991,1404,1358,1504,727,1272,612,497,876,1839,1180,556,539,1844,1517,1010,1866,1108,1421,465,1316,1084,1654,1412,1781,891,1590,1326,588,961,1481,652,1629,1745,1244,1558,1030,568,667,929,478,899,1607,763,1444,1442,1348,1725,833,1546,1380,854,1097,835,1527,1148,1436,1657,807,437,1561,664,1610,1172,897,1033,1710,1197,624,1352,1261,1537,1378,1019,644,459,822,1713,1880,691,871,1399,1532,860,1331,935,1848,639,491,1912,882,1463,659]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP023^7 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.09 % 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
% 0.22/0.27 % Computer : n018.cluster.edu
% 0.22/0.27 % Model : x86_64 x86_64
% 0.22/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.27 % Memory : 8046.5625MB
% 0.22/0.27 % OS : Linux 6.8.0-71-generic
% 0.22/0.27 % CPULimit : 300
% 0.22/0.27 % WCLimit : 300
% 0.22/0.27 % DateTime : Tue Sep 29 19:38:13 UTC 2026
% 0.22/0.27 % CPUTime :
% 0.22/0.27 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
% 1.00/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 11.03/4.39 % [INFO] Parsing done (3503ms).
% 11.17/4.42 % [INFO] Running in sequential loop mode.
% 11.83/4.81 % [INFO] eprover registered as external prover.
% 11.83/4.82 % [INFO] Scanning for conjecture ...
% 15.81/5.94 % [INFO] Found a conjecture (or negated_conjecture) and 15523 axioms. Running axiom selection ...
% 18.03/6.83 % [INFO] Axiom selection finished. Selected 409 axioms (removed 15114 axioms).
% 19.02/7.18 % [INFO] Problem is higher-order (TPTP THF).
% 19.22/7.21 % [INFO] Type checking passed.
% 19.22/7.22 % [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 ...
% 57.99/18.65 % External prover 'e' found a proof!
% 57.99/18.65 % [INFO] Killing All external provers ...
% 57.99/18.66 % Time passed: 18217ms (effective reasoning time: 14228ms)
% 57.99/18.66 % 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)>
% 57.99/18.67 % Axioms used in derivation (409): thm_2Ereal_2EREAL__ADD__LDISTRIB, thm_2Epred__set_2EEMPTY__UNION, thm_2Epred__set_2EINTER__ASSOC, thm_2Ereal__topology_2EINTERIOR__EQ, thm_2Epred__set_2EUNION__DIFF, thm_2Epred__set_2EIN__UNION, thm_2Ereal__topology_2ECLOSURE__CLOSURE, thm_2Efmapal_2EAP__SND, thm_2Epred__set_2EIN__ABS, thm_2Ereal__topology_2ECONNECTED__FROM__OPEN__UNION__AND__INTER, thm_2Ereal__topology_2EMIDPOINT__REFL, thm_2Ereal__topology_2EOPEN__EMPTY, thm_2Epred__set_2EIMAGE__DEF, thm_2Ereal_2EREAL__MAX__LT, thm_2Epred__set_2EDIFF__EMPTY, thm_2Epred__set_2EEXISTS__IN__IMAGE, thm_2Ereal__topology_2EFRONTIER__SUBSET__CLOSED, thm_2Ereal_2EREAL__MIN__LE, thm_2Ereal_2EREAL__RDISTRIB, thm_2Epred__set_2EIMAGE__IN, thm_2Ereal__topology_2ECLOSURE__UNION, thm_2Ereal__topology_2EOPEN__SUBSET__INTERIOR, thm_2Ecardinal_2EINJECTIVE__IMAGE, thm_2Epred__set_2EDIFF__INTER__SUBSET, thm_2Ereal__topology_2EDIST__SYM, thm_2Ereal__topology_2ESIMPLE__IMAGE__GEN, thm_2Ereal_2EREAL__LE__MAX1, thm_2Epred__set_2EIMAGE__ID, thm_2Ereal__topology_2EINTERIOR__CLOSURE__IDEMP, thm_2Ereal_2EREAL__MIN__LT, thm_2Erealax_2EREAL__MUL__SYM, thm_2Ereal__topology_2ENOWHERE__DENSE__UNION, thm_2Ereal_2EREAL__LE__LT, thm_2Ereal__topology_2EBETWEEN__REFL, thm_2Epred__set_2ESUBSET__THM, thm_2Epred__set_2EUNION__applied, thm_2Ereal_2EREAL__MAX__REFL, thm_2Eposet_2Erelation__def, thm_2Ewellorder_2EZL__SUBSETS, thm_2Epair_2EPROD__ALL__THM, thm_2Epred__set_2EINTER__applied, thm_2Ereal_2EREAL__LT__TRANS, thm_2Ereal_2Ereal__lte, thm_2Ecardinal_2ESURJECTIVE__IMAGE, thm_2Ecardinal_2EUNION__ACI, thm_2Eiterate_2EREAL__LT__BETWEEN, thm_2Epred__set_2EDIFF__INTER, thm_2Ecardinal_2ESURJECTIVE__ON__IMAGE, thm_2Epred__set_2EIN__IMAGE, thm_2Ebool_2EIN__DEF, thm_2Epred__set_2EFORALL__IN__UNION, thm_2Ewellorder_2Eposet, thm_2Ereal__topology_2ENOWHERE__DENSE, thm_2Elim_2EIVT2, thm_2Ereal_2EREAL__LT__MIN, thm_2Ereal__topology_2EIN__SPHERE, thm_2Ereal__topology_2ECLOSURE__EQ__EMPTY, thm_2Epred__set_2EIMAGE__SUBSET__gen, thm_2Eintegral_2EDINT__LINEAR, thm_2Ereal__topology_2ECLOSURE__UNIQUE, thm_2EHolSmt_2Er219, thm_2Ereal__topology_2EREAL__WLOG__LE, thm_2Ereal_2ESETOK__LE__LT, thm_2Epair_2ELEX__CONG, thm_2Epred__set_2EIMAGE__EMPTY, thm_2Ereal__topology_2EUNION__FRONTIER, thm_2Ereal__topology_2EINTERIOR__EMPTY, thm_2Epred__set_2ESUBSET__BIGINTER, thm_2Etransc_2EDINT__UNIQ, thm_2Epred__set_2ESUBSET__ANTISYM, thm_2Ereal_2Ereal__lt, thm_2Elim_2EIVT, thm_2Ereal_2EREAL__MAX__ALT, thm_2Ereal__topology_2ESUBSET__CLOSURE, thm_2Ewellorder_2EZL, thm_2Ereal_2EREAL__LET__TOTAL, thm_2Ereal_2EREAL__LTE__ANTISYM, thm_2Ereal__topology_2EBALL__TRANSLATION, thm_2Eintegral_2EDINT__EQ, thm_2Ereal__topology_2ECLOSURE__INTER__SUBSET, thm_2Ereal__topology_2ECBALL__MIN__INTER, thm_2Epair_2EPAIR__EQ, thm_2Ereal__topology_2EFRONTIER__FRONTIER__FRONTIER, thm_2Ereal_2EREAL__ADD__RDISTRIB, thm_2Ereal_2EREAL__LTE__ANTSYM, thm_2Ereal_2EREAL__LT__GT, thm_2Ereal_2EREAL__MAX__ADD, thm_2Ewellorder_2EINJECTIVE__LEFT__INVERSE__NONEMPTY, thm_2Ereal__topology_2EREAL__LE__BETWEEN, thm_2Ereal__topology_2ECLOSURE__MINIMAL__EQ, thm_2Ereal__topology_2EBETWEEN__SYM, thm_2Erealax_2EREAL__ADD__ASSOC, thm_2Ereal__topology_2EBETWEEN__ANTISYM, thm_2Ereal_2EREAL__MUL__ASSOC, thm_2Ereal_2EREAL__LE__TOTAL, thm_2Ereal_2EREAL__LET__ANTISYM, thm_2Ereal__topology_2EFRONTIER__DISJOINT__EQ, thm_2Epred__set_2EDIFF__SUBSET, thm_2Ereal__topology_2ECLOSED__EMPTY, thm_2Ewellorder_2Echain, thm_2Ereal__topology_2EFRONTIER__CLOSURE__SUBSET, thm_2Erealax_2EREAL__LDISTRIB, thm_2Elim_2ECONT__ATTAINS, thm_2Ereal__topology_2EREGULAR__CLOSED__UNION, thm_2Ereal__topology_2EFRONTIER__CLOSED, thm_2Ereal__topology_2EINTERIOR__CLOSED__UNION__EMPTY__INTERIOR, thm_2Eintegral_2EDINT__INTEGRAL, thm_2Ecomparison_2Epair__cmp__cong, thm_2Ereal__topology_2EDIFF__CLOSURE__SUBSET, thm_2Ereal_2EREAL__IMP__MAX__LE2, thm_2Ereal__topology_2EDIST__TRIANGLE, thm_2Ereal__topology_2EBALL__UNION__SPHERE, thm_2Ereal__topology_2Ecball, thm_2Ereal__topology_2Econnected, thm_2Ereal__topology_2ECONNECTED__DIFF__OPEN__FROM__CLOSED, thm_2Ereal_2EREAL__LE__ANTISYM, thm_2Ereal__topology_2ECONNECTED__FROM__CLOSED__UNION__AND__INTER, thm_2Ereal__topology_2ECBALL__DIFF__SPHERE, thm_2Ereal__topology_2EDIST__TRIANGLE__ALT, thm_2Eintegral_2EDINT__CMUL, thm_2Epred__set_2EDIFF__applied, thm_2Ereal__topology_2EDIST__TRIANGLE__LT, thm_2Ereal__topology_2ECONNECTED__IFF__CONNECTABLE__POINTS, thm_2Epath_2Eparallel__comp__def, thm_2Epred__set_2EFORALL__IN__IMAGE, thm_2Ereal__topology_2EFRONTIER__FRONTIER__SUBSET, thm_2Epred__set_2EGSPEC__ETA, thm_2Ereal__topology_2EIN__BALL, thm_2Ereal__topology_2ECONNECTED__CLOSURE, thm_2Epred__set_2EIN__GSPEC, thm_2Epred__set_2EUNION__OVER__INTER, thm_2Ereal_2EREAL__MIN__LE2, thm_2Ereal__topology_2EINTERIOR__FRONTIER, thm_2Epred__set_2EIN__DIFF, thm_2Epair_2EFORALL__PROD, thm_2Ereal__topology_2ESUBSET__CBALL, thm_2Ereal__topology_2ECLOSURE__OPEN__INTER__CLOSURE, thm_2Ereal_2EREAL__MIN__ALT, thm_2Eintegral_2EDINT__LE, thm_2Epred__set_2ESPECIFICATION, thm_2EHolSmt_2Er215, thm_2Ereal_2ESUP__LEMMA1, thm_2Eintegral_2Eintegrable__def, thm_2Epred__set_2EEMPTY__DIFF, thm_2Ereal_2EREAL__LT__MAX, thm_2Ereal_2EREAL__LT__ANTISYM, thm_2Epred__set_2EIMAGE__applied, thm_2Epred__set_2EIN__GSPEC__IFF, thm_2Ereal_2EREAL__ADD__COMM, thm_2Epred__set_2EDIFF__SAME__UNION, thm_2Ewellorder_2Eseteq__wlog, thm_2Ereal__topology_2ESUBSET__INTERIOR, thm_2Epred__set_2EMEMBER__NOT__EMPTY, thm_2Epred__set_2EIN__BIGINTER, thm_2Ereal__topology_2EBOUNDED__INTERIOR, thm_2Ereal_2EREAL__MAX__LE, thm_2Epred__set_2EDIFF__DIFF__SUBSET, thm_2Ereal__topology_2ECONNECTED__UNION, thm_2Ereal__topology_2ECLOSURE__UNION__FRONTIER, thm_2Ereal_2EREAL__LE__RADD, thm_2Epred__set_2ESUBSET__TRANS, thm_2Ereal_2EREAL__IMP__MIN__LE2, thm_2Eintegral_2EINTEGRAL__COMBINE, thm_2Elim_2ECONT__HASSUP, thm_2Emeasure_2ESUBSET__BIGINTER, thm_2Erealax_2EREAL__MUL__ASSOC, thm_2Ereal__topology_2ESPHERE__TRANSLATION, thm_2Epred__set_2EIMAGE__CONG, thm_2Eintegral_2EINTEGRABLE__DINT, thm_2Eintegral_2EINTEGRABLE__CONTINUOUS, thm_2Epred__set_2EBIGINTER__SUBSET, thm_2Eintegral_2EINTEGRABLE__ADD, thm_2Ereal__topology_2EINTERIOR__CLOSURE__INTER__OPEN, thm_2Ereal_2EREAL__LET__ADD2, thm_2Ereal__topology_2ECONNECTED__CLOSED, thm_2Ereal_2EREAL__LT__TOTAL, thm_2Ecardinal_2ESURJECTIVE__ON__RIGHT__INVERSE, thm_2Epred__set_2ESUBSET__INTER2, thm_2Ereal__topology_2ESUBSET__INTERIOR__EQ, thm_2Epred__set_2EDIFF__COMM, thm_2Eiterate_2EREAL__WLOG__LT, thm_2Ereal_2EREAL__MIN__REFL, thm_2Ereal__topology_2EINTERIOR__MAXIMAL__EQ, thm_2Ereal__topology_2ESET__DIFF__FRONTIER, thm_2Ereal__topology_2EINTERIOR__FRONTIER__EMPTY, thm_2Ereal__topology_2EFUN__IN__IMAGE, thm_2Epred__set_2EINTER__IDEMPOT, thm_2Ereal__topology_2EFRONTIER__SUBSET__EQ, thm_2Ereal__topology_2ECBALL__MAX__UNION, thm_2Ereal_2EREAL__LT__IMP__LE, thm_2Ereal__topology_2ECONNECTED__CLOSED__SET, thm_2Epred__set_2EUNION__DIFF__2, thm_2Ereal__topology_2EFRONTIER__INTERIOR__SUBSET, thm_2Ereal__topology_2ESPHERE__SUBSET__CBALL, thm_2Elim_2ECONT__ATTAINS__ALL, thm_2Epred__set_2ESUBSET__UNION, thm_2Eintegral_2EDINT__ADD, thm_2Ereal__topology_2EOPEN__INTER__CLOSURE__SUBSET, thm_2Ereal__topology_2EUNION__INTERIOR__SUBSET, thm_2Elim_2ECONT__CONST, thm_2Ereal_2EREAL__MUL__SYM, thm_2Ereal__topology_2EOPEN__INTER, thm_2Eintegral_2EINTEGRABLE__CONST, thm_2Ereal_2EREAL__MEAN, thm_2Ereal_2EREAL__LTE__TRANS, thm_2Eintegral_2EINTEGRAL__ADD, thm_2Ereal__topology_2ECLOSED__UNION, thm_2Ereal__topology_2EFRONTIER__CBALL, thm_2Ereal_2EREAL__EQ__RADD, thm_2Epred__set_2EIN__BIGINTER__IMAGE, thm_2Ereal__topology_2ECONNECTED__OPEN__SET, thm_2Ereal__topology_2EOPEN__UNION, thm_2Ereal__topology_2EINTERIOR__EQ__EMPTY, thm_2Epred__set_2EUNION__COMM, thm_2Erealax_2EREAL__ADD__SYM, thm_2Eintegral_2EDINT__WRONG, thm_2Epair_2ECURRY__ONE__ONE__THM, thm_2Ereal__topology_2EINTERIOR__UNION__EQ__EMPTY, thm_2Ereal_2EREAL__LE__MIN, thm_2Elim_2ECONT__ADD, thm_2Epred__set_2EDIFF__INTER2, thm_2Ereal__topology_2EDIST__TRIANGLE__ADD, thm_2Ereal__topology_2EOPEN__INTER__CLOSURE__EQ__EMPTY, thm_2Ecardinal_2EINJECTIVE__ON__LEFT__INVERSE, thm_2Ereal__topology_2ECLOSED__CBALL, thm_2Ereal_2EREAL__LE__ADD2, thm_2EHolSmt_2Er220, thm_2Ereal_2EREAL__LE__MAX, thm_2Ereal__topology_2EINTERIOR__OPEN, thm_2Ereal__topology_2EINTERIOR__CBALL, thm_2Epred__set_2EUNION__ASSOC, thm_2Epred__set_2EIMAGE__EQ__EMPTY, thm_2Ereal_2EREAL__MAX__ACI, thm_2Epred__set_2EIN__APP, thm_2Ereal_2EREAL__LTE__TOTAL, thm_2Epred__set_2EUNION__SUBSET, thm_2Ereal__topology_2EINTERIOR__INTER, thm_2Ereal_2EREAL__EQ__LADD, thm_2Ereal__topology_2EBALL__MIN__INTER, thm_2Epred__set_2EBIGINTER__applied, thm_2Epair_2Epair__induction, thm_2Ereal_2EREAL__MUL__COMM, thm_2Ereal_2EREAL__LT__IMP__NE, thm_2Ereal__topology_2ECONNECTED__INTERMEDIATE__CLOSURE, thm_2Epred__set_2ESUBSET__DIFF__EMPTY, thm_2Ereal__topology_2EINTERIOR__BIGINTER__SUBSET, thm_2Epred__set_2EEQ__SUBSET__SUBSET, thm_2Ereal__topology_2EMIDPOINT__EQ__ENDPOINT, thm_2Eintegral_2EINTEGRABLE__COMBINE, thm_2Epred__set_2ESUBSET__REFL, thm_2Eintegral_2EINTEGRAL__CMUL, thm_2Ecardinal_2EINJECTIVE__ON__IMAGE, thm_2Ereal__topology_2EBOUNDED__CBALL, thm_2Epred__set_2EINTER__EMPTY, thm_2Ecardinal_2ESURJECTIVE__IMAGE__THM, thm_2Ereal__topology_2EIN__CBALL, thm_2Epair_2Epair__CASES, thm_2Ereal__topology_2Efrontier, thm_2Ereal__topology_2EINTERIOR__MAXIMAL, thm_2Eintegral_2EINTEGRABLE__CMUL, thm_2Erealax_2EREAL__LT__IADD, thm_2Epred__set_2EDIFF__EQ__EMPTY, thm_2Ereal__topology_2EBOUNDED__CLOSURE, thm_2Ereal_2EREAL__MIN__ADD, thm_2Ereal__topology_2EBOUNDED__EMPTY, thm_2Ereal__topology_2EINTERIOR__INTERIOR, thm_2Ereal_2EREAL__NOT__LT, thm_2Eintegral_2EINTEGRABLE__POINT__SPIKE, thm_2Eintegral_2EDINT__COMBINE, thm_2Ereal_2EREAL__LET__TRANS, thm_2Ereal__topology_2EBOUNDED__CLOSURE__EQ, thm_2Epred__set_2EIMAGE__11, thm_2Ereal__topology_2EBALL__SUBSET__CBALL, thm_2Ereal_2EREAL__MIN__LE1, thm_2Epair_2ELEX__DEF__THM, thm_2Epred__set_2EINTER__UNION, thm_2Ewellorder_2EFLATTEN__LEMMA, thm_2Ereal_2EREAL__LT__REFL, thm_2Ereal__topology_2EBETWEEN__REFL__EQ, thm_2EHolSmt_2Er217, thm_2Ereal__topology_2ECLOSED__BIGINTER, thm_2Elim_2ECONT__ATTAINS2, thm_2Ereal__topology_2EREAL__WLOG__LT, thm_2Ereal__topology_2EFRONTIER__EMPTY, thm_2Ereal__topology_2EFRONTIER__INTER__SUBSET, thm_2Ereal__topology_2ESPHERE__UNION__BALL, thm_2Ereal__topology_2ECONNECTED__INTER__FRONTIER, thm_2Ereal__topology_2EFRONTIER__UNION__SUBSET, thm_2Ereal__topology_2EBETWEEN__TRANS, thm_2Ereal_2EREAL__LT__LE, thm_2Epred__set_2EINTER__OVER__UNION, thm_2Ereal__topology_2ESURJECTIVE__IMAGE__EQ, thm_2Ereal__topology_2EINTERIOR__BALL, thm_2Ereal__topology_2ECLOSURE__MINIMAL, thm_2Ereal__topology_2ECLOSED__INTER, thm_2Ereal__topology_2EINTERIOR__DIFF, thm_2Ereal__topology_2EINTERIOR__CLOSED__EQ__EMPTY__AS__FRONTIER, thm_2Epred__set_2ENOT__IN__EMPTY, thm_2Etransfer_2EPAIR__REL__def, thm_2Epred__set_2EINTER__SUBSET__EQN, thm_2Ereal__topology_2ECLOSURE__SUBSET__EQ, thm_2Ereal__topology_2ECBALL__TRANSLATION, thm_2Ereal__topology_2ECLOSED__CLOSURE, thm_2Ereal__topology_2ECONNECTED__UNION__STRONG, thm_2Ereal__topology_2EOPEN__BALL, thm_2Ereal_2EREAL__LE__LADD__IMP, thm_2Epred__set_2ESUBSET__INTER1, thm_2Ereal__topology_2EREGULAR__OPEN__INTER, thm_2Epred__set_2ESUBSET__UNION__ABSORPTION, thm_2Ereal__topology_2ECBALL__DIFF__BALL, thm_2Erealax_2EREAL__LT__TOTAL, thm_2Eiterate_2EREAL__COMPLETE, thm_2Epred__set_2EEXTENSION, thm_2Elim_2ECONT__MUL, thm_2Ereal__topology_2ECLOSURE__NONEMPTY__OPEN__INTER, thm_2Ereal_2EREAL__ADD__SYM, thm_2Epred__set_2EUNION__EMPTY, thm_2Epair_2ECLOSED__PAIR__EQ, thm_2Epair_2ELEX__MONO, thm_2Elim_2ECONT__BOUNDED, thm_2Ecardinal_2EINTER__ACI, thm_2Ereal_2EREAL__ADD__ASSOC, thm_2Epred__set_2EDIFF__DIFF, thm_2Ereal__topology_2EBOUNDED__SUBSET, thm_2Epred__set_2EDIFF__UNION, thm_2Erealax_2EREAL__LT__TRANS, thm_2Eintegral_2EINTEGRABLE__SUBINTERVAL__LEFT, thm_2Ereal_2EREAL__LT__RADD, thm_2Elim_2ECONT__COMPOSE, thm_2Eintegral_2EINTEGRABLE__SUBINTERVAL, thm_2Epred__set_2EINTER__SUBSET, thm_2Ereal__topology_2EDIST__TRIANGLE__LE, thm_2Ereal_2EREAL__LE__LADD, thm_2Ereal__topology_2ECLOSURE__CLOSED, thm_2Ereal__topology_2ECLOSURE__BIGINTER__SUBSET, thm_2Epair_2ECURRY__DEF, thm_2Ereal__topology_2EFRONTIER__FRONTIER, thm_2Epred__set_2EIMAGE__UNION, thm_2Ereal__topology_2ECONNECTED__EMPTY, thm_2Ereal_2EREAL__LE__MAX2, thm_2Erealax_2EREAL__LT__REFL, thm_2Ereal_2EREAL__SUP__EXISTS, thm_2Ereal__topology_2ESUBSET__ANTISYM__EQ, thm_2Epred__set_2EBIGINTER__UNION, thm_2Ewellorder_2ETARSKI__SET, thm_2Epair_2EPROD__ALL__MONO, thm_2Ereal_2EREAL__LTE__ADD2, thm_2Ereal__topology_2ECLOSURE__INTERIOR__IDEMP, thm_2Estate__transformer_2EREAD__def, thm_2Ereal__topology_2EBALL__MAX__UNION, thm_2Eintegral_2EINTEGRAL__EQ, thm_2Ereal__topology_2EOPEN__DIFF, thm_2Epred__set_2EGSPEC__ID, thm_2Ereal__topology_2ESUBSET__IMAGE, thm_2Epred__set_2ESUBSET__applied, thm_2Ereal_2EREAL__EQ__IMP__LE, thm_2Ereal__topology_2ECLOSURE__EMPTY, thm_2Epred__set_2ESUBSET__DEF, thm_2Ereal_2ESUP__LEMMA3, thm_2Epred__set_2ESUBSET__EMPTY, thm_2Ereal__topology_2ECLOSURE__SUBSET, thm_2Ereal__topology_2ECLOSURE__EQ, thm_2Ereal__topology_2Eball, thm_2Ereal_2EREAL__LT__IADD, thm_2Ereal__topology_2ECLOSURE__INTERIOR__UNION__CLOSED, thm_2Ereal__topology_2ECLOSED__DIFF, thm_2Ereal__topology_2ESUBSET__BALL, thm_2Ereal__topology_2ECLOSURE__OPEN__INTER__SUPERSET, thm_2Ereal__topology_2EMIDPOINT__SYM, thm_2Epred__set_2EIMAGE__SUBSET, thm_2Epred__set_2EIN__INTER, thm_2Epred__set_2ENOT__EQUAL__SETS, thm_2Ereal__topology_2EFRONTIER__UNION, thm_2Eintegral_2EINTEGRABLE__SUBINTERVAL__RIGHT, thm_2Ereal__topology_2Ebetween, thm_2EHolSmt_2Er218, thm_2Ereal__topology_2EINTERIOR__SUBSET, thm_2Eintegral_2EINTEGRAL__LE, thm_2Ereal_2EREAL__LT__ADD2, thm_2Ereal__topology_2EOPEN__SUB__OPEN, thm_2Epair_2EEXISTS__PROD, thm_2Ereal__topology_2EINTERIOR__EQ__EMPTY__ALT, thm_2Ereal_2EREAL__LDISTRIB, thm_2Ereal__topology_2EINTERIOR__UNIQUE, thm_2Epair_2Epair__Axiom, thm_2Epred__set_2ESUBSET__SUBSET__EQ, thm_2Ereal__topology_2EFRONTIER__INTER__SUBSET__INTER, thm_2Epred__set_2ESET__EQ__SUBSET, thm_2Epair_2EPROD__ALL__CONG, thm_2Eintegral_2EDINT__POINT__SPIKE, thm_2Epair_2EABS__PAIR__THM, thm_2Ewellorder_2Efl, thm_2Ereal__topology_2EOPEN__INTERIOR, thm_2Ereal__topology_2EBETWEEN__MIDPOINT, thm_2Epred__set_2EUNION__IDEMPOT, thm_2Eintegral_2ESUP__INTERVAL, thm_2Epred__set_2EINTER__COMM, thm_2Epred__set_2EIMAGE__INTER, thm_2Eproduct_2EREAL__ADD__AC, thm_2Epred__set_2EEMPTY__SUBSET, thm_2Ereal_2EREAL__LT__LADD, thm_2Epred__set_2ESUBSET__INTER__ABSORPTION, thm_2Ereal_2EREAL__LE__TRANS, thm_2Ereal_2EREAL__MIN__ACI, thm_2Eintegral_2EREAL__LT__MIN, thm_2Ereal_2EREAL__NOT__LE, thm_2Epred__set_2ESUBSET__INTER, thm_2Ereal_2EREAL__LE__REFL, thm_2Ereal__topology_2EBETWEEN__TRANS__2
% 57.99/18.67 % No. of inferences in proof: 822
% 57.99/18.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 18217 ms resp. 14228 ms w/o parsing
% 61.66/19.30 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 61.66/19.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------