TSTP Solution File: ITP021_7 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP021_7 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:47:07 EDT 2024
% Result : Theorem 93.23s 25.82s
% Output : Refutation 93.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 289
% Syntax : Number of formulae : 582 ( 112 unt; 62 typ; 0 def)
% Number of atoms : 2384 ( 244 equ; 0 cnn)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 6000 ( 524 ~; 413 |; 532 &;3624 @)
% ( 127 <=>; 780 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 24 ( 23 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 45 usr; 15 con; 0-5 aty)
% Number of variables : 1293 ( 0 ^1266 !; 10 ?;1293 :)
% ( 17 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(p_type,type,
p: tyop_2Emin_2Ebool > $o ).
thf(tyop_2Emin_2Eind_type,type,
tyop_2Emin_2Eind: $tType ).
thf(c_2Ebool_2ECOND_2E3_type,type,
c_2Ebool_2ECOND_2E3:
!>[TA: $tType] : ( tyop_2Emin_2Ebool > TA > TA > TA ) ).
thf(c_2Emarker_2EAC_2E2_type,type,
c_2Emarker_2EAC_2E2: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(tyop_2Enum_2Enum_type,type,
tyop_2Enum_2Enum: $tType ).
thf(tyop_2Eone_2Eone_type,type,
tyop_2Eone_2Eone: $tType ).
thf(c_2Erelation_2EEQC_2E3_type,type,
c_2Erelation_2EEQC_2E3:
!>[TA: $tType] : ( ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) ) > TA > TA > tyop_2Emin_2Ebool ) ).
thf(c_2Eprim__rec_2ESIMP__REC__REL_2E4_type,type,
c_2Eprim__rec_2ESIMP__REC__REL_2E4:
!>[TA: $tType] : ( ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ TA ) > TA > ( tyop_2Emin_2Efun @ TA @ TA ) > tyop_2Enum_2Enum > tyop_2Emin_2Ebool ) ).
thf(c_2Eind__type_2EINJA_2E3_type,type,
c_2Eind__type_2EINJA_2E3:
!>[TA: $tType] : ( TA > tyop_2Enum_2Enum > TA > tyop_2Emin_2Ebool ) ).
thf(c_2Eind__type_2EINJN_2E3_type,type,
c_2Eind__type_2EINJN_2E3:
!>[TA: $tType] : ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > TA > tyop_2Emin_2Ebool ) ).
thf(c_2Egcd_2Eis__gcd_2E3_type,type,
c_2Egcd_2Eis__gcd_2E3: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Emin_2Ebool ).
thf(c_2Epred__set_2EUNIV_2E1_type,type,
c_2Epred__set_2EUNIV_2E1:
!>[TA: $tType] : ( TA > tyop_2Emin_2Ebool ) ).
thf(c_2Erich__list_2EIS__SUFFIX_2E2_type,type,
c_2Erich__list_2EIS__SUFFIX_2E2:
!>[TA: $tType] : ( ( tyop_2Elist_2Elist @ TA ) > ( tyop_2Elist_2Elist @ TA ) > tyop_2Emin_2Ebool ) ).
thf(c_2EEncode_2Ebiprefix_2E2_type,type,
c_2EEncode_2Ebiprefix_2E2:
!>[TA: $tType] : ( ( tyop_2Elist_2Elist @ TA ) > ( tyop_2Elist_2Elist @ TA ) > tyop_2Emin_2Ebool ) ).
thf(c_2Ebag_2EPSUB__BAG_2E2_type,type,
c_2Ebag_2EPSUB__BAG_2E2:
!>[TA: $tType] : ( ( tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum ) > ( tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ) ).
thf(c_2Esorting_2EPERM__SINGLE__SWAP_2E2_type,type,
c_2Esorting_2EPERM__SINGLE__SWAP_2E2:
!>[TA: $tType] : ( ( tyop_2Elist_2Elist @ TA ) > ( tyop_2Elist_2Elist @ TA ) > tyop_2Emin_2Ebool ) ).
thf(tyop_2Estring_2Echar_type,type,
tyop_2Estring_2Echar: $tType ).
thf(c_2Estring_2Estring__lt_2E2_type,type,
c_2Estring_2Estring__lt_2E2: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > tyop_2Emin_2Ebool ).
thf(c_2Efinite__map_2Efmap__EQ__UPTO_2E3_type,type,
c_2Efinite__map_2Efmap__EQ__UPTO_2E3:
!>[TA: $tType,TB: $tType] : ( ( tyop_2Efinite__map_2Efmap @ TB @ TA ) > ( tyop_2Efinite__map_2Efmap @ TB @ TA ) > ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ) ).
thf(c_2Elbtree_2Eis__mmindex_2E4_type,type,
c_2Elbtree_2Eis__mmindex_2E4:
!>[TA: $tType] : ( ( tyop_2Emin_2Efun @ TA @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) > ( tyop_2Elist_2Elist @ TA ) > tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Emin_2Ebool ) ).
thf(c_2Emergesort_2Estable_2E3_type,type,
c_2Emergesort_2Estable_2E3:
!>[TA: $tType] : ( ( tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ) ) > ( tyop_2Elist_2Elist @ TA ) > ( tyop_2Elist_2Elist @ TA ) > tyop_2Emin_2Ebool ) ).
thf(c_2Epath_2EfirstP__at_2E3_type,type,
c_2Epath_2EfirstP__at_2E3:
!>[TA: $tType,TB: $tType] : ( ( tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool ) > ( tyop_2Epath_2Epath @ TB @ TA ) > tyop_2Enum_2Enum > tyop_2Emin_2Ebool ) ).
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(c_2Eblast_2Ebcarry_2E3_type,type,
c_2Eblast_2Ebcarry_2E3: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(c_2Eblast_2Ebsum_2E3_type,type,
c_2Eblast_2Ebsum_2E3: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(tyop_2Ehreal_2Ehreal_type,type,
tyop_2Ehreal_2Ehreal: $tType ).
thf(c_2Eint__arith_2Ebmarker_2E1_type,type,
c_2Eint__arith_2Ebmarker_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
thf(c_2Esptree_2Esubspt_2E2_type,type,
c_2Esptree_2Esubspt_2E2:
!>[TA: $tType] : ( ( tyop_2Esptree_2Espt @ TA ) > ( tyop_2Esptree_2Espt @ TA ) > tyop_2Emin_2Ebool ) ).
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(c_2EHolSmt_2Exor_2E2_type,type,
c_2EHolSmt_2Exor_2E2: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
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_2Eextreal_2Eextreal__abs_2E1_type,type,
c_2Eextreal_2Eextreal__abs_2E1: tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal ).
thf(c_2Eextreal_2Eextreal__add_2E2_type,type,
c_2Eextreal_2Eextreal__add_2E2: tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal ).
thf(c_2Eextreal_2Eextreal__ainv_2E1_type,type,
c_2Eextreal_2Eextreal__ainv_2E1: tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal ).
thf(c_2Eextreal_2Eextreal__le_2E2_type,type,
c_2Eextreal_2Eextreal__le_2E2: tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal > tyop_2Emin_2Ebool ).
thf(c_2Eextreal_2Eextreal__lt_2E2_type,type,
c_2Eextreal_2Eextreal__lt_2E2: tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal > tyop_2Emin_2Ebool ).
thf(c_2Eextreal_2Eextreal__max_2E2_type,type,
c_2Eextreal_2Eextreal__max_2E2: tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal ).
thf(c_2Eextreal_2Eextreal__min_2E2_type,type,
c_2Eextreal_2Eextreal__min_2E2: tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal ).
thf(c_2Eextreal_2Eextreal__sub_2E2_type,type,
c_2Eextreal_2Eextreal__sub_2E2: tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal ).
thf(sk1_type,type,
sk1: $o ).
thf(sk2_type,type,
sk2: tyop_2Eextreal_2Eextreal ).
thf(sk3_type,type,
sk3: tyop_2Eextreal_2Eextreal ).
thf(sk4_type,type,
sk4: tyop_2Eextreal_2Eextreal ).
thf(sk5_type,type,
sk5: tyop_2Eextreal_2Eextreal ).
thf(sk6_type,type,
sk6: tyop_2Eextreal_2Eextreal ).
thf(sk7_type,type,
sk7: tyop_2Eextreal_2Eextreal ).
thf(sk8_type,type,
sk8: tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal ).
thf(200,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
| ( p @ A ) )
<=> ( ( p @ A )
| ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er041) ).
thf(1586,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
| ( p @ A ) )
=> ( ( p @ A )
| ( p @ B ) ) )
& ( ( ( p @ A )
| ( p @ B ) )
=> ( ( p @ B )
| ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(100,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ B )
| ( p @ A )
| ~ ( ~ ( p @ B )
<=> ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed011) ).
thf(760,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ B )
| ( p @ A )
| ~ ( ( ~ ( p @ B )
=> ( p @ A ) )
& ( ( p @ A )
=> ~ ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(64,axiom,
! [TA: $tType,A: tyop_2Elist_2Elist @ TA] : ( p @ ( c_2Erich__list_2EIS__SUFFIX_2E2 @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erich__list_2EIS__SUFFIX__REFL) ).
thf(517,plain,
! [TA: $tType,A: tyop_2Elist_2Elist @ TA] : ( p @ ( c_2Erich__list_2EIS__SUFFIX_2E2 @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(518,plain,
! [TA: $tType,A: tyop_2Elist_2Elist @ TA] : ( p @ ( c_2Erich__list_2EIS__SUFFIX_2E2 @ TA @ A @ A ) ),
inference(cnf,[status(esa)],[517]) ).
thf(56,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ C )
=> ( p @ B ) )
& ( ( p @ A )
=> ( p @ D ) ) )
=> ( ( ( p @ C )
| ( p @ A ) )
=> ( ( p @ B )
| ( p @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EMONO__OR) ).
thf(468,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ C )
=> ( p @ B ) )
& ( ( p @ A )
=> ( p @ D ) ) )
=> ( ( ( p @ C )
| ( p @ A ) )
=> ( ( p @ B )
| ( p @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(1,conjecture,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ B @ C ) @ A ) )
<=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Emax__le) ).
thf(2,negated_conjecture,
~ ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ B @ C ) @ A ) )
<=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(228,plain,
~ ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ B @ C ) @ A ) )
=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ A ) ) ) )
& ( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ A ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(229,plain,
~ ( ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ B @ C ) @ A ) )
=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ A ) ) ) )
& ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ A ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ B @ C ) @ A ) ) ) ),
inference(miniscope,[status(thm)],[228]) ).
thf(234,plain,
( sk1
| ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ sk7 @ sk5 ) ) ),
inference(cnf,[status(esa)],[229]) ).
thf(196,axiom,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ),B: tyop_2Elist_2Elist @ TA,C: tyop_2Elist_2Elist @ TA,D: tyop_2Elist_2Elist @ TA] :
( ( ( p @ ( c_2Emergesort_2Estable_2E3 @ TA @ A @ B @ C ) )
& ( p @ ( c_2Emergesort_2Estable_2E3 @ TA @ A @ C @ D ) ) )
=> ( p @ ( c_2Emergesort_2Estable_2E3 @ TA @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Emergesort_2Estable__trans) ).
thf(1554,plain,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ),B: tyop_2Elist_2Elist @ TA,C: tyop_2Elist_2Elist @ TA,D: tyop_2Elist_2Elist @ TA] :
( ( ( p @ ( c_2Emergesort_2Estable_2E3 @ TA @ A @ B @ C ) )
& ( p @ ( c_2Emergesort_2Estable_2E3 @ TA @ A @ C @ D ) ) )
=> ( p @ ( c_2Emergesort_2Estable_2E3 @ TA @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(216,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( p @ B )
<=> ( p @ A ) )
| ( p @ B )
| ~ ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed004) ).
thf(1686,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ~ ( p @ B )
=> ( p @ A ) )
& ( ( p @ A )
=> ~ ( p @ B ) ) )
| ( p @ B )
| ~ ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(74,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( p @ A )
| ~ ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEXCLUDED__MIDDLE) ).
thf(582,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(130,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
=> ( p @ A ) )
=> ( p @ B ) )
=> ( p @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EPEIRCE) ).
thf(1005,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
=> ( p @ A ) )
=> ( p @ B ) )
=> ( p @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(129,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( ( p @ C )
=> ( p @ D ) ) )
& ( ~ ( p @ D )
=> ( ( p @ B )
=> ( p @ A ) ) ) )
=> ( ( ( p @ A )
=> ( p @ C ) )
=> ( ( p @ B )
=> ( p @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__imp__weaken) ).
thf(994,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( ( p @ C )
=> ( p @ D ) ) )
& ( ~ ( p @ D )
=> ( ( p @ B )
=> ( p @ A ) ) ) )
=> ( ( ( p @ A )
=> ( p @ C ) )
=> ( ( p @ B )
=> ( p @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(176,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ B )
=> ( ( p @ A )
| ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EOR__INTRO__THM2) ).
thf(1401,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ B )
=> ( ( p @ A )
| ( p @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(22,axiom,
! [A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__ainv_2E1 @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Eneg__neg) ).
thf(306,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__ainv_2E1 @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(307,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__ainv_2E1 @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ A ) )
= A ),
inference(cnf,[status(esa)],[306]) ).
thf(308,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__ainv_2E1 @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ A ) )
= A ),
inference(lifteq,[status(thm)],[307]) ).
thf(52,axiom,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ),B: TA] : ( p @ ( c_2Erelation_2EEQC_2E3 @ TA @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erelation_2EEQC__REFL) ).
thf(448,plain,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ),B: TA] : ( p @ ( c_2Erelation_2EEQC_2E3 @ TA @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(449,plain,
! [TA: $tType,B: TA,A: tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool )] : ( p @ ( c_2Erelation_2EEQC_2E3 @ TA @ A @ B @ B ) ),
inference(cnf,[status(esa)],[448]) ).
thf(116,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
=> ( ~ ( p @ B )
=> ~ ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EMONO__NOT) ).
thf(878,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
=> ( ~ ( p @ B )
=> ~ ( p @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(115,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( ( p @ B )
| ( p @ C ) ) )
<=> ( ( ( p @ A )
& ( p @ B ) )
| ( ( p @ A )
& ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__AND__OVER__OR) ).
thf(861,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
& ( ( p @ B )
| ( p @ C ) ) )
=> ( ( ( p @ A )
& ( p @ B ) )
| ( ( p @ A )
& ( p @ C ) ) ) )
& ( ( ( ( p @ A )
& ( p @ B ) )
| ( ( p @ A )
& ( p @ C ) ) )
=> ( ( p @ A )
& ( ( p @ B )
| ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(40,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ B )
=> ( p @ A ) )
=> ~ ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Epth__ni2) ).
thf(385,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ B )
=> ( p @ A ) )
=> ~ ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(104,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
<=> ( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__lt) ).
thf(797,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
=> ( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
| ( A = B ) ) )
& ( ( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
| ( A = B ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(108,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ ( c_2Eextreal_2Eextreal__min_2E2 @ B @ C ) ) )
<=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__min) ).
thf(814,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ ( c_2Eextreal_2Eextreal__min_2E2 @ B @ C ) ) )
=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ C ) ) ) )
& ( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ C ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ ( c_2Eextreal_2Eextreal__min_2E2 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(121,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
| ( p @ B ) )
<=> ( ~ ( p @ A )
=> ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EDISJ__EQ__IMP) ).
thf(913,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
| ( p @ B ) )
=> ( ~ ( p @ A )
=> ( p @ B ) ) )
& ( ( ~ ( p @ A )
=> ( p @ B ) )
=> ( ( p @ A )
| ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(33,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: TA] :
( ( c_2Ebool_2ECOND_2E3 @ TA @ A @ B @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__ID) ).
thf(340,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: TA] :
( ( c_2Ebool_2ECOND_2E3 @ TA @ A @ B @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(227,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
<=> ~ ( p @ A ) )
| ~ ( p @ B )
| ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed003) ).
thf(1782,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( p @ B ) ) )
| ~ ( p @ B )
| ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(211,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ~ ( p @ C )
=> ( A = B ) )
& ( ~ ( p @ B )
=> ( C = D ) ) )
=> ( ( ( p @ A )
| ( p @ C ) )
<=> ( ( p @ B )
| ( p @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EOR__CONG) ).
thf(1650,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ~ ( p @ C )
=> ( A = B ) )
& ( ~ ( p @ B )
=> ( C = D ) ) )
=> ( ( ( ( p @ A )
| ( p @ C ) )
=> ( ( p @ B )
| ( p @ D ) ) )
& ( ( ( p @ B )
| ( p @ D ) )
=> ( ( p @ A )
| ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(172,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ C ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__sub_2E2 @ A @ C ) @ ( c_2Eextreal_2Eextreal__sub_2E2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__lsub__imp) ).
thf(1359,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ C ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__sub_2E2 @ A @ C ) @ ( c_2Eextreal_2Eextreal__sub_2E2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(20,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal,D: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ C @ D ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ ( c_2Eextreal_2Eextreal__add_2E2 @ A @ C ) @ ( c_2Eextreal_2Eextreal__add_2E2 @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Elt__add2) ).
thf(301,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal,D: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ C @ D ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ ( c_2Eextreal_2Eextreal__add_2E2 @ A @ C ) @ ( c_2Eextreal_2Eextreal__add_2E2 @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(159,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ B )
=> ( p @ C ) )
=> ( ( ( p @ B )
| ( p @ A ) )
=> ( ( p @ C )
| ( p @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2ERIGHT__IMP__OR__INTRO) ).
thf(1228,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ B )
=> ( p @ C ) )
=> ( ( ( p @ B )
| ( p @ A ) )
=> ( ( p @ C )
| ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(42,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: TA] :
( ( p @ ( c_2Eind__type_2EINJN_2E3 @ TA @ A @ B @ C ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eind__type_2EINJN) ).
thf(389,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: TA] :
( ( ( p @ ( c_2Eind__type_2EINJN_2E3 @ TA @ A @ B @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( p @ ( c_2Eind__type_2EINJN_2E3 @ TA @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(167,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( ( p @ B )
& ( p @ C ) ) )
<=> ( ( ( p @ A )
=> ( p @ B ) )
& ( ( p @ A )
=> ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CONJ__THM) ).
thf(1298,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( ( p @ B )
& ( p @ C ) ) )
=> ( ( ( p @ A )
=> ( p @ B ) )
& ( ( p @ A )
=> ( p @ C ) ) ) )
& ( ( ( ( p @ A )
=> ( p @ B ) )
& ( ( p @ A )
=> ( p @ C ) ) )
=> ( ( p @ A )
=> ( ( p @ B )
& ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(95,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
<=> ~ ( p @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2ENEG__IFF__2__1) ).
thf(719,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ~ ( p @ B ) )
& ( ~ ( p @ B )
=> ( p @ A ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(39,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ~ ( p @ C )
=> ( ( p @ B )
=> ( p @ A ) ) )
& ( ~ ( p @ B )
=> ( ( p @ D )
=> ( p @ C ) ) ) )
=> ( ( ( p @ B )
| ( p @ D ) )
=> ( ( p @ A )
| ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__disj__strengthen) ).
thf(372,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ~ ( p @ C )
=> ( ( p @ B )
=> ( p @ A ) ) )
& ( ~ ( p @ B )
=> ( ( p @ D )
=> ( p @ C ) ) ) )
=> ( ( ( p @ B )
| ( p @ D ) )
=> ( ( p @ A )
| ( p @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(83,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ B )
| ~ ( p @ A )
| ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed010) ).
thf(619,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ B )
| ~ ( p @ A )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(92,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool] :
( ? [B: TA] : ( p @ A )
<=> ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEXISTS__SIMP) ).
thf(702,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(126,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ C )
<=> ( B = A ) )
<=> ( ( ( p @ C )
| ( p @ B )
| ( p @ A ) )
& ( ( p @ C )
| ~ ( p @ A )
| ~ ( p @ B ) )
& ( ( p @ B )
| ~ ( p @ A )
| ~ ( p @ C ) )
& ( ( p @ A )
| ~ ( p @ B )
| ~ ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__eq) ).
thf(934,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( ( p @ C )
=> ( B = A ) )
& ( ( B = A )
=> ( p @ C ) ) )
=> ( ( ( p @ C )
| ( p @ B )
| ( p @ A ) )
& ( ( p @ C )
| ~ ( p @ A )
| ~ ( p @ B ) )
& ( ( p @ B )
| ~ ( p @ A )
| ~ ( p @ C ) )
& ( ( p @ A )
| ~ ( p @ B )
| ~ ( p @ C ) ) ) )
& ( ( ( ( p @ C )
| ( p @ B )
| ( p @ A ) )
& ( ( p @ C )
| ~ ( p @ A )
| ~ ( p @ B ) )
& ( ( p @ B )
| ~ ( p @ A )
| ~ ( p @ C ) )
& ( ( p @ A )
| ~ ( p @ B )
| ~ ( p @ C ) ) )
=> ( ( ( p @ C )
=> ( B = A ) )
& ( ( B = A )
=> ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(195,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ B )
<=> ~ ( p @ A ) )
| ( p @ B )
| ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed008) ).
thf(1545,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( ( p @ B )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( p @ B ) ) )
| ( p @ B )
| ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(86,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( p @ ( c_2Eblast_2Ebcarry_2E3 @ A @ B @ C ) )
<=> ( ( ( p @ A )
& ( p @ B ) )
| ( ( ( p @ A )
| ( p @ B ) )
& ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eblast_2Ebcarry__def) ).
thf(638,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ ( c_2Eblast_2Ebcarry_2E3 @ A @ B @ C ) )
=> ( ( ( p @ A )
& ( p @ B ) )
| ( ( ( p @ A )
| ( p @ B ) )
& ( p @ C ) ) ) )
& ( ( ( ( p @ A )
& ( p @ B ) )
| ( ( ( p @ A )
| ( p @ B ) )
& ( p @ C ) ) )
=> ( p @ ( c_2Eblast_2Ebcarry_2E3 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(137,axiom,
! [A: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
~ ( p @ ( c_2Estring_2Estring__lt_2E2 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Estring_2Estring__lt__nonrefl) ).
thf(1085,plain,
! [A: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
~ ( p @ ( c_2Estring_2Estring__lt_2E2 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(1086,plain,
~ ? [A: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] : ( p @ ( c_2Estring_2Estring__lt_2E2 @ A @ A ) ),
inference(miniscope,[status(thm)],[1085]) ).
thf(1087,plain,
! [A: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
~ ( p @ ( c_2Estring_2Estring__lt_2E2 @ A @ A ) ),
inference(cnf,[status(esa)],[1086]) ).
thf(169,axiom,
! [TA: $tType,A: tyop_2Esptree_2Espt @ TA] : ( p @ ( c_2Esptree_2Esubspt_2E2 @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esptree_2Esubspt__refl) ).
thf(1318,plain,
! [TA: $tType,A: tyop_2Esptree_2Espt @ TA] : ( p @ ( c_2Esptree_2Esubspt_2E2 @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(1319,plain,
! [TA: $tType,A: tyop_2Esptree_2Espt @ TA] : ( p @ ( c_2Esptree_2Esubspt_2E2 @ TA @ A @ A ) ),
inference(cnf,[status(esa)],[1318]) ).
thf(187,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Elt__imp__le) ).
thf(1479,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(81,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ C ) )
<=> ( ( p @ A )
=> ( ( p @ B )
=> ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2EAND__IMP) ).
thf(606,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ C ) )
=> ( ( p @ A )
=> ( ( p @ B )
=> ( p @ C ) ) ) )
& ( ( ( p @ A )
=> ( ( p @ B )
=> ( p @ C ) ) )
=> ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(117,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( A = B )
<=> ( ( ( p @ A )
=> ( p @ B ) )
& ( ( p @ B )
=> ( p @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__IMP__THM) ).
thf(881,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( A = B )
=> ( ( ( p @ A )
=> ( p @ B ) )
& ( ( p @ B )
=> ( p @ A ) ) ) )
& ( ( ( ( p @ A )
=> ( p @ B ) )
& ( ( p @ B )
=> ( p @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(28,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__min_2E2 @ A @ B )
= ( c_2Eextreal_2Eextreal__min_2E2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Emin__comm) ).
thf(325,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__min_2E2 @ A @ B )
= ( c_2Eextreal_2Eextreal__min_2E2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(17,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__min_2E2 @ A @ B )
= ( c_2Ebool_2ECOND_2E3 @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Eextreal__min__def) ).
thf(289,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__min_2E2 @ A @ B )
= ( c_2Ebool_2ECOND_2E3 @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
! [TA: $tType,A: tyop_2Elist_2Elist @ TA,B: tyop_2Elist_2Elist @ TA] :
( ( c_2Esorting_2EPERM__SINGLE__SWAP_2E2 @ TA @ A @ B )
= ( c_2Esorting_2EPERM__SINGLE__SWAP_2E2 @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esorting_2EPERM__SINGLE__SWAP__SYM) ).
thf(261,plain,
! [TA: $tType,A: tyop_2Elist_2Elist @ TA,B: tyop_2Elist_2Elist @ TA] :
( ( c_2Esorting_2EPERM__SINGLE__SWAP_2E2 @ TA @ A @ B )
= ( c_2Esorting_2EPERM__SINGLE__SWAP_2E2 @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(59,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( A = B )
=> ( ( C = D )
=> ( ( ( p @ A )
& ( p @ C ) )
<=> ( ( p @ B )
& ( p @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2ECONJ__CONG) ).
thf(492,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( A = B )
=> ( ( C = D )
=> ( ( ( ( p @ A )
& ( p @ C ) )
=> ( ( p @ B )
& ( p @ D ) ) )
& ( ( ( p @ B )
& ( p @ D ) )
=> ( ( p @ A )
& ( p @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(103,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B ) )
<=> ( ( p @ B )
& ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECONJ__SYM) ).
thf(789,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
& ( p @ B ) )
=> ( ( p @ B )
& ( p @ A ) ) )
& ( ( ( p @ B )
& ( p @ A ) )
=> ( ( p @ A )
& ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(27,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Elt__imp__ne) ).
thf(321,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(8,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( c_2Eint__arith_2Ebmarker_2E1 @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2Ebmarker__def) ).
thf(253,plain,
! [A: tyop_2Emin_2Ebool] :
( ( c_2Eint__arith_2Ebmarker_2E1 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(232,plain,
( sk1
| ~ ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ sk6 @ sk7 ) @ sk5 ) ) ),
inference(cnf,[status(esa)],[229]) ).
thf(1825,plain,
( sk1
| ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ sk6 @ sk7 ) @ sk5 ) )
!= ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ sk7 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[234,232]) ).
thf(1828,plain,
( sk1
| ( ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ sk6 @ sk7 ) @ sk5 )
!= ( c_2Eextreal_2Eextreal__le_2E2 @ sk7 @ sk5 ) ) ),
inference(simp,[status(thm)],[1825]) ).
thf(63,axiom,
! [A: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,B: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
~ ( ( p @ ( c_2Estring_2Estring__lt_2E2 @ A @ B ) )
& ( p @ ( c_2Estring_2Estring__lt_2E2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Estring_2Estring__lt__antisym) ).
thf(514,plain,
! [A: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,B: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
~ ( ( p @ ( c_2Estring_2Estring__lt_2E2 @ A @ B ) )
& ( p @ ( c_2Estring_2Estring__lt_2E2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(73,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
& ~ ( p @ A ) )
<=> ~ ( ~ ( p @ B )
| ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er055) ).
thf(574,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
& ~ ( p @ A ) )
=> ~ ( ~ ( p @ B )
| ( p @ A ) ) )
& ( ~ ( ~ ( p @ B )
| ( p @ A ) )
=> ( ( p @ B )
& ~ ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(214,axiom,
! [A: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,B: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,C: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
( ( ( p @ ( c_2Estring_2Estring__lt_2E2 @ A @ B ) )
& ( p @ ( c_2Estring_2Estring__lt_2E2 @ B @ C ) ) )
=> ( p @ ( c_2Estring_2Estring__lt_2E2 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Estring_2Estring__lt__trans) ).
thf(1677,plain,
! [A: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,B: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,C: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
( ( ( p @ ( c_2Estring_2Estring__lt_2E2 @ A @ B ) )
& ( p @ ( c_2Estring_2Estring__lt_2E2 @ B @ C ) ) )
=> ( p @ ( c_2Estring_2Estring__lt_2E2 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(105,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ A ) )
<=> ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EConseqConv_2EAND__CLAUSES__XX) ).
thf(806,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(154,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ C )
<=> ( ( p @ B )
| ( p @ A ) ) )
<=> ( ( ( p @ C )
| ~ ( p @ B ) )
& ( ( p @ C )
| ~ ( p @ A ) )
& ( ( p @ B )
| ( p @ A )
| ~ ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__disj) ).
thf(1183,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( ( p @ C )
=> ( ( p @ B )
| ( p @ A ) ) )
& ( ( ( p @ B )
| ( p @ A ) )
=> ( p @ C ) ) )
=> ( ( ( p @ C )
| ~ ( p @ B ) )
& ( ( p @ C )
| ~ ( p @ A ) )
& ( ( p @ B )
| ( p @ A )
| ~ ( p @ C ) ) ) )
& ( ( ( ( p @ C )
| ~ ( p @ B ) )
& ( ( p @ C )
| ~ ( p @ A ) )
& ( ( p @ B )
| ( p @ A )
| ~ ( p @ C ) ) )
=> ( ( ( p @ C )
=> ( ( p @ B )
| ( p @ A ) ) )
& ( ( ( p @ B )
| ( p @ A ) )
=> ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(57,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( ( p @ A )
& ( p @ B ) )
<=> ( ~ ( p @ A )
| ~ ( p @ B ) ) )
& ( ~ ( ( p @ A )
| ( p @ B ) )
<=> ( ~ ( p @ A )
& ~ ( p @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EDE__MORGAN__THM) ).
thf(475,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( ( p @ A )
& ( p @ B ) )
=> ( ~ ( p @ A )
| ~ ( p @ B ) ) )
& ( ( ~ ( p @ A )
| ~ ( p @ B ) )
=> ~ ( ( p @ A )
& ( p @ B ) ) )
& ( ~ ( ( p @ A )
| ( p @ B ) )
=> ( ~ ( p @ A )
& ~ ( p @ B ) ) )
& ( ( ~ ( p @ A )
& ~ ( p @ B ) )
=> ~ ( ( p @ A )
| ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(123,axiom,
! [A: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,B: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
( ( A = B )
| ( p @ ( c_2Estring_2Estring__lt_2E2 @ A @ B ) )
| ( p @ ( c_2Estring_2Estring__lt_2E2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Estring_2Estring__lt__cases) ).
thf(924,plain,
! [A: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,B: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
( ( A = B )
| ( p @ ( c_2Estring_2Estring__lt_2E2 @ A @ B ) )
| ( p @ ( c_2Estring_2Estring__lt_2E2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(179,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] : ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__min_2E2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Emin__le1) ).
thf(1418,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] : ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__min_2E2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(84,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( p @ B )
=> ( p @ A ) )
<=> ( ( p @ A )
| ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er030) ).
thf(623,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ~ ( p @ B )
=> ( p @ A ) )
=> ( ( p @ A )
| ( p @ B ) ) )
& ( ( ( p @ A )
| ( p @ B ) )
=> ( ~ ( p @ B )
=> ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(14,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__add_2E2 @ A @ ( c_2Eextreal_2Eextreal__add_2E2 @ B @ C ) )
= ( c_2Eextreal_2Eextreal__add_2E2 @ ( c_2Eextreal_2Eextreal__add_2E2 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Eadd__assoc) ).
thf(280,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__add_2E2 @ A @ ( c_2Eextreal_2Eextreal__add_2E2 @ B @ C ) )
= ( c_2Eextreal_2Eextreal__add_2E2 @ ( c_2Eextreal_2Eextreal__add_2E2 @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(184,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ ( c_2EHolSmt_2Exor_2E2 @ A @ B ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Exor__def) ).
thf(1440,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ ( c_2EHolSmt_2Exor_2E2 @ A @ B ) )
=> ( A != B ) )
& ( ( A != B )
=> ( p @ ( c_2EHolSmt_2Exor_2E2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(1441,plain,
( ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ ( c_2EHolSmt_2Exor_2E2 @ A @ B ) )
=> ( A != B ) )
& ! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( A != B )
=> ( p @ ( c_2EHolSmt_2Exor_2E2 @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[1440]) ).
thf(1443,plain,
! [B: tyop_2Emin_2Ebool,A: tyop_2Emin_2Ebool] :
( ~ ( p @ ( c_2EHolSmt_2Exor_2E2 @ A @ B ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[1441]) ).
thf(1446,plain,
! [B: tyop_2Emin_2Ebool,A: tyop_2Emin_2Ebool] :
( ( A != B )
| ~ ( p @ ( c_2EHolSmt_2Exor_2E2 @ A @ B ) ) ),
inference(lifteq,[status(thm)],[1443]) ).
thf(1447,plain,
! [A: tyop_2Emin_2Ebool] :
~ ( p @ ( c_2EHolSmt_2Exor_2E2 @ A @ A ) ),
inference(simp,[status(thm)],[1446]) ).
thf(182,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
=> ( ~ ( p @ A )
| ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2EIMP__DISJ__1) ).
thf(1433,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
=> ( ~ ( p @ A )
| ( p @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(198,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
<=> ~ ( p @ A ) )
<=> ( ( ( p @ B )
| ( p @ A ) )
& ( ~ ( p @ A )
| ~ ( p @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__neg) ).
thf(1564,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( ( p @ B )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( p @ B ) ) )
=> ( ( ( p @ B )
| ( p @ A ) )
& ( ~ ( p @ A )
| ~ ( p @ B ) ) ) )
& ( ( ( ( p @ B )
| ( p @ A ) )
& ( ~ ( p @ A )
| ~ ( p @ B ) ) )
=> ( ( ( p @ B )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(66,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
=> ( p @ A ) )
& ( ( p @ B )
=> ( ( p @ C )
=> ( p @ D ) ) ) )
=> ( ( ( p @ A )
=> ( p @ C ) )
=> ( ( p @ B )
=> ( p @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__simple__imp__weaken) ).
thf(527,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
=> ( p @ A ) )
& ( ( p @ B )
=> ( ( p @ C )
=> ( p @ D ) ) ) )
=> ( ( ( p @ A )
=> ( p @ C ) )
=> ( ( p @ B )
=> ( p @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(24,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__sub_2E2 @ A @ B )
= ( c_2Eextreal_2Eextreal__add_2E2 @ A @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Eextreal__sub__add) ).
thf(312,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__sub_2E2 @ A @ B )
= ( c_2Eextreal_2Eextreal__add_2E2 @ A @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(18,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: TA] :
( ( c_2Ebool_2ECOND_2E3 @ TA @ A @ B @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__ID) ).
thf(292,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: TA] :
( ( c_2Ebool_2ECOND_2E3 @ TA @ A @ B @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(233,plain,
( ~ ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ sk3 @ sk2 ) )
| ~ ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ sk4 @ sk2 ) )
| ~ sk1 ),
inference(cnf,[status(esa)],[229]) ).
thf(62,axiom,
! [TA: $tType,A: tyop_2Elist_2Elist @ TA] : ( p @ ( c_2EEncode_2Ebiprefix_2E2 @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EEncode_2Ebiprefix__refl) ).
thf(512,plain,
! [TA: $tType,A: tyop_2Elist_2Elist @ TA] : ( p @ ( c_2EEncode_2Ebiprefix_2E2 @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(217,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( p @ B ) )
& ( ( p @ B )
=> ( ( p @ D )
=> ( p @ C ) ) ) )
=> ( ( ( p @ B )
=> ( p @ D ) )
=> ( ( p @ A )
=> ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__simple__imp__strengthen) ).
thf(1691,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( p @ B ) )
& ( ( p @ B )
=> ( ( p @ D )
=> ( p @ C ) ) ) )
=> ( ( ( p @ B )
=> ( p @ D ) )
=> ( ( p @ A )
=> ( p @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(31,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ECOND_2E3 @ TA @ D @ C @ ( c_2Ebool_2ECOND_2E3 @ TA @ D @ B @ A ) )
= ( c_2Ebool_2ECOND_2E3 @ TA @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er023) ).
thf(334,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ECOND_2E3 @ TA @ D @ C @ ( c_2Ebool_2ECOND_2E3 @ TA @ D @ B @ A ) )
= ( c_2Ebool_2ECOND_2E3 @ TA @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(175,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ~ ( p @ A )
<=> ( p @ C ) )
=> ( ( ~ ( p @ B )
<=> ( p @ D ) )
=> ( ~ ( ( p @ A )
& ( p @ B ) )
<=> ( ( p @ C )
| ( p @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2ENNF__CONJ) ).
thf(1387,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ~ ( p @ A )
=> ( p @ C ) )
& ( ( p @ C )
=> ~ ( p @ A ) ) )
=> ( ( ( ~ ( p @ B )
=> ( p @ D ) )
& ( ( p @ D )
=> ~ ( p @ B ) ) )
=> ( ( ~ ( ( p @ A )
& ( p @ B ) )
=> ( ( p @ C )
| ( p @ D ) ) )
& ( ( ( p @ C )
| ( p @ D ) )
=> ~ ( ( p @ A )
& ( p @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(156,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ C ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Elte__trans) ).
thf(1217,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ C ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(109,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( A = B )
& ( ( p @ B )
=> ( C = D ) ) )
=> ( ( ( p @ A )
=> ( p @ C ) )
<=> ( ( p @ B )
=> ( p @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CONG) ).
thf(820,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( A = B )
& ( ( p @ B )
=> ( C = D ) ) )
=> ( ( ( ( p @ A )
=> ( p @ C ) )
=> ( ( p @ B )
=> ( p @ D ) ) )
& ( ( ( p @ B )
=> ( p @ D ) )
=> ( ( p @ A )
=> ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(70,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
( ( ( p @ ( c_2Egcd_2Eis__gcd_2E3 @ A @ B @ C ) )
& ( p @ ( c_2Egcd_2Eis__gcd_2E3 @ A @ B @ D ) ) )
=> ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__UNIQUE) ).
thf(561,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
( ( ( p @ ( c_2Egcd_2Eis__gcd_2E3 @ A @ B @ C ) )
& ( p @ ( c_2Egcd_2Eis__gcd_2E3 @ A @ B @ D ) ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(102,axiom,
! [A: tyop_2Emin_2Ebool] :
( ~ ~ ( p @ A )
<=> ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EConseqConv_2ENOT__CLAUSES__X) ).
thf(788,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(113,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B ) )
<=> ! [C: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( ( p @ B )
=> ( p @ C ) ) )
=> ( p @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EAND__DEF) ).
thf(847,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
& ( p @ B ) )
=> ! [C: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( ( p @ B )
=> ( p @ C ) ) )
=> ( p @ C ) ) )
& ( ! [C: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( ( p @ B )
=> ( p @ C ) ) )
=> ( p @ C ) )
=> ( ( p @ A )
& ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(36,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( A = B )
=> ( ~ ~ ( p @ A )
<=> ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2ENNF__NOT__NOT) ).
thf(361,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( A = B )
=> ( ( ( p @ A )
=> ( p @ B ) )
& ( ( p @ B )
=> ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(206,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( p @ B )
& ~ ( p @ A ) )
| ( p @ B )
| ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed013) ).
thf(1624,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( p @ B )
& ~ ( p @ A ) )
| ( p @ B )
| ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(75,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ A ) @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) )
= ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__neg) ).
thf(583,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ A ) @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) )
= ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(54,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ B )
=> ( p @ C ) )
=> ( ( ( p @ B )
& ( p @ A ) )
=> ( ( p @ C )
& ( p @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2ERIGHT__IMP__AND__INTRO) ).
thf(461,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ B )
=> ( p @ C ) )
=> ( ( ( p @ B )
& ( p @ A ) )
=> ( ( p @ C )
& ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(135,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] : ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__min_2E2 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Emin__le2) ).
thf(1079,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] : ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__min_2E2 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(163,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
=> ( p @ A ) )
<=> ( ~ ( p @ B )
| ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er031) ).
thf(1281,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
=> ( p @ A ) )
=> ( ~ ( p @ B )
| ( p @ A ) ) )
& ( ( ~ ( p @ B )
| ( p @ A ) )
=> ( ( p @ B )
=> ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(223,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
<=> ~ ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Eextreal__lt__def) ).
thf(1740,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
=> ~ ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) ) )
& ( ~ ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) )
=> ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(322,plain,
! [B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ~ ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[321]) ).
thf(323,plain,
! [B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ( A != B )
| ~ ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) ) ),
inference(lifteq,[status(thm)],[322]) ).
thf(324,plain,
! [A: tyop_2Eextreal_2Eextreal] :
~ ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ A ) ),
inference(simp,[status(thm)],[323]) ).
thf(166,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] : ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ ( c_2Eextreal_2Eextreal__max_2E2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__max1) ).
thf(1296,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] : ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ ( c_2Eextreal_2Eextreal__max_2E2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(88,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( p @ B )
& ( p @ A ) )
<=> ~ ( ( p @ B )
| ~ ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er054) ).
thf(665,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ~ ( p @ B )
& ( p @ A ) )
=> ~ ( ( p @ B )
| ~ ( p @ A ) ) )
& ( ~ ( ( p @ B )
| ~ ( p @ A ) )
=> ( ~ ( p @ B )
& ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(171,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ B )
| ( p @ A )
| ~ ( ( p @ B )
<=> ~ ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed012) ).
thf(1350,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ B )
| ( p @ A )
| ~ ( ( ( p @ B )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(65,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
| ( p @ B ) )
<=> ( ( p @ B )
| ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EDISJ__COMM) ).
thf(519,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
| ( p @ B ) )
=> ( ( p @ B )
| ( p @ A ) ) )
& ( ( ( p @ B )
| ( p @ A ) )
=> ( ( p @ A )
| ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(160,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( p @ B )
<=> ~ ( p @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er007) ).
thf(1234,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( ~ ( p @ B )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ~ ( p @ B ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( ~ ( p @ B )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ~ ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(1794,plain,
( ~ ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ sk3 @ sk2 ) )
| ~ sk1
| ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ sk4 @ sk2 ) )
!= ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ sk3 @ sk2 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[233]) ).
thf(1798,plain,
( ~ ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ sk3 @ sk2 ) )
| ~ sk1
| ( ( c_2Eextreal_2Eextreal__le_2E2 @ sk4 @ sk2 )
!= ( c_2Eextreal_2Eextreal__le_2E2 @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[1794]) ).
thf(1799,plain,
( ~ ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ sk3 @ sk2 ) )
| ~ sk1
| ( sk4 != sk3 )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[1798]) ).
thf(1804,plain,
( ~ ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ sk3 @ sk2 ) )
| ~ sk1
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[1799]) ).
thf(44,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal,D: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ C ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ D ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__min_2E2 @ A @ B ) @ ( c_2Eextreal_2Eextreal__min_2E2 @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Emin__le2__imp) ).
thf(403,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal,D: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ C ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ D ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__min_2E2 @ A @ B ) @ ( c_2Eextreal_2Eextreal__min_2E2 @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(41,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ! [C: TA] :
( ( p @ A )
| ( p @ B ) )
<=> ( ! [C: TA] : ( p @ A )
| ! [C: TA] : ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EBOTH__FORALL__OR__THM) ).
thf(388,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(35,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ A )
<=> ~ ( p @ B ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2ENEG__IFF__1__2) ).
thf(356,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( ( p @ A )
=> ~ ( p @ B ) )
& ( ~ ( p @ B )
=> ( p @ A ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(143,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ C )
=> ( A = B ) )
& ( ( p @ B )
=> ( C = D ) ) )
=> ( ( ( p @ A )
& ( p @ C ) )
<=> ( ( p @ B )
& ( p @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EAND__CONG) ).
thf(1118,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ C )
=> ( A = B ) )
& ( ( p @ B )
=> ( C = D ) ) )
=> ( ( ( ( p @ A )
& ( p @ C ) )
=> ( ( p @ B )
& ( p @ D ) ) )
& ( ( ( p @ B )
& ( p @ D ) )
=> ( ( p @ A )
& ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(149,axiom,
! [TA: $tType,A: tyop_2Esptree_2Espt @ TA,B: tyop_2Esptree_2Espt @ TA,C: tyop_2Esptree_2Espt @ TA] :
( ( ( p @ ( c_2Esptree_2Esubspt_2E2 @ TA @ C @ B ) )
& ( p @ ( c_2Esptree_2Esubspt_2E2 @ TA @ B @ A ) ) )
=> ( p @ ( c_2Esptree_2Esubspt_2E2 @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esptree_2Esubspt__trans) ).
thf(1160,plain,
! [TA: $tType,A: tyop_2Esptree_2Espt @ TA,B: tyop_2Esptree_2Espt @ TA,C: tyop_2Esptree_2Espt @ TA] :
( ( ( p @ ( c_2Esptree_2Esubspt_2E2 @ TA @ C @ B ) )
& ( p @ ( c_2Esptree_2Esubspt_2E2 @ TA @ B @ A ) ) )
=> ( p @ ( c_2Esptree_2Esubspt_2E2 @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(173,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
<=> ( ( p @ B )
| ( p @ A ) ) )
<=> ( ( p @ B )
=> ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EOR__IMP__THM) ).
thf(1361,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( ( p @ A )
=> ( ( p @ B )
| ( p @ A ) ) )
& ( ( ( p @ B )
| ( p @ A ) )
=> ( p @ A ) ) )
=> ( ( p @ B )
=> ( p @ A ) ) )
& ( ( ( p @ B )
=> ( p @ A ) )
=> ( ( ( p @ A )
=> ( ( p @ B )
| ( p @ A ) ) )
& ( ( ( p @ B )
| ( p @ A ) )
=> ( p @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(67,axiom,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum,B: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum] :
( ( p @ ( c_2Ebag_2EPSUB__BAG_2E2 @ TA @ A @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebag_2EPSUB__BAG__NOT__EQ) ).
thf(537,plain,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum,B: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum] :
( ( p @ ( c_2Ebag_2EPSUB__BAG_2E2 @ TA @ A @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(118,axiom,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum] :
~ ( p @ ( c_2Ebag_2EPSUB__BAG_2E2 @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebag_2EPSUB__BAG__IRREFL) ).
thf(901,plain,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum] :
~ ( p @ ( c_2Ebag_2EPSUB__BAG_2E2 @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(178,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
| ( p @ B ) )
=> ( p @ C ) )
=> ( ( p @ A )
=> ( p @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2EDISJ__ELIM__1) ).
thf(1414,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
| ( p @ B ) )
=> ( p @ C ) )
=> ( ( p @ A )
=> ( p @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(199,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ B )
| ( p @ A ) )
=> ~ ( p @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Epth__no1) ).
thf(1584,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ B )
| ( p @ A ) )
=> ~ ( p @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(6,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( ( c_2Eextreal_2Eextreal__ainv_2E1 @ A )
= ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Eeq__neg) ).
thf(242,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( ( ( c_2Eextreal_2Eextreal__ainv_2E1 @ A )
= ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( c_2Eextreal_2Eextreal__ainv_2E1 @ A )
= ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(243,plain,
( ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( ( c_2Eextreal_2Eextreal__ainv_2E1 @ A )
= ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) )
=> ( A = B ) )
& ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( A = B )
=> ( ( c_2Eextreal_2Eextreal__ainv_2E1 @ A )
= ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) ) ) ),
inference(miniscope,[status(thm)],[242]) ).
thf(245,plain,
! [B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ( ( c_2Eextreal_2Eextreal__ainv_2E1 @ A )
!= ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[243]) ).
thf(248,plain,
! [B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ( ( c_2Eextreal_2Eextreal__ainv_2E1 @ A )
!= ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[245]) ).
thf(249,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ( sk8 @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(c_2Eextreal_2Eextreal__ainv_2E1),[sk8])]) ).
thf(1789,plain,
! [B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ( ( sk8 @ A )
= B )
| ( ( c_2Eextreal_2Eextreal__ainv_2E1 @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ A ) )
!= ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[308,249]) ).
thf(1790,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ( sk8 @ A )
= ( c_2Eextreal_2Eextreal__ainv_2E1 @ A ) ),
inference(pattern_uni,[status(thm)],[1789:[bind(A,$thf( C )),bind(B,$thf( c_2Eextreal_2Eextreal__ainv_2E1 @ C ))]]) ).
thf(1791,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ( sk8 @ A )
= ( c_2Eextreal_2Eextreal__ainv_2E1 @ A ) ),
inference(simp,[status(thm)],[1790]) ).
thf(79,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
=> ( ( ( p @ B )
=> ( p @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__ANTISYM__AX) ).
thf(590,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
=> ( ( ( p @ B )
=> ( p @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(147,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] : ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ ( c_2Eextreal_2Eextreal__max_2E2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__max2) ).
thf(1155,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] : ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ ( c_2Eextreal_2Eextreal__max_2E2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(94,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ~ ( p @ C )
=> ( ( p @ A )
=> ( p @ B ) ) )
& ( ~ ( p @ B )
=> ( ( p @ C )
=> ( p @ D ) ) ) )
=> ( ( ( p @ A )
| ( p @ C ) )
=> ( ( p @ B )
| ( p @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__disj__weaken) ).
thf(706,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ~ ( p @ C )
=> ( ( p @ A )
=> ( p @ B ) ) )
& ( ~ ( p @ B )
=> ( ( p @ C )
=> ( p @ D ) ) ) )
=> ( ( ( p @ A )
| ( p @ C ) )
=> ( ( p @ B )
| ( p @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(29,axiom,
! [A: tyop_2Eextreal_2Eextreal] :
~ ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Elt__refl) ).
thf(328,plain,
! [A: tyop_2Eextreal_2Eextreal] :
~ ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(9,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ ( c_2Eextreal_2Eextreal__add_2E2 @ B @ A ) @ C ) )
=> ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ B @ ( c_2Eextreal_2Eextreal__sub_2E2 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Elt__sub__imp) ).
thf(256,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ ( c_2Eextreal_2Eextreal__add_2E2 @ B @ A ) @ C ) )
=> ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ B @ ( c_2Eextreal_2Eextreal__sub_2E2 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(390,plain,
! [TA: $tType,C: TA,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( B != A )
| ( p @ ( c_2Eind__type_2EINJN_2E3 @ TA @ A @ B @ C ) ) ),
inference(cnf,[status(esa)],[389]) ).
thf(392,plain,
! [TA: $tType,C: TA,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( B != A )
| ( p @ ( c_2Eind__type_2EINJN_2E3 @ TA @ A @ B @ C ) ) ),
inference(lifteq,[status(thm)],[390]) ).
thf(393,plain,
! [TA: $tType,B: TA,A: tyop_2Enum_2Enum] : ( p @ ( c_2Eind__type_2EINJN_2E3 @ TA @ A @ A @ B ) ),
inference(simp,[status(thm)],[392]) ).
thf(194,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__abs_2E1 @ A ) @ B ) )
<=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) @ A ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Eabs__bounds) ).
thf(1539,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__abs_2E1 @ A ) @ B ) )
=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) @ A ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) ) ) )
& ( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) @ A ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__abs_2E1 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(38,axiom,
! [A: tyop_2Emin_2Ebool] :
~ ( ( p @ A )
& ~ ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__AND) ).
thf(371,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(207,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
& ( p @ A ) )
=> ( p @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Epth__an1) ).
thf(1627,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
& ( p @ A ) )
=> ( p @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(23,axiom,
! [A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__min_2E2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Emin__refl) ).
thf(309,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__min_2E2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(310,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__min_2E2 @ A @ A )
= A ),
inference(cnf,[status(esa)],[309]) ).
thf(311,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__min_2E2 @ A @ A )
= A ),
inference(lifteq,[status(thm)],[310]) ).
thf(122,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
& ~ ( p @ A ) )
| ~ ( p @ B )
| ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed015) ).
thf(921,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
& ~ ( p @ A ) )
| ~ ( p @ B )
| ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(68,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( p @ C ) )
& ( ( p @ B )
=> ( p @ D ) ) )
=> ( ( ( p @ A )
& ( p @ B ) )
=> ( ( p @ C )
& ( p @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2ECONJ__IMPLIES) ).
thf(541,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( p @ C ) )
& ( ( p @ B )
=> ( p @ D ) ) )
=> ( ( ( p @ A )
& ( p @ B ) )
=> ( ( p @ C )
& ( p @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(151,axiom,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ),B: TA,C: TA,D: TA] :
( ( ( p @ ( c_2Erelation_2EEQC_2E3 @ TA @ A @ B @ C ) )
& ( p @ ( c_2Erelation_2EEQC_2E3 @ TA @ A @ C @ D ) ) )
=> ( p @ ( c_2Erelation_2EEQC_2E3 @ TA @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erelation_2EEQC__TRANS) ).
thf(1170,plain,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ),B: TA,C: TA,D: TA] :
( ( ( p @ ( c_2Erelation_2EEQC_2E3 @ TA @ A @ B @ C ) )
& ( p @ ( c_2Erelation_2EEQC_2E3 @ TA @ A @ C @ D ) ) )
=> ( p @ ( c_2Erelation_2EEQC_2E3 @ TA @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool,B: tyop_2Efinite__map_2Efmap @ TB @ TA] : ( p @ ( c_2Efinite__map_2Efmap__EQ__UPTO_2E3 @ TB @ TA @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Efinite__map_2Efmap__EQ__UPTO______EQ) ).
thf(586,plain,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool,B: tyop_2Efinite__map_2Efmap @ TB @ TA] : ( p @ ( c_2Efinite__map_2Efmap__EQ__UPTO_2E3 @ TB @ TA @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(34,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: TA,D: TA,E: TA,F: TA] :
( ( ( A = B )
& ( ( p @ B )
=> ( C = D ) )
& ( ~ ( p @ B )
=> ( E = F ) ) )
=> ( ( c_2Ebool_2ECOND_2E3 @ TA @ A @ C @ E )
= ( c_2Ebool_2ECOND_2E3 @ TA @ B @ D @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CONG) ).
thf(343,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: TA,D: TA,E: TA,F: TA] :
( ( ( A = B )
& ( ( p @ B )
=> ( C = D ) )
& ( ~ ( p @ B )
=> ( E = F ) ) )
=> ( ( c_2Ebool_2ECOND_2E3 @ TA @ A @ C @ E )
= ( c_2Ebool_2ECOND_2E3 @ TA @ B @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(4,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Egcd_2Eis__gcd_2E3 @ A @ B @ C )
= ( c_2Egcd_2Eis__gcd_2E3 @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__SYM) ).
thf(237,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Egcd_2Eis__gcd_2E3 @ A @ B @ C )
= ( c_2Egcd_2Eis__gcd_2E3 @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(186,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ C )
=> ( ( p @ B )
=> ( p @ A ) ) )
& ( ( p @ B )
=> ( ( p @ D )
=> ( p @ C ) ) ) )
=> ( ( ( p @ B )
& ( p @ D ) )
=> ( ( p @ A )
& ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__conj__strengthen) ).
thf(1466,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ C )
=> ( ( p @ B )
=> ( p @ A ) ) )
& ( ( p @ B )
=> ( ( p @ D )
=> ( p @ C ) ) ) )
=> ( ( ( p @ B )
& ( p @ D ) )
=> ( ( p @ A )
& ( p @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(134,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
& ( p @ A ) )
<=> ( ( p @ A )
& ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er048) ).
thf(1071,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
& ( p @ A ) )
=> ( ( p @ A )
& ( p @ B ) ) )
& ( ( ( p @ A )
& ( p @ B ) )
=> ( ( p @ B )
& ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(47,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( B = A )
| ~ ( p @ B )
| ~ ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed005) ).
thf(412,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( B = A )
| ~ ( p @ B )
| ~ ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(221,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
& ( p @ C ) )
=> ( p @ A ) )
<=> ( ( p @ B )
=> ( ( p @ C )
=> ( p @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ECONJ__EQ__IMP) ).
thf(1727,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( ( p @ B )
& ( p @ C ) )
=> ( p @ A ) )
=> ( ( p @ B )
=> ( ( p @ C )
=> ( p @ A ) ) ) )
& ( ( ( p @ B )
=> ( ( p @ C )
=> ( p @ A ) ) )
=> ( ( ( p @ B )
& ( p @ C ) )
=> ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(513,plain,
! [TA: $tType,A: tyop_2Elist_2Elist @ TA] : ( p @ ( c_2EEncode_2Ebiprefix_2E2 @ TA @ A @ A ) ),
inference(cnf,[status(esa)],[512]) ).
thf(218,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( p @ ( c_2Eblast_2Ebsum_2E3 @ A @ B @ C ) )
<=> ( ( ( p @ A )
<=> ~ ( p @ B ) )
<=> ~ ( p @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eblast_2Ebsum__def) ).
thf(1698,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ ( c_2Eblast_2Ebsum_2E3 @ A @ B @ C ) )
=> ( ( ( ( ( p @ A )
=> ~ ( p @ B ) )
& ( ~ ( p @ B )
=> ( p @ A ) ) )
=> ~ ( p @ C ) )
& ( ~ ( p @ C )
=> ( ( ( p @ A )
=> ~ ( p @ B ) )
& ( ~ ( p @ B )
=> ( p @ A ) ) ) ) ) )
& ( ( ( ( ( ( p @ A )
=> ~ ( p @ B ) )
& ( ~ ( p @ B )
=> ( p @ A ) ) )
=> ~ ( p @ C ) )
& ( ~ ( p @ C )
=> ( ( ( p @ A )
=> ~ ( p @ B ) )
& ( ~ ( p @ B )
=> ( p @ A ) ) ) ) )
=> ( p @ ( c_2Eblast_2Ebsum_2E3 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(157,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool,B: tyop_2Epath_2Epath @ TB @ TA,C: tyop_2Enum_2Enum] :
( ( p @ ( c_2Epath_2EfirstP__at_2E3 @ TB @ TA @ A @ B @ C ) )
=> ! [D: tyop_2Enum_2Enum] :
( ( p @ ( c_2Epath_2EfirstP__at_2E3 @ TB @ TA @ A @ B @ D ) )
<=> ( D = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epath_2EfirstP__at__unique) ).
thf(1219,plain,
! [TA: $tType,TB: $tType,A: tyop_2Emin_2Efun @ TB @ tyop_2Emin_2Ebool,B: tyop_2Epath_2Epath @ TB @ TA,C: tyop_2Enum_2Enum] :
( ( p @ ( c_2Epath_2EfirstP__at_2E3 @ TB @ TA @ A @ B @ C ) )
=> ! [D: tyop_2Enum_2Enum] :
( ( ( p @ ( c_2Epath_2EfirstP__at_2E3 @ TB @ TA @ A @ B @ D ) )
=> ( D = C ) )
& ( ( D = C )
=> ( p @ ( c_2Epath_2EfirstP__at_2E3 @ TB @ TA @ A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(189,axiom,
! [TA: $tType,A: TA] : ( p @ ( c_2Epred__set_2EUNIV_2E1 @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EUNIV__applied) ).
thf(1483,plain,
! [TA: $tType,A: TA] : ( p @ ( c_2Epred__set_2EUNIV_2E1 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(12,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: TA,D: TA,E: TA,F: TA] :
( ( ( A = B )
& ( ( p @ B )
=> ( C = D ) )
& ( ~ ( p @ B )
=> ( E = F ) ) )
=> ( ( c_2Ebool_2ECOND_2E3 @ TA @ A @ C @ E )
= ( c_2Ebool_2ECOND_2E3 @ TA @ B @ D @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__CONG) ).
thf(264,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: TA,D: TA,E: TA,F: TA] :
( ( ( A = B )
& ( ( p @ B )
=> ( C = D ) )
& ( ~ ( p @ B )
=> ( E = F ) ) )
=> ( ( c_2Ebool_2ECOND_2E3 @ TA @ A @ C @ E )
= ( c_2Ebool_2ECOND_2E3 @ TA @ B @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(49,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
| ( p @ B ) )
<=> ! [C: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ C ) )
=> ( ( ( p @ B )
=> ( p @ C ) )
=> ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EOR__DEF) ).
thf(423,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
| ( p @ B ) )
=> ! [C: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ C ) )
=> ( ( ( p @ B )
=> ( p @ C ) )
=> ( p @ C ) ) ) )
& ( ! [C: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ C ) )
=> ( ( ( p @ B )
=> ( p @ C ) )
=> ( p @ C ) ) )
=> ( ( p @ A )
| ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(96,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Elist_2Elist @ TA,C: tyop_2Enum_2Enum,D: tyop_2Emin_2Efun @ TA @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum )] :
( ( p @ ( c_2Elbtree_2Eis__mmindex_2E4 @ TA @ D @ B @ C @ A ) )
=> ! [E: tyop_2Enum_2Enum,F: tyop_2Enum_2Enum] :
( ( p @ ( c_2Elbtree_2Eis__mmindex_2E4 @ TA @ D @ B @ E @ F ) )
<=> ( ( E = C )
& ( F = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Elbtree_2Emmindex__unique) ).
thf(732,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Elist_2Elist @ TA,C: tyop_2Enum_2Enum,D: tyop_2Emin_2Efun @ TA @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum )] :
( ( p @ ( c_2Elbtree_2Eis__mmindex_2E4 @ TA @ D @ B @ C @ A ) )
=> ! [E: tyop_2Enum_2Enum,F: tyop_2Enum_2Enum] :
( ( ( p @ ( c_2Elbtree_2Eis__mmindex_2E4 @ TA @ D @ B @ E @ F ) )
=> ( ( E = C )
& ( F = A ) ) )
& ( ( ( E = C )
& ( F = A ) )
=> ( p @ ( c_2Elbtree_2Eis__mmindex_2E4 @ TA @ D @ B @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(16,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
~ ( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Elt__antisym) ).
thf(286,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
~ ( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(177,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( ( p @ B )
=> ( p @ C ) ) )
<=> ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EAND__IMP__INTRO) ).
thf(1403,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( ( p @ B )
=> ( p @ C ) ) )
=> ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ C ) ) )
& ( ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ C ) )
=> ( ( p @ A )
=> ( ( p @ B )
=> ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(191,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ A )
=> ( ( p @ A )
| ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EOR__INTRO__THM1) ).
thf(1503,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ A )
=> ( ( p @ A )
| ( p @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(213,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( p @ B )
=> ( p @ A ) )
<=> ( ( p @ B )
| ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er029) ).
thf(1669,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ~ ( p @ B )
=> ( p @ A ) )
=> ( ( p @ B )
| ( p @ A ) ) )
& ( ( ( p @ B )
| ( p @ A ) )
=> ( ~ ( p @ B )
=> ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(72,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B ) )
=> ( p @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EAND2__THM) ).
thf(572,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B ) )
=> ( p @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(55,axiom,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum,B: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum] :
~ ( ( p @ ( c_2Ebag_2EPSUB__BAG_2E2 @ TA @ A @ B ) )
& ( p @ ( c_2Ebag_2EPSUB__BAG_2E2 @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebag_2EPSUB__BAG__ANTISYM) ).
thf(466,plain,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum,B: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum] :
~ ( ( p @ ( c_2Ebag_2EPSUB__BAG_2E2 @ TA @ A @ B ) )
& ( p @ ( c_2Ebag_2EPSUB__BAG_2E2 @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(538,plain,
! [TA: $tType,B: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum,A: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum] :
( ~ ( p @ ( c_2Ebag_2EPSUB__BAG_2E2 @ TA @ A @ B ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[537]) ).
thf(539,plain,
! [TA: $tType,B: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum,A: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum] :
( ( A != B )
| ~ ( p @ ( c_2Ebag_2EPSUB__BAG_2E2 @ TA @ A @ B ) ) ),
inference(lifteq,[status(thm)],[538]) ).
thf(540,plain,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum] :
~ ( p @ ( c_2Ebag_2EPSUB__BAG_2E2 @ TA @ A @ A ) ),
inference(simp,[status(thm)],[539]) ).
thf(139,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
| ( p @ B ) )
=> ( p @ C ) )
=> ( ( p @ B )
=> ( p @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2EDISJ__ELIM__2) ).
thf(1090,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
| ( p @ B ) )
=> ( p @ C ) )
=> ( ( p @ B )
=> ( p @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(3,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ B @ C ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Elt__trans) ).
thf(235,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ B @ C ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(236,plain,
! [C: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ~ ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
| ~ ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ B @ C ) )
| ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ C ) ) ),
inference(cnf,[status(esa)],[235]) ).
thf(127,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( ( p @ D )
=> ( p @ C ) ) )
& ( ~ ( p @ D )
=> ( ( p @ A )
=> ( p @ B ) ) ) )
=> ( ( ( p @ B )
=> ( p @ D ) )
=> ( ( p @ A )
=> ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__imp__strengthen) ).
thf(979,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( ( p @ D )
=> ( p @ C ) ) )
& ( ~ ( p @ D )
=> ( ( p @ A )
=> ( p @ B ) ) ) )
=> ( ( ( p @ B )
=> ( p @ D ) )
=> ( ( p @ A )
=> ( p @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(110,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ? [C: TA] :
( ( p @ A )
=> ( p @ B ) )
<=> ( ! [C: TA] : ( p @ A )
=> ? [C: TA] : ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EBOTH__EXISTS__IMP__THM) ).
thf(831,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(1484,plain,
! [TA: $tType,A: TA] : ( p @ ( c_2Epred__set_2EUNIV_2E1 @ TA @ A ) ),
inference(cnf,[status(esa)],[1483]) ).
thf(1800,plain,
! [TA: $tType,A: TA] :
( ~ sk1
| ( ( c_2Eextreal_2Eextreal__le_2E2 @ sk4 @ sk2 )
!= ( c_2Eextreal_2Eextreal__le_2E2 @ sk3 @ sk2 ) )
| ( ( p @ ( c_2Epred__set_2EUNIV_2E1 @ TA @ A ) )
!= ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1484,1798]) ).
thf(1803,plain,
! [TA: $tType,A: TA] :
( ~ sk1
| ( sk4 != sk3 )
| ( sk2 != sk2 )
| ( ( c_2Epred__set_2EUNIV_2E1 @ TA @ A )
!= ( c_2Eextreal_2Eextreal__le_2E2 @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[1800]) ).
thf(1806,plain,
! [TA: $tType,A: TA] :
( ~ sk1
| ( sk4 != sk3 )
| ( ( c_2Epred__set_2EUNIV_2E1 @ TA @ A )
!= ( c_2Eextreal_2Eextreal__le_2E2 @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[1803]) ).
thf(133,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( C = B )
=> ( p @ A ) )
<=> ( ( p @ A )
| ( ( p @ B )
<=> ~ ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er037) ).
thf(1048,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( C = B )
=> ( p @ A ) )
=> ( ( p @ A )
| ( ( ( p @ B )
=> ~ ( p @ C ) )
& ( ~ ( p @ C )
=> ( p @ B ) ) ) ) )
& ( ( ( p @ A )
| ( ( ( p @ B )
=> ~ ( p @ C ) )
& ( ~ ( p @ C )
=> ( p @ B ) ) ) )
=> ( ( C = B )
=> ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(230,plain,
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ sk3 @ sk4 ) @ sk2 ) )
| ~ sk1 ),
inference(cnf,[status(esa)],[229]) ).
thf(219,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
& ( p @ A ) )
| ~ ( p @ B )
| ~ ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed016) ).
thf(1722,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
& ( p @ A ) )
| ~ ( p @ B )
| ~ ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(26,axiom,
! [TA: $tType,A: TA,B: TA,C: tyop_2Emin_2Ebool] :
( ( p @ C )
| ( ( c_2Ebool_2ECOND_2E3 @ TA @ C @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed019) ).
thf(318,plain,
! [TA: $tType,A: TA,B: TA,C: tyop_2Emin_2Ebool] :
( ( p @ C )
| ( ( c_2Ebool_2ECOND_2E3 @ TA @ C @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(21,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__sub_2E2 @ A @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) )
= ( c_2Eextreal_2Eextreal__add_2E2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Esub__rneg) ).
thf(303,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__sub_2E2 @ A @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) )
= ( c_2Eextreal_2Eextreal__add_2E2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(80,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ ( c_2Eextreal_2Eextreal__max_2E2 @ B @ C ) ) )
<=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
| ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__max) ).
thf(599,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ ( c_2Eextreal_2Eextreal__max_2E2 @ B @ C ) ) )
=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
| ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ C ) ) ) )
& ( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
| ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ C ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ ( c_2Eextreal_2Eextreal__max_2E2 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1815,plain,
( ~ sk1
| ( ( c_2Eextreal_2Eextreal__le_2E2 @ sk4 @ sk2 )
!= ( c_2Eextreal_2Eextreal__le_2E2 @ sk3 @ sk2 ) )
| ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ sk3 @ sk4 ) @ sk2 ) )
!= ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[230,1798]) ).
thf(1820,plain,
( ~ sk1
| ( sk4 != sk3 )
| ( sk2 != sk2 )
| ( ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ sk3 @ sk4 ) @ sk2 )
!= ( c_2Eextreal_2Eextreal__le_2E2 @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[1815]) ).
thf(1822,plain,
( ~ sk1
| ( sk4 != sk3 )
| ( ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ sk3 @ sk4 ) @ sk2 )
!= ( c_2Eextreal_2Eextreal__le_2E2 @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[1820]) ).
thf(1876,plain,
( ~ sk1
| ( sk4 != sk3 )
| ( ( c_2Eextreal_2Eextreal__max_2E2 @ sk3 @ sk4 )
!= sk3 )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[1822]) ).
thf(1877,plain,
( ~ sk1
| ( sk4 != sk3 )
| ( ( c_2Eextreal_2Eextreal__max_2E2 @ sk3 @ sk4 )
!= sk3 ) ),
inference(simp,[status(thm)],[1876]) ).
thf(85,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
=> ( p @ C ) )
& ( ( p @ A )
=> ( p @ D ) ) )
=> ( ( ( p @ C )
=> ( p @ A ) )
=> ( ( p @ B )
=> ( p @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EMONO__IMP) ).
thf(631,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
=> ( p @ C ) )
& ( ( p @ A )
=> ( p @ D ) ) )
=> ( ( ( p @ C )
=> ( p @ A ) )
=> ( ( p @ B )
=> ( p @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(150,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
| ( p @ B ) )
<=> ( ( p @ B )
| ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EDISJ__SYM) ).
thf(1162,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
| ( p @ B ) )
=> ( ( p @ B )
| ( p @ A ) ) )
& ( ( ( p @ B )
| ( p @ A ) )
=> ( ( p @ A )
| ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(5,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__add_2E2 @ B @ A ) @ C ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ ( c_2Eextreal_2Eextreal__sub_2E2 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__sub__imp) ).
thf(240,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__add_2E2 @ B @ A ) @ C ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ ( c_2Eextreal_2Eextreal__sub_2E2 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(132,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ A )
| ( ( p @ B )
& ( p @ C ) ) )
<=> ( ( ( p @ A )
| ( p @ B ) )
& ( ( p @ A )
| ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__OR__OVER__AND) ).
thf(1029,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
| ( ( p @ B )
& ( p @ C ) ) )
=> ( ( ( p @ A )
| ( p @ B ) )
& ( ( p @ A )
| ( p @ C ) ) ) )
& ( ( ( ( p @ A )
| ( p @ B ) )
& ( ( p @ A )
| ( p @ C ) ) )
=> ( ( p @ A )
| ( ( p @ B )
& ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(174,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ B )
=> ( p @ C ) )
=> ( ( ( p @ A )
| ( p @ B ) )
=> ( ( p @ A )
| ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2ELEFT__IMP__OR__INTRO) ).
thf(1381,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ B )
=> ( p @ C ) )
=> ( ( ( p @ A )
| ( p @ B ) )
=> ( ( p @ A )
| ( p @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(125,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ B @ C ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Elet__trans) ).
thf(932,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ B @ C ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(197,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
& ~ ( p @ A ) )
<=> ~ ( ( p @ A )
| ~ ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er059) ).
thf(1556,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
& ~ ( p @ A ) )
=> ~ ( ( p @ A )
| ~ ( p @ B ) ) )
& ( ~ ( ( p @ A )
| ~ ( p @ B ) )
=> ( ( p @ B )
& ~ ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(101,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
& ( p @ C ) )
| ( p @ A ) )
<=> ( ( ( p @ B )
| ( p @ A ) )
& ( ( p @ C )
| ( p @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__OR__OVER__AND) ).
thf(769,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( ( p @ B )
& ( p @ C ) )
| ( p @ A ) )
=> ( ( ( p @ B )
| ( p @ A ) )
& ( ( p @ C )
| ( p @ A ) ) ) )
& ( ( ( ( p @ B )
| ( p @ A ) )
& ( ( p @ C )
| ( p @ A ) ) )
=> ( ( ( p @ B )
& ( p @ C ) )
| ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(120,axiom,
! [A: tyop_2Emin_2Ebool] :
( ~ ~ ( p @ A )
=> ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2ENOT__NOT__ELIM) ).
thf(912,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(201,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( p @ B )
& ( p @ A ) )
| ( p @ B )
| ~ ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed014) ).
thf(1594,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( p @ B )
& ( p @ A ) )
| ( p @ B )
| ~ ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(155,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( A = B )
=> ( ( p @ A )
=> ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EEQ__IMPLIES) ).
thf(1213,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( A = B )
=> ( ( p @ A )
=> ( p @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(50,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ B )
| ( p @ C ) )
=> ( ( ( p @ B )
=> ( p @ A ) )
=> ( ( ( p @ C )
=> ( p @ A ) )
=> ( p @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EOR__ELIM__THM) ).
thf(438,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ B )
| ( p @ C ) )
=> ( ( ( p @ B )
=> ( p @ A ) )
=> ( ( ( p @ C )
=> ( p @ A ) )
=> ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(241,plain,
! [C: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ~ ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__add_2E2 @ B @ A ) @ C ) )
| ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ ( c_2Eextreal_2Eextreal__sub_2E2 @ C @ A ) ) ) ),
inference(cnf,[status(esa)],[240]) ).
thf(220,axiom,
! [TA: $tType,A: tyop_2Elist_2Elist @ TA] : ( p @ ( c_2Esorting_2EPERM__SINGLE__SWAP_2E2 @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esorting_2EPERM__SINGLE__SWAP__REFL) ).
thf(1725,plain,
! [TA: $tType,A: tyop_2Elist_2Elist @ TA] : ( p @ ( c_2Esorting_2EPERM__SINGLE__SWAP_2E2 @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(1726,plain,
! [TA: $tType,A: tyop_2Elist_2Elist @ TA] : ( p @ ( c_2Esorting_2EPERM__SINGLE__SWAP_2E2 @ TA @ A @ A ) ),
inference(cnf,[status(esa)],[1725]) ).
thf(161,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ C ) )
<=> ( ( p @ A )
=> ( ( p @ B )
=> ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2EAND__IMP__INTRO__SYM) ).
thf(1250,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ C ) )
=> ( ( p @ A )
=> ( ( p @ B )
=> ( p @ C ) ) ) )
& ( ( ( p @ A )
=> ( ( p @ B )
=> ( p @ C ) ) )
=> ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(90,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
<=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Elt__le) ).
thf(675,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
& ( A != B ) ) )
& ( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
& ( A != B ) )
=> ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(2106,plain,
( sk1
| ( ( c_2Eextreal_2Eextreal__max_2E2 @ sk6 @ sk7 )
!= sk7 )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[1828]) ).
thf(2107,plain,
( sk1
| ( ( c_2Eextreal_2Eextreal__max_2E2 @ sk6 @ sk7 )
!= sk7 ) ),
inference(simp,[status(thm)],[2106]) ).
thf(78,axiom,
! [A: tyop_2Emin_2Ebool] :
( ~ ~ ( p @ A )
<=> ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er040) ).
thf(589,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(69,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( B = A )
=> ~ ( ( p @ A )
<=> ~ ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2ENEG__IFF__1__1) ).
thf(548,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( B = A )
=> ~ ( ( ( p @ A )
=> ~ ( p @ B ) )
& ( ~ ( p @ B )
=> ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(180,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ C )
=> ( p @ A ) )
& ( ( p @ B )
=> ( p @ D ) ) )
=> ( ( ( p @ A )
=> ( p @ B ) )
=> ( ( p @ C )
=> ( p @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EIMP__IMPLIES) ).
thf(1420,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ C )
=> ( p @ A ) )
& ( ( p @ B )
=> ( p @ D ) ) )
=> ( ( ( p @ A )
=> ( p @ B ) )
=> ( ( p @ C )
=> ( p @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(124,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( A != B )
=> ( ( p @ A )
<=> ~ ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2ENEG__IFF__2__2) ).
thf(927,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( A != B )
=> ( ( ( p @ A )
=> ~ ( p @ B ) )
& ( ~ ( p @ B )
=> ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(254,plain,
! [A: tyop_2Emin_2Ebool] :
( ( c_2Eint__arith_2Ebmarker_2E1 @ A )
= A ),
inference(cnf,[status(esa)],[253]) ).
thf(255,plain,
! [A: tyop_2Emin_2Ebool] :
( ( c_2Eint__arith_2Ebmarker_2E1 @ A )
= A ),
inference(lifteq,[status(thm)],[254]) ).
thf(136,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ A )
=> ( ( p @ B )
=> ( ( p @ A )
& ( p @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EAND__INTRO__THM) ).
thf(1081,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ A )
=> ( ( p @ B )
=> ( ( p @ A )
& ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(82,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ B )
=> ( p @ A ) )
=> ( p @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Epth__ni1) ).
thf(617,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ B )
=> ( p @ A ) )
=> ( p @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(153,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ C ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__add_2E2 @ A @ B ) @ ( c_2Eextreal_2Eextreal__add_2E2 @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__ladd__imp) ).
thf(1181,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ C ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__add_2E2 @ A @ B ) @ ( c_2Eextreal_2Eextreal__add_2E2 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(19,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ ( c_2Eextreal_2Eextreal__abs_2E1 @ A ) @ B ) )
<=> ( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) @ A ) )
& ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Eabs__bounds__lt) ).
thf(295,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ ( c_2Eextreal_2Eextreal__abs_2E1 @ A ) @ B ) )
=> ( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) @ A ) )
& ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) ) ) )
& ( ( ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) @ A ) )
& ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ ( c_2Eextreal_2Eextreal__abs_2E1 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(158,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
=> ( p @ A ) )
=> ( ~ ( p @ A )
=> ~ ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2ENOT__IMPLIES) ).
thf(1225,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
=> ( p @ A ) )
=> ( ~ ( p @ A )
=> ~ ( p @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(203,axiom,
! [A: tyop_2Emin_2Ebool] :
( ~ ~ ( p @ A )
=> ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Epth__nn) ).
thf(1605,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(210,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ B )
| ( p @ A ) )
=> ~ ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Epth__no2) ).
thf(1647,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ B )
| ( p @ A ) )
=> ~ ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(225,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
& ( p @ C ) )
<=> ( ( p @ C )
& ( p @ B ) ) )
& ( ( ( p @ B )
& ( p @ C )
& ( p @ A ) )
<=> ( ( p @ B )
& ( p @ C )
& ( p @ A ) ) )
& ( ( ( p @ B )
& ( p @ C )
& ( p @ A ) )
<=> ( ( p @ C )
& ( p @ B )
& ( p @ A ) ) )
& ( ( ( p @ B )
& ( p @ B ) )
<=> ( p @ B ) )
& ( ( ( p @ B )
& ( p @ B )
& ( p @ C ) )
<=> ( ( p @ B )
& ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ECONJ__ACI) ).
thf(1753,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
& ( p @ C ) )
=> ( ( p @ C )
& ( p @ B ) ) )
& ( ( ( p @ C )
& ( p @ B ) )
=> ( ( p @ B )
& ( p @ C ) ) )
& ( ( ( p @ B )
& ( p @ C )
& ( p @ A ) )
=> ( ( p @ C )
& ( p @ B )
& ( p @ A ) ) )
& ( ( ( p @ C )
& ( p @ B )
& ( p @ A ) )
=> ( ( p @ B )
& ( p @ C )
& ( p @ A ) ) )
& ( ( ( p @ B )
& ( p @ B )
& ( p @ C ) )
=> ( ( p @ B )
& ( p @ C ) ) )
& ( ( ( p @ B )
& ( p @ C ) )
=> ( ( p @ B )
& ( p @ B )
& ( p @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(46,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( B = A )
| ( p @ B )
| ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed006) ).
thf(409,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( B = A )
| ( p @ B )
| ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(89,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
| ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__total) ).
thf(673,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
| ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(30,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__lt_2E2 @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ A ) @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) )
= ( c_2Eextreal_2Eextreal__lt_2E2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Elt__neg) ).
thf(331,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__lt_2E2 @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ A ) @ ( c_2Eextreal_2Eextreal__ainv_2E1 @ B ) )
= ( c_2Eextreal_2Eextreal__lt_2E2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(215,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( p @ C ) )
& ( ( p @ B )
=> ( p @ D ) ) )
=> ( ( ( p @ A )
| ( p @ B ) )
=> ( ( p @ C )
| ( p @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EDISJ__IMPLIES) ).
thf(1679,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( p @ C ) )
& ( ( p @ B )
=> ( p @ D ) ) )
=> ( ( ( p @ A )
| ( p @ B ) )
=> ( ( p @ C )
| ( p @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(222,axiom,
! [A: tyop_2Enum_2Enum] : ( p @ ( c_2Egcd_2Eis__gcd_2E3 @ A @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__REF) ).
thf(1738,plain,
! [A: tyop_2Enum_2Enum] : ( p @ ( c_2Egcd_2Eis__gcd_2E3 @ A @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(93,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( p @ A )
=> ( p @ B ) )
=> ( ( p @ A )
| ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2EIMP__DISJ__2) ).
thf(703,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( p @ A )
=> ( p @ B ) )
=> ( ( p @ A )
| ( p @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(193,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B ) )
=> ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EAND1__THM) ).
thf(1536,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B ) )
=> ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(181,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ ( c_2Emarker_2EAC_2E2 @ A @ B ) )
<=> ( ( p @ A )
& ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Emarker_2EAC__DEF) ).
thf(1427,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ ( c_2Emarker_2EAC_2E2 @ A @ B ) )
=> ( ( p @ A )
& ( p @ B ) ) )
& ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ ( c_2Emarker_2EAC_2E2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(1797,plain,
( ~ ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ sk3 @ sk2 ) )
| ~ sk1
| ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ sk4 @ sk2 ) )
!= ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ sk3 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[1794]) ).
thf(51,axiom,
! [A: tyop_2Eextreal_2Eextreal] : ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__refl) ).
thf(446,plain,
! [A: tyop_2Eextreal_2Eextreal] : ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(190,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
| ( p @ B ) )
=> ( p @ C ) )
<=> ( ( ( p @ A )
=> ( p @ C ) )
& ( ( p @ B )
=> ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EDISJ__IMP__THM) ).
thf(1485,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( ( p @ A )
| ( p @ B ) )
=> ( p @ C ) )
=> ( ( ( p @ A )
=> ( p @ C ) )
& ( ( p @ B )
=> ( p @ C ) ) ) )
& ( ( ( ( p @ A )
=> ( p @ C ) )
& ( ( p @ B )
=> ( p @ C ) ) )
=> ( ( ( p @ A )
| ( p @ B ) )
=> ( p @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(192,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ C )
<=> ( ( p @ B )
=> ( p @ A ) ) )
<=> ( ( ( p @ C )
| ( p @ B ) )
& ( ( p @ C )
| ~ ( p @ A ) )
& ( ~ ( p @ B )
| ( p @ A )
| ~ ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__imp) ).
thf(1506,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( ( p @ C )
=> ( ( p @ B )
=> ( p @ A ) ) )
& ( ( ( p @ B )
=> ( p @ A ) )
=> ( p @ C ) ) )
=> ( ( ( p @ C )
| ( p @ B ) )
& ( ( p @ C )
| ~ ( p @ A ) )
& ( ~ ( p @ B )
| ( p @ A )
| ~ ( p @ C ) ) ) )
& ( ( ( ( p @ C )
| ( p @ B ) )
& ( ( p @ C )
| ~ ( p @ A ) )
& ( ~ ( p @ B )
| ( p @ A )
| ~ ( p @ C ) ) )
=> ( ( ( p @ C )
=> ( ( p @ B )
=> ( p @ A ) ) )
& ( ( ( p @ B )
=> ( p @ A ) )
=> ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(140,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ~ ( p @ A )
<=> ( p @ C ) )
=> ( ( ~ ( p @ B )
<=> ( p @ D ) )
=> ( ~ ( ( p @ A )
| ( p @ B ) )
<=> ( ( p @ C )
& ( p @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2ENNF__DISJ) ).
thf(1094,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ~ ( p @ A )
=> ( p @ C ) )
& ( ( p @ C )
=> ~ ( p @ A ) ) )
=> ( ( ( ~ ( p @ B )
=> ( p @ D ) )
& ( ( p @ D )
=> ~ ( p @ B ) ) )
=> ( ( ~ ( ( p @ A )
| ( p @ B ) )
=> ( ( p @ C )
& ( p @ D ) ) )
& ( ( ( p @ C )
& ( p @ D ) )
=> ~ ( ( p @ A )
| ( p @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(145,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B ) )
<=> ~ ( ~ ( p @ A )
| ~ ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2ECONJ__NOT__OR__THM) ).
thf(1140,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
& ( p @ B ) )
=> ~ ( ~ ( p @ A )
| ~ ( p @ B ) ) )
& ( ~ ( ~ ( p @ A )
| ~ ( p @ B ) )
=> ( ( p @ A )
& ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(148,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
& ( p @ A ) )
=> ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Epth__an2) ).
thf(1157,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
& ( p @ A ) )
=> ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(119,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ~ ( p @ B )
<=> ( p @ A ) )
| ( p @ B )
| ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed007) ).
thf(903,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( ~ ( p @ B )
=> ( p @ A ) )
& ( ( p @ A )
=> ~ ( p @ B ) ) )
| ( p @ B )
| ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(99,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ? [C: TA] :
( ( p @ A )
& ( p @ B ) )
<=> ( ? [C: TA] : ( p @ A )
& ? [C: TA] : ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EBOTH__EXISTS__AND__THM) ).
thf(759,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(226,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool] :
( ! [B: TA] : ( p @ A )
<=> ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EFORALL__SIMP) ).
thf(1781,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(185,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ~ ( p @ B )
<=> ( p @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er009) ).
thf(1448,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( ( ~ ( p @ B )
=> ( p @ A ) )
& ( ( p @ A )
=> ~ ( p @ B ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ~ ( ( ~ ( p @ B )
=> ( p @ A ) )
& ( ( p @ A )
=> ~ ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(141,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
& ( p @ A ) )
<=> ~ ( ~ ( p @ B )
| ~ ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er053) ).
thf(1108,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
& ( p @ A ) )
=> ~ ( ~ ( p @ B )
| ~ ( p @ A ) ) )
& ( ~ ( ~ ( p @ B )
| ~ ( p @ A ) )
=> ( ( p @ B )
& ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(7,axiom,
! [TA: $tType,A: TA,B: TA,C: tyop_2Emin_2Ebool] :
( ~ ( p @ C )
| ( B
= ( c_2Ebool_2ECOND_2E3 @ TA @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed018) ).
thf(250,plain,
! [TA: $tType,A: TA,B: TA,C: tyop_2Emin_2Ebool] :
( ~ ( p @ C )
| ( B
= ( c_2Ebool_2ECOND_2E3 @ TA @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(231,plain,
( sk1
| ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ sk6 @ sk5 ) ) ),
inference(cnf,[status(esa)],[229]) ).
thf(168,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ C ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__add_2E2 @ B @ A ) @ ( c_2Eextreal_2Eextreal__add_2E2 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__radd__imp) ).
thf(1316,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ C ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__add_2E2 @ B @ A ) @ ( c_2Eextreal_2Eextreal__add_2E2 @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(53,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( A = B )
& ( ( p @ B )
=> ( C = D ) ) )
=> ( ( ( p @ A )
& ( p @ C ) )
<=> ( ( p @ B )
& ( p @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__AND__CONG) ).
thf(450,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( A = B )
& ( ( p @ B )
=> ( C = D ) ) )
=> ( ( ( ( p @ A )
& ( p @ C ) )
=> ( ( p @ B )
& ( p @ D ) ) )
& ( ( ( p @ B )
& ( p @ D ) )
=> ( ( p @ A )
& ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(164,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ B )
=> ( p @ C ) )
=> ( ( ( p @ A )
& ( p @ B ) )
=> ( ( p @ A )
& ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2ELEFT__IMP__AND__INTRO) ).
thf(1289,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ B )
=> ( p @ C ) )
=> ( ( ( p @ A )
& ( p @ B ) )
=> ( ( p @ A )
& ( p @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(37,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__max_2E2 @ A @ B )
= ( c_2Ebool_2ECOND_2E3 @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Eextreal__max__def) ).
thf(368,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__max_2E2 @ A @ B )
= ( c_2Ebool_2ECOND_2E3 @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(209,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ A )
| ( p @ B )
| ( p @ C ) )
<=> ( ( p @ A )
| ( p @ B )
| ( p @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EDISJ__ASSOC) ).
thf(1646,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(77,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B )
& ( p @ C ) )
<=> ( ( p @ A )
& ( p @ B )
& ( p @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECONJ__ASSOC) ).
thf(588,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(107,axiom,
! [A: tyop_2Emin_2Ebool] :
( ~ ~ ( p @ A )
<=> ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2ENOT__NOT) ).
thf(813,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(98,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
& ( p @ C ) )
=> ( p @ A ) )
<=> ( ( p @ C )
=> ( ( p @ B )
=> ( p @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EIMP__CONJ__ALT) ).
thf(748,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( ( p @ B )
& ( p @ C ) )
=> ( p @ A ) )
=> ( ( p @ C )
=> ( ( p @ B )
=> ( p @ A ) ) ) )
& ( ( ( p @ C )
=> ( ( p @ B )
=> ( p @ A ) ) )
=> ( ( ( p @ B )
& ( p @ C ) )
=> ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(188,axiom,
! [TA: $tType,A: TA,B: tyop_2Emin_2Efun @ TA @ TA,C: tyop_2Enum_2Enum] :
? [D: tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ TA] : ( p @ ( c_2Eprim__rec_2ESIMP__REC__REL_2E4 @ TA @ D @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eprim__rec_2ESIMP__REC__EXISTS) ).
thf(1481,plain,
! [TA: $tType,A: TA,B: tyop_2Emin_2Efun @ TA @ TA,C: tyop_2Enum_2Enum] :
? [D: tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ TA] : ( p @ ( c_2Eprim__rec_2ESIMP__REC__REL_2E4 @ TA @ D @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(10,axiom,
! [TA: $tType,A: TA,B: TA,C: tyop_2Emin_2Ebool] :
( ~ ( p @ C )
| ( ( c_2Ebool_2ECOND_2E3 @ TA @ C @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed020) ).
thf(258,plain,
! [TA: $tType,A: TA,B: TA,C: tyop_2Emin_2Ebool] :
( ~ ( p @ C )
| ( ( c_2Ebool_2ECOND_2E3 @ TA @ C @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(87,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ C )
=> ( ( p @ A )
=> ( p @ B ) ) )
& ( ( p @ B )
=> ( ( p @ C )
=> ( p @ D ) ) ) )
=> ( ( ( p @ A )
& ( p @ C ) )
=> ( ( p @ B )
& ( p @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__conj__weaken) ).
thf(652,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ C )
=> ( ( p @ A )
=> ( p @ B ) ) )
& ( ( p @ B )
=> ( ( p @ C )
=> ( p @ D ) ) ) )
=> ( ( ( p @ A )
& ( p @ C ) )
=> ( ( p @ B )
& ( p @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(224,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( p @ B )
& ( p @ A ) )
<=> ~ ( ~ ( p @ A )
| ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er058) ).
thf(1745,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ~ ( p @ B )
& ( p @ A ) )
=> ~ ( ~ ( p @ A )
| ( p @ B ) ) )
& ( ~ ( ~ ( p @ A )
| ( p @ B ) )
=> ( ~ ( p @ B )
& ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(208,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
| ( p @ C ) )
& ( p @ A ) )
<=> ( ( ( p @ B )
& ( p @ A ) )
| ( ( p @ C )
& ( p @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__AND__OVER__OR) ).
thf(1629,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( ( p @ B )
| ( p @ C ) )
& ( p @ A ) )
=> ( ( ( p @ B )
& ( p @ A ) )
| ( ( p @ C )
& ( p @ A ) ) ) )
& ( ( ( ( p @ B )
& ( p @ A ) )
| ( ( p @ C )
& ( p @ A ) ) )
=> ( ( ( p @ B )
| ( p @ C ) )
& ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(1824,plain,
( sk1
| ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ sk6 @ sk7 ) @ sk5 ) )
!= ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ sk6 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[231,232]) ).
thf(1827,plain,
( sk1
| ( ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__max_2E2 @ sk6 @ sk7 ) @ sk5 )
!= ( c_2Eextreal_2Eextreal__le_2E2 @ sk6 @ sk5 ) ) ),
inference(simp,[status(thm)],[1824]) ).
thf(2003,plain,
( sk1
| ( ( c_2Eextreal_2Eextreal__max_2E2 @ sk6 @ sk7 )
!= sk6 )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[1827]) ).
thf(2004,plain,
( sk1
| ( ( c_2Eextreal_2Eextreal__max_2E2 @ sk6 @ sk7 )
!= sk6 ) ),
inference(simp,[status(thm)],[2003]) ).
thf(61,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal,D: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ D ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__add_2E2 @ A @ C ) @ ( c_2Eextreal_2Eextreal__add_2E2 @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__add2) ).
thf(510,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal,D: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ D ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__add_2E2 @ A @ C ) @ ( c_2Eextreal_2Eextreal__add_2E2 @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(165,axiom,
! [TA: $tType,A: tyop_2Elist_2Elist @ TA,B: tyop_2Elist_2Elist @ TA] :
( ( p @ ( c_2EEncode_2Ebiprefix_2E2 @ TA @ A @ B ) )
=> ( p @ ( c_2EEncode_2Ebiprefix_2E2 @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EEncode_2Ebiprefix__sym) ).
thf(1294,plain,
! [TA: $tType,A: tyop_2Elist_2Elist @ TA,B: tyop_2Elist_2Elist @ TA] :
( ( p @ ( c_2EEncode_2Ebiprefix_2E2 @ TA @ A @ B ) )
=> ( p @ ( c_2EEncode_2Ebiprefix_2E2 @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(212,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( p @ B )
& ~ ( p @ A ) )
<=> ~ ( ( p @ B )
| ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er056) ).
thf(1661,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ~ ( p @ B )
& ~ ( p @ A ) )
=> ~ ( ( p @ B )
| ( p @ A ) ) )
& ( ~ ( ( p @ B )
| ( p @ A ) )
=> ( ~ ( p @ B )
& ~ ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(205,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__antisym) ).
thf(1614,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(111,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__min_2E2 @ B @ C ) @ A ) )
<=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) )
| ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Emin__le) ).
thf(832,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__min_2E2 @ B @ C ) @ A ) )
=> ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) )
| ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ A ) ) ) )
& ( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ A ) )
| ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ C @ A ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ ( c_2Eextreal_2Eextreal__min_2E2 @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(91,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ B )
<=> ~ ( p @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er008) ).
thf(684,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( ( ( p @ B )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( p @ B ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ~ ( ( ( p @ B )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(142,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ C ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__trans) ).
thf(1116,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ B ) )
& ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ B @ C ) ) )
=> ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(447,plain,
! [A: tyop_2Eextreal_2Eextreal] : ( p @ ( c_2Eextreal_2Eextreal__le_2E2 @ A @ A ) ),
inference(cnf,[status(esa)],[446]) ).
thf(45,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( B != A )
| ~ ( p @ B )
| ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed001) ).
thf(405,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( B != A )
| ~ ( p @ B )
| ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(146,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ C )
=> ( p @ B ) )
& ( ( p @ A )
=> ( p @ D ) ) )
=> ( ( ( p @ C )
& ( p @ A ) )
=> ( ( p @ B )
& ( p @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EMONO__AND) ).
thf(1148,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( ( p @ C )
=> ( p @ B ) )
& ( ( p @ A )
=> ( p @ D ) ) )
=> ( ( ( p @ C )
& ( p @ A ) )
=> ( ( p @ B )
& ( p @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(25,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__add_2E2 @ A @ B )
= ( c_2Eextreal_2Eextreal__add_2E2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Eadd__comm) ).
thf(315,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__add_2E2 @ A @ B )
= ( c_2Eextreal_2Eextreal__add_2E2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(71,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( p @ B )
& ~ ( p @ A ) )
<=> ~ ( ( p @ A )
| ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er060) ).
thf(564,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ~ ( p @ B )
& ~ ( p @ A ) )
=> ~ ( ( p @ A )
| ( p @ B ) ) )
& ( ~ ( ( p @ A )
| ( p @ B ) )
=> ( ~ ( p @ B )
& ~ ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(183,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( p @ B )
| ( p @ A )
| ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed009) ).
thf(1436,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( p @ B )
| ( p @ A )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(60,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( B != A )
| ( p @ B )
| ~ ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed002) ).
thf(506,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( B != A )
| ( p @ B )
| ~ ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(106,axiom,
! [TA: $tType,A: TA,B: tyop_2Enum_2Enum,C: TA] :
( ( p @ ( c_2Eind__type_2EINJA_2E3 @ TA @ A @ B @ C ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eind__type_2EINJA) ).
thf(807,plain,
! [TA: $tType,A: TA,B: tyop_2Enum_2Enum,C: TA] :
( ( ( p @ ( c_2Eind__type_2EINJA_2E3 @ TA @ A @ B @ C ) )
=> ( C = A ) )
& ( ( C = A )
=> ( p @ ( c_2Eind__type_2EINJA_2E3 @ TA @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(152,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
<=> ( p @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eboolext) ).
thf(1172,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( p @ B ) )
& ( ( p @ B )
=> ( p @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(15,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: TA] :
( ( c_2Ebool_2ECOND_2E3 @ TA @ A @ B @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EConseqConv_2ECOND__CLAUSES__ID) ).
thf(283,plain,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: TA] :
( ( c_2Ebool_2ECOND_2E3 @ TA @ A @ B @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(48,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
& ( p @ A ) )
<=> ~ ( ~ ( p @ A )
| ~ ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er057) ).
thf(415,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
& ( p @ A ) )
=> ~ ( ~ ( p @ A )
| ~ ( p @ B ) ) )
& ( ~ ( ~ ( p @ A )
| ~ ( p @ B ) )
=> ( ( p @ B )
& ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(238,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Egcd_2Eis__gcd_2E3 @ A @ B @ C )
= ( c_2Egcd_2Eis__gcd_2E3 @ B @ A @ C ) ),
inference(cnf,[status(esa)],[237]) ).
thf(239,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Egcd_2Eis__gcd_2E3 @ A @ B @ C )
= ( c_2Egcd_2Eis__gcd_2E3 @ B @ A @ C ) ),
inference(lifteq,[status(thm)],[238]) ).
thf(97,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ A )
=> ( p @ B ) )
<=> ( ( p @ A )
& ~ ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__IMP) ).
thf(740,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ~ ( ( p @ A )
=> ( p @ B ) )
=> ( ( p @ A )
& ~ ( p @ B ) ) )
& ( ( ( p @ A )
& ~ ( p @ B ) )
=> ~ ( ( p @ A )
=> ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(144,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( A = B )
& ( ~ ( p @ B )
=> ( C = D ) ) )
=> ( ( ( p @ A )
| ( p @ C ) )
<=> ( ( p @ B )
| ( p @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__OR__CONG) ).
thf(1129,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool,D: tyop_2Emin_2Ebool] :
( ( ( A = B )
& ( ~ ( p @ B )
=> ( C = D ) ) )
=> ( ( ( ( p @ A )
| ( p @ C ) )
=> ( ( p @ B )
| ( p @ D ) ) )
& ( ( ( p @ B )
| ( p @ D ) )
=> ( ( p @ A )
| ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(114,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ! [C: TA] :
( ( p @ A )
=> ( p @ B ) )
<=> ( ? [C: TA] : ( p @ A )
=> ! [C: TA] : ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EBOTH__FORALL__IMP__THM) ).
thf(860,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(128,axiom,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum,B: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum,C: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum] :
( ( ( p @ ( c_2Ebag_2EPSUB__BAG_2E2 @ TA @ A @ B ) )
& ( p @ ( c_2Ebag_2EPSUB__BAG_2E2 @ TA @ B @ C ) ) )
=> ( p @ ( c_2Ebag_2EPSUB__BAG_2E2 @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebag_2EPSUB__BAG__TRANS) ).
thf(992,plain,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum,B: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum,C: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum] :
( ( ( p @ ( c_2Ebag_2EPSUB__BAG_2E2 @ TA @ A @ B ) )
& ( p @ ( c_2Ebag_2EPSUB__BAG_2E2 @ TA @ B @ C ) ) )
=> ( p @ ( c_2Ebag_2EPSUB__BAG_2E2 @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(202,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
<=> ( ~ ( p @ B )
=> ~ ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EMONO__NOT__EQ) ).
thf(1597,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( p @ B ) )
=> ( ~ ( p @ B )
=> ~ ( p @ A ) ) )
& ( ( ~ ( p @ B )
=> ~ ( p @ A ) )
=> ( ( p @ A )
=> ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(13,axiom,
! [TA: $tType,A: TA,B: TA,C: tyop_2Emin_2Ebool] :
( ( p @ C )
| ( A
= ( c_2Ebool_2ECOND_2E3 @ TA @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed017) ).
thf(277,plain,
! [TA: $tType,A: TA,B: TA,C: tyop_2Emin_2Ebool] :
( ( p @ C )
| ( A
= ( c_2Ebool_2ECOND_2E3 @ TA @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(43,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
<=> ( ~ ( p @ A )
| ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__DISJ__THM) ).
thf(395,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( p @ B ) )
=> ( ~ ( p @ A )
| ( p @ B ) ) )
& ( ( ~ ( p @ A )
| ( p @ B ) )
=> ( ( p @ A )
=> ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(112,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
=> ( p @ A ) )
<=> ( ( p @ A )
| ~ ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er032) ).
thf(839,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
=> ( p @ A ) )
=> ( ( p @ A )
| ~ ( p @ B ) ) )
& ( ( ( p @ A )
| ~ ( p @ B ) )
=> ( ( p @ B )
=> ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(162,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
& ( p @ ( c_2Eint__arith_2Ebmarker_2E1 @ A ) ) )
<=> ( ( p @ ( c_2Eint__arith_2Ebmarker_2E1 @ A ) )
& ( p @ B ) ) )
& ( ( ( p @ B )
& ( p @ ( c_2Eint__arith_2Ebmarker_2E1 @ A ) )
& ( p @ C ) )
<=> ( ( p @ ( c_2Eint__arith_2Ebmarker_2E1 @ A ) )
& ( p @ B )
& ( p @ C ) ) )
& ( ( ( p @ ( c_2Eint__arith_2Ebmarker_2E1 @ A ) )
& ( p @ B )
& ( p @ C ) )
<=> ( ( p @ ( c_2Eint__arith_2Ebmarker_2E1 @ A ) )
& ( p @ B )
& ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2Ebmarker__rewrites) ).
thf(1261,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
& ( p @ ( c_2Eint__arith_2Ebmarker_2E1 @ A ) ) )
=> ( ( p @ ( c_2Eint__arith_2Ebmarker_2E1 @ A ) )
& ( p @ B ) ) )
& ( ( ( p @ ( c_2Eint__arith_2Ebmarker_2E1 @ A ) )
& ( p @ B ) )
=> ( ( p @ B )
& ( p @ ( c_2Eint__arith_2Ebmarker_2E1 @ A ) ) ) )
& ( ( ( p @ B )
& ( p @ ( c_2Eint__arith_2Ebmarker_2E1 @ A ) )
& ( p @ C ) )
=> ( ( p @ ( c_2Eint__arith_2Ebmarker_2E1 @ A ) )
& ( p @ B )
& ( p @ C ) ) )
& ( ( ( p @ ( c_2Eint__arith_2Ebmarker_2E1 @ A ) )
& ( p @ B )
& ( p @ C ) )
=> ( ( p @ B )
& ( p @ ( c_2Eint__arith_2Ebmarker_2E1 @ A ) )
& ( p @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(204,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B ) )
<=> ( ( p @ B )
& ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECONJ__COMM) ).
thf(1606,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ A )
& ( p @ B ) )
=> ( ( p @ B )
& ( p @ A ) ) )
& ( ( ( p @ B )
& ( p @ A ) )
=> ( ( p @ A )
& ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(170,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( p @ C )
<=> ( ( p @ B )
& ( p @ A ) ) )
<=> ( ( ( p @ C )
| ~ ( p @ B )
| ~ ( p @ A ) )
& ( ( p @ B )
| ~ ( p @ C ) )
& ( ( p @ A )
| ~ ( p @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__conj) ).
thf(1320,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool,C: tyop_2Emin_2Ebool] :
( ( ( ( ( p @ C )
=> ( ( p @ B )
& ( p @ A ) ) )
& ( ( ( p @ B )
& ( p @ A ) )
=> ( p @ C ) ) )
=> ( ( ( p @ C )
| ~ ( p @ B )
| ~ ( p @ A ) )
& ( ( p @ B )
| ~ ( p @ C ) )
& ( ( p @ A )
| ~ ( p @ C ) ) ) )
& ( ( ( ( p @ C )
| ~ ( p @ B )
| ~ ( p @ A ) )
& ( ( p @ B )
| ~ ( p @ C ) )
& ( ( p @ A )
| ~ ( p @ C ) ) )
=> ( ( ( p @ C )
=> ( ( p @ B )
& ( p @ A ) ) )
& ( ( ( p @ B )
& ( p @ A ) )
=> ( p @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(32,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( A = B )
| ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
| ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Elt__total) ).
thf(337,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( A = B )
| ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ A @ B ) )
| ( p @ ( c_2Eextreal_2Eextreal__lt_2E2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(131,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( A = B )
<=> ( ( ( p @ A )
& ( p @ B ) )
| ( ~ ( p @ A )
& ~ ( p @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__EXPAND) ).
thf(1009,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( A = B )
=> ( ( ( p @ A )
& ( p @ B ) )
| ( ~ ( p @ A )
& ~ ( p @ B ) ) ) )
& ( ( ( ( p @ A )
& ( p @ B ) )
| ( ~ ( p @ A )
& ~ ( p @ B ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(58,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( ( p @ A )
| ( p @ A ) )
<=> ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EConseqConv_2EOR__CLAUSES__XX) ).
thf(491,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(138,axiom,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ),B: TA,C: TA] :
( ( p @ ( c_2Erelation_2EEQC_2E3 @ TA @ A @ B @ C ) )
=> ( p @ ( c_2Erelation_2EEQC_2E3 @ TA @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erelation_2EEQC__SYM) ).
thf(1088,plain,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ ( tyop_2Emin_2Efun @ TA @ tyop_2Emin_2Ebool ),B: TA,C: TA] :
( ( p @ ( c_2Erelation_2EEQC_2E3 @ TA @ A @ B @ C ) )
=> ( p @ ( c_2Erelation_2EEQC_2E3 @ TA @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(53992,plain,
$false,
inference(cvc4,[status(thm)],[1586,760,518,468,234,1554,1686,582,1005,994,1401,308,449,878,861,385,797,814,913,340,1782,1650,1359,301,1228,389,1298,719,372,619,702,934,1545,638,1087,1319,1479,606,881,325,228,289,448,261,492,789,321,253,1828,514,574,1677,806,1183,475,924,1418,623,280,1447,1433,1564,527,312,292,233,512,1691,334,1387,1217,820,561,788,847,361,1624,583,461,1079,1281,1740,324,1296,665,1350,519,1234,1804,403,388,356,1118,1160,1361,537,901,1414,1584,1791,590,1155,706,328,256,393,1539,371,1627,311,921,541,1170,586,343,237,1318,1466,1071,412,1727,513,1698,1219,1483,264,423,732,286,1403,1503,1669,572,466,540,1090,236,979,831,1806,1048,230,1722,318,303,599,1877,631,1162,240,1029,1381,932,1556,769,912,1594,1213,306,438,241,1726,1250,675,2107,589,548,1420,927,255,1081,617,1181,1798,295,1225,1605,1647,1753,409,1484,673,331,1085,1679,1738,703,1536,1427,1797,446,1485,1506,1094,1140,1157,903,759,1781,1448,1108,250,231,1316,450,1289,368,1646,588,813,517,748,1481,258,652,1745,1822,1629,2004,235,510,1294,1440,1661,1614,832,684,1116,447,405,1148,315,1725,564,1436,506,807,1172,283,415,239,242,740,1129,860,992,1597,277,395,839,1827,1261,1606,1320,337,1009,309,232,491,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP021_7 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 14:32:11 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.94/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 8.03/3.26 % [INFO] Parsing done (2403ms).
% 8.03/3.28 % [INFO] Running in sequential loop mode.
% 8.46/3.47 % [INFO] eprover registered as external prover.
% 8.46/3.47 % [INFO] cvc4 registered as external prover.
% 8.46/3.47 % [INFO] Scanning for conjecture ...
% 13.94/4.87 % [INFO] Found a conjecture and 25708 axioms. Running axiom selection ...
% 16.30/5.68 % [INFO] Axiom selection finished. Selected 225 axioms (removed 25483 axioms).
% 16.78/5.81 % [INFO] Problem is typed first-order (TPTP TFF).
% 16.93/5.83 % [INFO] Type checking passed.
% 16.93/5.83 % [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 ...
% 93.23/25.82 % External prover 'cvc4' found a proof!
% 93.23/25.82 % [INFO] Killing All external provers ...
% 93.23/25.82 % Time passed: 25290ms (effective reasoning time: 22536ms)
% 93.23/25.82 % 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)>
% 93.23/25.82 % Axioms used in derivation (225): thm_2Ebool_2EDISJ__SYM, thm_2EConseqConv_2EIMP__CONG__conj__strengthen, thm_2Ebool_2ERIGHT__AND__OVER__OR, thm_2Estring_2Estring__lt__cases, thm_2Ebag_2EPSUB__BAG__NOT__EQ, thm_2Eextreal_2Eextreal__lt__def, thm_2Ebool_2ELEFT__AND__CONG, thm_2Ebool_2EOR__IMP__THM, thm_2EHolSmt_2Ed014, thm_2EConseqConv_2ENOT__CLAUSES__X, thm_2Eextreal_2Eeq__neg, thm_2Eextreal_2Elt__trans, thm_2EConseqConv_2EIMP__CONG__conj__weaken, thm_2EHolSmt_2EAND__IMP__INTRO__SYM, thm_2EHolSmt_2Ed009, thm_2Eextra_2Dho_2Eboolext, thm_2Ecardinal_2ECONJ__EQ__IMP, thm_2EHolSmt_2Ed004, thm_2Eextreal_2Ele__neg, thm_2EHolSmt_2Ed020, thm_2Epath_2EfirstP__at__unique, thm_2Ebool_2EBOTH__FORALL__OR__THM, thm_2Esat_2Edc__conj, thm_2EquantHeuristics_2ERIGHT__IMP__AND__INTRO, thm_2Eextreal_2Ele__min, thm_2EHolSmt_2Ed013, thm_2EHolSmt_2Er031, thm_2Eextreal_2Elt__neg, thm_2Eextreal_2Emin__le2__imp, thm_2EHolSmt_2EIMP__DISJ__1, thm_2Ebool_2EBOTH__FORALL__IMP__THM, thm_2Ebool_2EDISJ__COMM, thm_2EHolSmt_2Er023, thm_2EHolSmt_2Ed008, thm_2Ebool_2EPEIRCE, thm_2Egcd_2EIS__GCD__UNIQUE, thm_2Ebool_2EEQ__IMP__THM, thm_2EHolSmt_2ENNF__NOT__NOT, thm_2Eextreal_2Ele__max1, thm_2Eextreal_2Eextreal__sub__add, thm_2Equotient_2EEQ__IMPLIES, thm_2Eprim__rec_2ESIMP__REC__EXISTS, thm_2Ebool_2EIMP__ANTISYM__AX, thm_2Ebool_2EIMP__CONG, thm_2Esptree_2Esubspt__refl, thm_2Eextreal_2Emin__le1, thm_2EHolSmt_2Ed018, thm_2Epred__set_2EUNIV__applied, thm_2Eblast_2Ebcarry__def, thm_2Eblast_2Ebsum__def, thm_2EConseqConv_2EIMP__CONG__disj__weaken, thm_2Ebool_2ECONJ__ASSOC, thm_2EHolSmt_2Er056, thm_2Eextreal_2Elt__sub__imp, thm_2Ebool_2EMONO__OR, thm_2Efinite__map_2Efmap__EQ__UPTO______EQ, thm_2Esat_2Edc__eq, thm_2Ebool_2EMONO__AND, thm_2Eextreal_2Ele__max2, thm_2Ebool_2EMONO__NOT, thm_2EHolSmt_2Ed017, thm_2Eextreal_2Ele__max, thm_2Eextreal_2Ele__refl, thm_2Eextreal_2Ele__trans, thm_2EHolSmt_2Er030, thm_2EHolSmt_2ENEG__IFF__2__1, thm_2Esat_2Epth__no1, thm_2Erelation_2EEQC__TRANS, thm_2EHolSmt_2Er060, thm_2Esat_2Edc__imp, thm_2EConseqConv_2EIMP__CONG__simple__imp__weaken, thm_2Eextreal_2Eadd__comm, thm_2Eextreal_2Elte__trans, thm_2EHolSmt_2Er053, thm_2Ebool_2EOR__DEF, thm_2Eextreal_2Ele__ladd__imp, thm_2Ebool_2ELEFT__AND__OVER__OR, thm_2Eextreal_2Emin__refl, thm_2EHolSmt_2Ed005, thm_2EHolSmt_2Er041, thm_2Esat_2Epth__ni1, thm_2Esat_2Epth__an1, thm_2Ebool_2ERIGHT__OR__OVER__AND, thm_2EConseqConv_2EIMP__CONG__imp__weaken, thm_2Eextreal_2Emin__le, thm_2Eextreal_2Emin__le2, thm_2Ebool_2Ebool__case__CONG, thm_2Eextreal_2Eabs__bounds, thm_2Ebool_2EOR__CONG, thm_2EHolSmt_2EIMP__DISJ__2, thm_2EHolSmt_2Ed011, thm_2Esat_2Epth__no2, thm_2Eextreal_2Elt__antisym, thm_2EHolSmt_2Er057, thm_2Estring_2Estring__lt__trans, thm_2Erelation_2EEQC__SYM, thm_2Emarker_2EAC__DEF, thm_2EHolSmt_2Er007, thm_2Ebool_2EOR__INTRO__THM2, thm_2Egcd_2EIS__GCD__REF, thm_2Esat_2Edc__neg, thm_2Esptree_2Esubspt__trans, thm_2EConseqConv_2ECOND__CLAUSES__ID, thm_2Ebool_2ECOND__CONG, thm_2EquantHeuristics_2ERIGHT__IMP__OR__INTRO, thm_2Ebag_2EPSUB__BAG__IRREFL, thm_2Ebool_2EAND__IMP__INTRO, thm_2EquantHeuristics_2ELEFT__IMP__AND__INTRO, thm_2EHolSmt_2Ed016, thm_2EquantHeuristics_2ELEFT__IMP__OR__INTRO, thm_2Ebool_2EAND__CONG, thm_2Ebool_2EEQ__EXPAND, thm_2Eextreal_2Elt__add2, thm_2Ebool_2ENOT__AND, thm_2EHolSmt_2Er058, thm_2Eextreal_2Eneg__neg, thm_2Ebool_2ECOND__ID, thm_2Eextreal_2Ele__lt, thm_2EEncode_2Ebiprefix__refl, thm_2Ebool_2EMONO__NOT__EQ, thm_2EHolSmt_2Er029, thm_2Eextreal_2Elt__le, thm_2Ebool_2EDISJ__EQ__IMP, thm_2Ebool_2EAND2__THM, thm_2Ebool_2EIMP__CONJ__THM, thm_2EConseqConv_2EIMP__CONG__disj__strengthen, thm_2Erich__list_2EIS__SUFFIX__REFL, thm_2EHolSmt_2Er008, thm_2Eextreal_2Ele__radd__imp, thm_2Esorting_2EPERM__SINGLE__SWAP__SYM, thm_2Ebool_2EEXCLUDED__MIDDLE, thm_2EConseqConv_2EIMP__CONG__imp__strengthen, thm_2Ebool_2EDISJ__ASSOC, thm_2Ebool_2EBOTH__EXISTS__IMP__THM, thm_2Egcd_2EIS__GCD__SYM, thm_2Erelation_2EEQC__REFL, thm_2Ebool_2EAND1__THM, thm_2Ebool_2EMONO__IMP, thm_2Ebool_2EDE__MORGAN__THM, thm_2Esat_2Epth__ni2, thm_2Eextreal_2Eadd__assoc, thm_2Ebool_2EOR__INTRO__THM1, thm_2Ecardinal_2ECONJ__ACI, thm_2EHolSmt_2Ed010, thm_2Equotient_2ECONJ__IMPLIES, thm_2Ebool_2ECONJ__COMM, thm_2Ebool_2EBOTH__EXISTS__AND__THM, thm_2EHolSmt_2Ed006, thm_2Ebool_2ENOT__IMP, thm_2Ebool_2Ebool__case__ID, thm_2Eextreal_2Eabs__bounds__lt, thm_2Esat_2ENOT__NOT, thm_2EHolSmt_2ENEG__IFF__2__2, thm_2Emergesort_2Estable__trans, thm_2Ebool_2EDISJ__IMP__THM, thm_2EHolSmt_2ENEG__IFF__1__1, thm_2Ebool_2EFORALL__SIMP, thm_2EHolSmt_2Er040, thm_2Esorting_2EPERM__SINGLE__SWAP__REFL, thm_2Eextreal_2Ele__total, thm_2EHolSmt_2Ed001, thm_2EConseqConv_2EOR__CLAUSES__XX, thm_2Ebool_2ELEFT__OR__OVER__AND, thm_2EHolSmt_2EDISJ__ELIM__2, thm_2Eextreal_2Elt__imp__le, thm_2Ebool_2EIMP__DISJ__THM, thm_2Elbtree_2Emmindex__unique, thm_2Eextreal_2Elt__imp__ne, thm_2Eextreal_2Elt__refl, thm_2Equotient_2EIMP__IMPLIES, thm_2EHolSmt_2Ed015, thm_2Estring_2Estring__lt__nonrefl, thm_2Eextreal_2Elt__total, thm_2EConseqConv_2EIMP__CONG__simple__imp__strengthen, thm_2EHolSmt_2Er009, thm_2EHolSmt_2Ed012, thm_2EHolSmt_2Er048, thm_2EHolSmt_2ENNF__CONJ, thm_2Esat_2Epth__nn, thm_2EHolSmt_2Er037, thm_2Ebool_2EEXISTS__SIMP, thm_2Ebool_2EAND__DEF, thm_2Ebool_2EAND__INTRO__THM, thm_2Eextreal_2Ele__antisym, thm_2Eind__type_2EINJN, thm_2EHolSmt_2ENOT__NOT__ELIM, thm_2EHolSmt_2ECONJ__CONG, thm_2EHolSmt_2Ed003, thm_2Eextreal_2Eextreal__max__def, thm_2Equotient_2EDISJ__IMPLIES, thm_2Eind__type_2EINJA, thm_2Esat_2EAND__IMP, thm_2EHolSmt_2EDISJ__ELIM__1, thm_2EHolSmt_2Exor__def, thm_2Eextreal_2Elet__trans, thm_2Esat_2Epth__an2, thm_2Ebool_2EOR__ELIM__THM, thm_2EHolSmt_2ENNF__DISJ, thm_2EEncode_2Ebiprefix__sym, thm_2EHolSmt_2Er054, thm_2Eint__arith_2Ebmarker__def, thm_2Equotient_2ENOT__IMPLIES, thm_2EquantHeuristics_2ECONJ__NOT__OR__THM, thm_2Ebag_2EPSUB__BAG__TRANS, thm_2EHolSmt_2Er059, thm_2Ebag_2EPSUB__BAG__ANTISYM, thm_2Eextreal_2Esub__rneg, thm_2EHolSmt_2Ed007, thm_2Eextreal_2Ele__add2, thm_2Esat_2Edc__disj, thm_2EHolSmt_2Ed019, thm_2Ebool_2ECONJ__SYM, thm_2EHolSmt_2Ed002, thm_2Eextreal_2Eextreal__min__def, thm_2EHolSmt_2Er032, thm_2Eextreal_2Ele__lsub__imp, thm_2Ecardinal_2EIMP__CONJ__ALT, thm_2Ebool_2ELEFT__OR__CONG, thm_2Eextreal_2Emin__comm, thm_2EHolSmt_2ENEG__IFF__1__2, thm_2Eint__arith_2Ebmarker__rewrites, thm_2Eextreal_2Ele__sub__imp, thm_2EConseqConv_2EAND__CLAUSES__XX, thm_2EHolSmt_2Er055, thm_2Estring_2Estring__lt__antisym
% 93.23/25.82 % No. of inferences in proof: 520
% 93.23/25.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 25290 ms resp. 22536 ms w/o parsing
% 93.23/25.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 93.23/25.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------