TSTP Solution File: ITP012_7 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP012_7 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 07:46:48 EDT 2024
% Result : Theorem 19.42s 5.85s
% Output : Refutation 19.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 207
% Syntax : Number of formulae : 381 ( 108 unt; 35 typ; 0 def)
% Number of atoms : 1555 ( 179 equ; 0 cnn)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 4103 ( 176 ~; 202 |; 355 &;2718 @)
% ( 73 <=>; 579 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 35 usr; 10 con; 0-5 aty)
% Number of variables : 966 ( 0 ^ 933 !; 12 ?; 966 :)
% ( 21 !>; 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_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_2EquantHeuristics_2ESIMPLE__GUESS__FORALL_2E3_type,type,
c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL_2E3:
!>[TA: $tType] : ( TA > TA > tyop_2Emin_2Ebool > 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_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3_type,type,
c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3:
!>[TA: $tType,TB: $tType] : ( TB > ( tyop_2Elist_2Elist @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Eoption_2Eoption @ TA ) ) ) > ( tyop_2Elist_2Elist @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Eoption_2Eoption @ 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_2Ellist_2ELPREFIX_2E2_type,type,
c_2Ellist_2ELPREFIX_2E2:
!>[TA: $tType] : ( ( tyop_2Ellist_2Ellist @ TA ) > ( tyop_2Ellist_2Ellist @ TA ) > 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_2Ewellorder_2Eorderlt_2E2_type,type,
c_2Ewellorder_2Eorderlt_2E2:
!>[TA: $tType,TB: $tType] : ( ( tyop_2Ewellorder_2Ewellorder @ TB ) > ( tyop_2Ewellorder_2Ewellorder @ TA ) > 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(c_2Einteger_2Eint__add_2E2_type,type,
c_2Einteger_2Eint__add_2E2: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__divides_2E2_type,type,
c_2Einteger_2Eint__divides_2E2: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Emin_2Ebool ).
thf(c_2Einteger_2Eint__mul_2E2_type,type,
c_2Einteger_2Eint__mul_2E2: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__neg_2E1_type,type,
c_2Einteger_2Eint__neg_2E1: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__sub_2E2_type,type,
c_2Einteger_2Eint__sub_2E2: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Etint__lt_2E2_type,type,
c_2Einteger_2Etint__lt_2E2: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
thf(125,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/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__disj) ).
thf(892,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)],[125]) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EBOTH__EXISTS__IMP__THM) ).
thf(629,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(108,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/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__imp__weaken) ).
thf(760,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)],[108]) ).
thf(139,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EAND__IMP__INTRO) ).
thf(1031,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)],[139]) ).
thf(18,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__neg_2E1 @ A )
= B )
<=> ( A
= ( c_2Einteger_2Eint__neg_2E1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__EQ) ).
thf(234,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( ( c_2Einteger_2Eint__neg_2E1 @ A )
= B )
=> ( A
= ( c_2Einteger_2Eint__neg_2E1 @ B ) ) )
& ( ( A
= ( c_2Einteger_2Eint__neg_2E1 @ B ) )
=> ( ( c_2Einteger_2Eint__neg_2E1 @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(130,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
=> ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__mul_2E2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RMUL) ).
thf(941,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
=> ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__mul_2E2 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(71,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
=> ( ( ( p @ B )
=> ( p @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__ANTISYM__AX) ).
thf(481,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)],[71]) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__imp) ).
thf(1083,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)],[147]) ).
thf(66,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( p @ A )
| ~ ( p @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEXCLUDED__MIDDLE) ).
thf(468,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(51,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( ( p @ A )
| ( p @ A ) )
<=> ( p @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EOR__CLAUSES__XX) ).
thf(408,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(14,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add_2E2 @ A @ C )
= ( c_2Einteger_2Eint__add_2E2 @ B @ C ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__RADD) ).
thf(217,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( ( c_2Einteger_2Eint__add_2E2 @ A @ C )
= ( c_2Einteger_2Eint__add_2E2 @ B @ C ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( c_2Einteger_2Eint__add_2E2 @ A @ C )
= ( c_2Einteger_2Eint__add_2E2 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(46,axiom,
! [A: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,B: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,C: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
( ( ( p @ ( c_2Einteger_2Etint__lt_2E2 @ A @ B ) )
& ( p @ ( c_2Einteger_2Etint__lt_2E2 @ B @ C ) ) )
=> ( p @ ( c_2Einteger_2Etint__lt_2E2 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ETINT__LT__TRANS) ).
thf(379,plain,
! [A: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,B: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum,C: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
( ( ( p @ ( c_2Einteger_2Etint__lt_2E2 @ A @ B ) )
& ( p @ ( c_2Einteger_2Etint__lt_2E2 @ B @ C ) ) )
=> ( p @ ( c_2Einteger_2Etint__lt_2E2 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(92,axiom,
! [A: tyop_2Emin_2Ebool] :
( ~ ~ ( p @ A )
<=> ( p @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2ENOT__NOT) ).
thf(614,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(87,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EBOTH__EXISTS__AND__THM) ).
thf(597,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__simple__imp__strengthen) ).
thf(1205,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)],[165]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__UNIQUE) ).
thf(449,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)],[61]) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EMONO__OR) ).
thf(385,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)],[49]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: tyop_2Ewellorder_2Ewellorder @ TC,B: tyop_2Ewellorder_2Ewellorder @ TB,C: tyop_2Ewellorder_2Ewellorder @ TA] :
( ( ( p @ ( c_2Ewellorder_2Eorderlt_2E2 @ TC @ TB @ A @ B ) )
& ( p @ ( c_2Ewellorder_2Eorderlt_2E2 @ TB @ TA @ B @ C ) ) )
=> ( p @ ( c_2Ewellorder_2Eorderlt_2E2 @ TC @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewellorder_2Eorderlt__TRANS) ).
thf(533,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: tyop_2Ewellorder_2Ewellorder @ TC,B: tyop_2Ewellorder_2Ewellorder @ TB,C: tyop_2Ewellorder_2Ewellorder @ TA] :
( ( ( p @ ( c_2Ewellorder_2Eorderlt_2E2 @ TC @ TB @ A @ B ) )
& ( p @ ( c_2Ewellorder_2Eorderlt_2E2 @ TB @ TA @ B @ C ) ) )
=> ( p @ ( c_2Ewellorder_2Eorderlt_2E2 @ TC @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(157,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
& ( p @ A ) )
=> ( p @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Epth__an1) ).
thf(1164,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
& ( p @ A ) )
=> ( p @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(112,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ A )
=> ( ( p @ B )
=> ( ( p @ A )
& ( p @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EAND__INTRO__THM) ).
thf(814,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)],[112]) ).
thf(42,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EOR__DEF) ).
thf(340,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)],[42]) ).
thf(1,conjecture,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
=> ( ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__sub_2E2 @ C @ B ) )
= ( c_2Einteger_2Eint__divides_2E2 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RSUB) ).
thf(2,negated_conjecture,
~ ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
=> ( ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__sub_2E2 @ C @ B ) )
= ( c_2Einteger_2Eint__divides_2E2 @ A @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(174,plain,
~ ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
=> ( ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__sub_2E2 @ C @ B ) )
= ( c_2Einteger_2Eint__divides_2E2 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(161,axiom,
! [TA: $tType,TB: $tType,A: TB,B: tyop_2Elist_2Elist @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Eoption_2Eoption @ TA ) )] : ( p @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3 @ TB @ TA @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__is__equiv__1) ).
thf(1196,plain,
! [TA: $tType,TB: $tType,A: TB,B: tyop_2Elist_2Elist @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Eoption_2Eoption @ TA ) )] : ( p @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3 @ TB @ TA @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(5,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ C @ ( c_2Einteger_2Eint__add_2E2 @ B @ A ) )
= ( c_2Einteger_2Eint__add_2E2 @ ( c_2Einteger_2Eint__mul_2E2 @ C @ B ) @ ( c_2Einteger_2Eint__mul_2E2 @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LDISTRIB) ).
thf(185,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ C @ ( c_2Einteger_2Eint__add_2E2 @ B @ A ) )
= ( c_2Einteger_2Eint__add_2E2 @ ( c_2Einteger_2Eint__mul_2E2 @ C @ B ) @ ( c_2Einteger_2Eint__mul_2E2 @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(135,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
<=> ( ( p @ B )
| ( p @ A ) ) )
<=> ( ( p @ B )
=> ( p @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EOR__IMP__THM) ).
thf(973,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)],[135]) ).
thf(31,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__sub_2E2 @ A @ B )
= C )
<=> ( A
= ( c_2Einteger_2Eint__add_2E2 @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__SUB__RADD) ).
thf(288,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( ( c_2Einteger_2Eint__sub_2E2 @ A @ B )
= C )
=> ( A
= ( c_2Einteger_2Eint__add_2E2 @ C @ B ) ) )
& ( ( A
= ( c_2Einteger_2Eint__add_2E2 @ C @ B ) )
=> ( ( c_2Einteger_2Eint__sub_2E2 @ A @ B )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(173,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/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__conj__strengthen) ).
thf(1265,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)],[173]) ).
thf(142,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/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ESIMP__REC__EXISTS) ).
thf(1055,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)],[142]) ).
thf(172,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool] :
( ! [B: TA] : ( p @ A )
<=> ( p @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EFORALL__SIMP) ).
thf(1264,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(144,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub_2E2 @ A @ ( c_2Einteger_2Eint__sub_2E2 @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__SUB2) ).
thf(1059,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub_2E2 @ A @ ( c_2Einteger_2Eint__sub_2E2 @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(132,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/sandbox/benchmark/theBenchmark.p',thm_2EEncode_2Ebiprefix__sym) ).
thf(949,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)],[132]) ).
thf(134,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
=> ( ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__sub_2E2 @ B @ C ) )
= ( c_2Einteger_2Eint__divides_2E2 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__LSUB) ).
thf(969,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
=> ( ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__sub_2E2 @ B @ C ) )
= ( c_2Einteger_2Eint__divides_2E2 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(55,axiom,
! [A: tyop_2Einteger_2Eint] : ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__REFL) ).
thf(416,plain,
! [A: tyop_2Einteger_2Eint] : ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',thm_2Esorting_2EPERM__SINGLE__SWAP__SYM) ).
thf(228,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)],[16]) ).
thf(3,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg_2E1 @ ( c_2Einteger_2Eint__mul_2E2 @ A @ B ) )
= ( c_2Einteger_2Eint__mul_2E2 @ A @ ( c_2Einteger_2Eint__neg_2E1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__RMUL) ).
thf(179,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg_2E1 @ ( c_2Einteger_2Eint__mul_2E2 @ A @ B ) )
= ( c_2Einteger_2Eint__mul_2E2 @ A @ ( c_2Einteger_2Eint__neg_2E1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EOR__CONG) ).
thf(1183,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)],[159]) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EEQC__SYM) ).
thf(821,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)],[114]) ).
thf(12,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub_2E2 @ ( c_2Einteger_2Eint__add_2E2 @ A @ B ) @ ( c_2Einteger_2Eint__add_2E2 @ C @ D ) )
= ( c_2Einteger_2Eint__add_2E2 @ ( c_2Einteger_2Eint__sub_2E2 @ A @ C ) @ ( c_2Einteger_2Eint__sub_2E2 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD2__SUB2) ).
thf(211,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub_2E2 @ ( c_2Einteger_2Eint__add_2E2 @ A @ B ) @ ( c_2Einteger_2Eint__add_2E2 @ C @ D ) )
= ( c_2Einteger_2Eint__add_2E2 @ ( c_2Einteger_2Eint__sub_2E2 @ A @ C ) @ ( c_2Einteger_2Eint__sub_2E2 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EBOTH__FORALL__IMP__THM) ).
thf(646,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(21,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ ( c_2Einteger_2Eint__add_2E2 @ A @ B ) @ C )
= ( c_2Einteger_2Eint__add_2E2 @ ( c_2Einteger_2Eint__mul_2E2 @ A @ C ) @ ( c_2Einteger_2Eint__mul_2E2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__RDISTRIB) ).
thf(253,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ ( c_2Einteger_2Eint__add_2E2 @ A @ B ) @ C )
= ( c_2Einteger_2Eint__add_2E2 @ ( c_2Einteger_2Eint__mul_2E2 @ A @ C ) @ ( c_2Einteger_2Eint__mul_2E2 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(102,axiom,
! [TA: $tType,A: tyop_2Emin_2Efun @ TA @ tyop_2Enum_2Enum] :
~ ( p @ ( c_2Ebag_2EPSUB__BAG_2E2 @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebag_2EPSUB__BAG__IRREFL) ).
thf(687,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)],[102]) ).
thf(121,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
| ( p @ B ) )
<=> ( ( p @ B )
| ( p @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EDISJ__SYM) ).
thf(866,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)],[121]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',thm_2Estring_2Estring__lt__antisym) ).
thf(411,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)],[53]) ).
thf(58,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/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__simple__imp__weaken) ).
thf(428,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)],[58]) ).
thf(25,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ B @ A )
= ( c_2Einteger_2Eint__mul_2E2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__COMM) ).
thf(265,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ B @ A )
= ( c_2Einteger_2Eint__mul_2E2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(62,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__mul_2E2 @ A @ B ) ) )
& ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__mul_2E2 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__MUL) ).
thf(452,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__mul_2E2 @ A @ B ) ) )
& ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__mul_2E2 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(76,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/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__conj__weaken) ).
thf(512,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)],[76]) ).
thf(78,axiom,
! [TA: $tType,A: tyop_2Emin_2Ebool] :
( ? [B: TA] : ( p @ A )
<=> ( p @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEXISTS__SIMP) ).
thf(529,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(163,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ B )
| ( p @ A ) )
=> ~ ( p @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Epth__no2) ).
thf(1199,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ B )
| ( p @ A ) )
=> ~ ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(47,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/sandbox/benchmark/theBenchmark.p',thm_2Ebag_2EPSUB__BAG__ANTISYM) ).
thf(381,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)],[47]) ).
thf(143,axiom,
! [TA: $tType,A: TA] : ( p @ ( c_2Epred__set_2EUNIV_2E1 @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EUNIV__applied) ).
thf(1057,plain,
! [TA: $tType,A: TA] : ( p @ ( c_2Epred__set_2EUNIV_2E1 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(169,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/sandbox/benchmark/theBenchmark.p',thm_2Ecardinal_2ECONJ__EQ__IMP) ).
thf(1223,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)],[169]) ).
thf(140,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/sandbox/benchmark/theBenchmark.p',thm_2Equotient_2EIMP__IMPLIES) ).
thf(1042,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)],[140]) ).
thf(34,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub_2E2 @ ( c_2Einteger_2Eint__add_2E2 @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__SUB) ).
thf(302,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub_2E2 @ ( c_2Einteger_2Eint__add_2E2 @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(88,axiom,
! [A: tyop_2Emin_2Ebool] :
( ~ ~ ( p @ A )
<=> ( p @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ENOT__CLAUSES__X) ).
thf(598,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EDE__MORGAN__THM) ).
thf(392,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)],[50]) ).
thf(96,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub_2E2 @ ( c_2Einteger_2Eint__neg_2E1 @ A ) @ ( c_2Einteger_2Eint__neg_2E1 @ B ) )
= ( c_2Einteger_2Eint__sub_2E2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__NEG2) ).
thf(630,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub_2E2 @ ( c_2Einteger_2Eint__neg_2E1 @ A ) @ ( c_2Einteger_2Eint__neg_2E1 @ B ) )
= ( c_2Einteger_2Eint__sub_2E2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(9,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__neg_2E1 @ A )
= ( c_2Einteger_2Eint__neg_2E1 @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__NEG) ).
thf(197,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( ( c_2Einteger_2Eint__neg_2E1 @ A )
= ( c_2Einteger_2Eint__neg_2E1 @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( c_2Einteger_2Eint__neg_2E1 @ A )
= ( c_2Einteger_2Eint__neg_2E1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(40,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
<=> ( ~ ( p @ A )
| ( p @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__DISJ__THM) ).
thf(329,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)],[40]) ).
thf(85,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ ( c_2Einteger_2Eint__sub_2E2 @ A @ B ) @ C )
= ( c_2Einteger_2Eint__sub_2E2 @ ( c_2Einteger_2Eint__mul_2E2 @ A @ C ) @ ( c_2Einteger_2Eint__mul_2E2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__RDISTRIB) ).
thf(583,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ ( c_2Einteger_2Eint__sub_2E2 @ A @ B ) @ C )
= ( c_2Einteger_2Eint__sub_2E2 @ ( c_2Einteger_2Eint__mul_2E2 @ A @ C ) @ ( c_2Einteger_2Eint__mul_2E2 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(65,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__neg_2E1 @ B ) )
= ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
& ( ( c_2Einteger_2Eint__divides_2E2 @ ( c_2Einteger_2Eint__neg_2E1 @ A ) @ B )
= ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__NEG) ).
thf(461,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__neg_2E1 @ B ) )
= ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
& ( ( c_2Einteger_2Eint__divides_2E2 @ ( c_2Einteger_2Eint__neg_2E1 @ A ) @ B )
= ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(30,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add_2E2 @ ( c_2Einteger_2Eint__sub_2E2 @ A @ B ) @ ( c_2Einteger_2Eint__sub_2E2 @ B @ C ) )
= ( c_2Einteger_2Eint__sub_2E2 @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__TRIANGLE) ).
thf(285,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add_2E2 @ ( c_2Einteger_2Eint__sub_2E2 @ A @ B ) @ ( c_2Einteger_2Eint__sub_2E2 @ B @ C ) )
= ( c_2Einteger_2Eint__sub_2E2 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(122,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/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EEQC__TRANS) ).
thf(874,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)],[122]) ).
thf(93,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CONG) ).
thf(615,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)],[93]) ).
thf(6,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg_2E1 @ ( c_2Einteger_2Eint__mul_2E2 @ A @ B ) )
= ( c_2Einteger_2Eint__mul_2E2 @ ( c_2Einteger_2Eint__neg_2E1 @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__LMUL) ).
thf(188,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg_2E1 @ ( c_2Einteger_2Eint__mul_2E2 @ A @ B ) )
= ( c_2Einteger_2Eint__mul_2E2 @ ( c_2Einteger_2Eint__neg_2E1 @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(151,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ B )
| ( p @ A ) )
=> ~ ( p @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Epth__no1) ).
thf(1138,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ B )
| ( p @ A ) )
=> ~ ( p @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(104,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/sandbox/benchmark/theBenchmark.p',thm_2Estring_2Estring__lt__cases) ).
thf(697,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)],[104]) ).
thf(170,axiom,
! [A: tyop_2Enum_2Enum] : ( p @ ( c_2Egcd_2Eis__gcd_2E3 @ A @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__REF) ).
thf(1234,plain,
! [A: tyop_2Enum_2Enum] : ( p @ ( c_2Egcd_2Eis__gcd_2E3 @ A @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(57,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
| ( p @ B ) )
<=> ( ( p @ B )
| ( p @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EDISJ__COMM) ).
thf(420,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)],[57]) ).
thf(150,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
<=> ~ ( p @ A ) )
<=> ( ( ( p @ B )
| ( p @ A ) )
& ( ~ ( p @ A )
| ~ ( p @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__neg) ).
thf(1118,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)],[150]) ).
thf(156,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
=> ( ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__add_2E2 @ B @ C ) )
= ( c_2Einteger_2Eint__divides_2E2 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__LADD) ).
thf(1160,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
=> ( ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__add_2E2 @ B @ C ) )
= ( c_2Einteger_2Eint__divides_2E2 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(15,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub_2E2 @ A @ B )
= ( c_2Einteger_2Eint__add_2E2 @ A @ ( c_2Einteger_2Eint__neg_2E1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2Eint__sub) ).
thf(225,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub_2E2 @ A @ B )
= ( c_2Einteger_2Eint__add_2E2 @ A @ ( c_2Einteger_2Eint__neg_2E1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__disj__weaken) ).
thf(554,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)],[82]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',thm_2Equotient_2EDISJ__IMPLIES) ).
thf(1214,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)],[167]) ).
thf(68,axiom,
! [TA: $tType,A: tyop_2Ellist_2Ellist @ TA] : ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ellist_2ELPREFIX__REFL) ).
thf(471,plain,
! [TA: $tType,A: tyop_2Ellist_2Ellist @ TA] : ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(22,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg_2E1 @ ( c_2Einteger_2Eint__add_2E2 @ A @ B ) )
= ( c_2Einteger_2Eint__add_2E2 @ ( c_2Einteger_2Eint__neg_2E1 @ A ) @ ( c_2Einteger_2Eint__neg_2E1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__ADD) ).
thf(256,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg_2E1 @ ( c_2Einteger_2Eint__add_2E2 @ A @ B ) )
= ( c_2Einteger_2Eint__add_2E2 @ ( c_2Einteger_2Eint__neg_2E1 @ A ) @ ( c_2Einteger_2Eint__neg_2E1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__OR__CONG) ).
thf(837,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)],[117]) ).
thf(99,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__AND__OVER__OR) ).
thf(647,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)],[99]) ).
thf(63,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B ) )
=> ( p @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EAND2__THM) ).
thf(457,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B ) )
=> ( p @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(74,axiom,
! [TA: $tType,A: tyop_2Ellist_2Ellist @ TA,B: tyop_2Ellist_2Ellist @ TA,C: tyop_2Ellist_2Ellist @ TA] :
( ( ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ C @ B ) )
& ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ B @ A ) ) )
=> ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ellist_2ELPREFIX__TRANS) ).
thf(503,plain,
! [TA: $tType,A: tyop_2Ellist_2Ellist @ TA,B: tyop_2Ellist_2Ellist @ TA,C: tyop_2Ellist_2Ellist @ TA] :
( ( ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ C @ B ) )
& ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ B @ A ) ) )
=> ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(164,axiom,
! [TA: $tType,A: tyop_2Ellist_2Ellist @ TA,B: tyop_2Ellist_2Ellist @ TA] :
( ( ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ B @ A ) )
& ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ A @ B ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ellist_2ELPREFIX__ANTISYM) ).
thf(1202,plain,
! [TA: $tType,A: tyop_2Ellist_2Ellist @ TA,B: tyop_2Ellist_2Ellist @ TA] :
( ( ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ B @ A ) )
& ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ A @ B ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(97,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EAND__DEF) ).
thf(633,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)],[97]) ).
thf(10,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add_2E2 @ B @ A )
= ( c_2Einteger_2Eint__add_2E2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__SYM) ).
thf(205,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add_2E2 @ B @ A )
= ( c_2Einteger_2Eint__add_2E2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(79,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ A @ ( c_2Einteger_2Eint__sub_2E2 @ B @ C ) )
= ( c_2Einteger_2Eint__sub_2E2 @ ( c_2Einteger_2Eint__mul_2E2 @ A @ B ) @ ( c_2Einteger_2Eint__mul_2E2 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LDISTRIB) ).
thf(530,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ A @ ( c_2Einteger_2Eint__sub_2E2 @ B @ C ) )
= ( c_2Einteger_2Eint__sub_2E2 @ ( c_2Einteger_2Eint__mul_2E2 @ A @ B ) @ ( c_2Einteger_2Eint__mul_2E2 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',thm_2Ecardinal_2EIMP__CONJ__ALT) ).
thf(586,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)],[86]) ).
thf(127,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/sandbox/benchmark/theBenchmark.p',thm_2Epath_2EfirstP__at__unique) ).
thf(926,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)],[127]) ).
thf(119,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EMONO__AND) ).
thf(856,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)],[119]) ).
thf(106,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/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__imp__strengthen) ).
thf(745,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)],[106]) ).
thf(28,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add_2E2 @ B @ A )
= ( c_2Einteger_2Eint__add_2E2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__COMM) ).
thf(279,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add_2E2 @ B @ A )
= ( c_2Einteger_2Eint__add_2E2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(103,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
| ( p @ B ) )
<=> ( ~ ( p @ A )
=> ( p @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EDISJ__EQ__IMP) ).
thf(689,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)],[103]) ).
thf(32,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add_2E2 @ C @ ( c_2Einteger_2Eint__add_2E2 @ B @ A ) )
= ( c_2Einteger_2Eint__add_2E2 @ ( c_2Einteger_2Eint__add_2E2 @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__ASSOC) ).
thf(296,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add_2E2 @ C @ ( c_2Einteger_2Eint__add_2E2 @ B @ A ) )
= ( c_2Einteger_2Eint__add_2E2 @ ( c_2Einteger_2Eint__add_2E2 @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(7,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub_2E2 @ A @ ( c_2Einteger_2Eint__neg_2E1 @ B ) )
= ( c_2Einteger_2Eint__add_2E2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__RNEG) ).
thf(191,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub_2E2 @ A @ ( c_2Einteger_2Eint__neg_2E1 @ B ) )
= ( c_2Einteger_2Eint__add_2E2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(116,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EAND__CONG) ).
thf(826,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)],[116]) ).
thf(23,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/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__SYM) ).
thf(259,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)],[23]) ).
thf(160,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
& ( p @ ( c_2Einteger_2Eint__divides_2E2 @ B @ C ) ) )
=> ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__TRANS) ).
thf(1194,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
& ( p @ ( c_2Einteger_2Eint__divides_2E2 @ B @ C ) ) )
=> ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',thm_2Elbtree_2Emmindex__unique) ).
thf(567,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)],[83]) ).
thf(89,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B ) )
<=> ( ( p @ B )
& ( p @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECONJ__SYM) ).
thf(599,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)],[89]) ).
thf(120,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
& ( p @ A ) )
=> ( p @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Epth__an2) ).
thf(863,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
& ( p @ A ) )
=> ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(27,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add_2E2 @ A @ B )
= ( c_2Einteger_2Eint__add_2E2 @ A @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__LADD) ).
thf(271,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( ( c_2Einteger_2Eint__add_2E2 @ A @ B )
= ( c_2Einteger_2Eint__add_2E2 @ A @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( c_2Einteger_2Eint__add_2E2 @ A @ B )
= ( c_2Einteger_2Eint__add_2E2 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(11,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ C @ ( c_2Einteger_2Eint__mul_2E2 @ B @ A ) )
= ( c_2Einteger_2Eint__mul_2E2 @ ( c_2Einteger_2Eint__mul_2E2 @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__ASSOC) ).
thf(208,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ C @ ( c_2Einteger_2Eint__mul_2E2 @ B @ A ) )
= ( c_2Einteger_2Eint__mul_2E2 @ ( c_2Einteger_2Eint__mul_2E2 @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(146,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ A )
=> ( ( p @ A )
| ( p @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EOR__INTRO__THM1) ).
thf(1080,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ A )
=> ( ( p @ A )
| ( p @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',thm_2Ebag_2EPSUB__BAG__TRANS) ).
thf(758,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)],[107]) ).
thf(81,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__OR__OVER__AND) ).
thf(535,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)],[81]) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',thm_2Eind__type_2EINJN) ).
thf(323,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)],[39]) ).
thf(138,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ B )
=> ( ( p @ A )
| ( p @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EOR__INTRO__THM2) ).
thf(1029,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ B )
=> ( ( p @ A )
| ( p @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(154,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg_2E1 @ ( c_2Einteger_2Eint__sub_2E2 @ A @ B ) )
= ( c_2Einteger_2Eint__sub_2E2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__SUB) ).
thf(1149,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg_2E1 @ ( c_2Einteger_2Eint__sub_2E2 @ A @ B ) )
= ( c_2Einteger_2Eint__sub_2E2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(94,axiom,
! [A: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
~ ( p @ ( c_2Einteger_2Etint__lt_2E2 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ETINT__LT__REFL) ).
thf(626,plain,
! [A: tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum] :
~ ( p @ ( c_2Einteger_2Etint__lt_2E2 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(128,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ B )
=> ( p @ A ) )
=> ( ~ ( p @ A )
=> ~ ( p @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Equotient_2ENOT__IMPLIES) ).
thf(932,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)],[128]) ).
thf(118,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B ) )
<=> ~ ( ~ ( p @ A )
| ~ ( p @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EquantHeuristics_2ECONJ__NOT__OR__THM) ).
thf(848,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)],[118]) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__eq) ).
thf(700,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)],[105]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EDISJ__ASSOC) ).
thf(1198,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(124,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
<=> ( p @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eboolext) ).
thf(883,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)],[124]) ).
thf(91,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/sandbox/benchmark/theBenchmark.p',thm_2Eind__type_2EINJA) ).
thf(608,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)],[91]) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__disj__strengthen) ).
thf(306,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)],[36]) ).
thf(148,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B ) )
=> ( p @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EAND1__THM) ).
thf(1113,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B ) )
=> ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(33,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub_2E2 @ ( c_2Einteger_2Eint__neg_2E1 @ A ) @ B )
= ( c_2Einteger_2Eint__neg_2E1 @ ( c_2Einteger_2Eint__add_2E2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LNEG) ).
thf(299,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub_2E2 @ ( c_2Einteger_2Eint__neg_2E1 @ A ) @ B )
= ( c_2Einteger_2Eint__neg_2E1 @ ( c_2Einteger_2Eint__add_2E2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(126,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( A = B )
=> ( ( p @ A )
=> ( p @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Equotient_2EEQ__IMPLIES) ).
thf(922,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( A = B )
=> ( ( p @ A )
=> ( p @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(75,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EMONO__IMP) ).
thf(505,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)],[75]) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',thm_2Ebag_2EPSUB__BAG__NOT__EQ) ).
thf(438,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)],[59]) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECONJ__ASSOC) ).
thf(473,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EAND__IMP) ).
thf(490,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)],[72]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__AND__OVER__OR) ).
thf(1166,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)],[158]) ).
thf(131,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/sandbox/benchmark/theBenchmark.p',thm_2EquantHeuristics_2ELEFT__IMP__AND__INTRO) ).
thf(944,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)],[131]) ).
thf(111,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__OR__OVER__AND) ).
thf(795,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)],[111]) ).
thf(45,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/sandbox/benchmark/theBenchmark.p',thm_2EquantHeuristics_2ERIGHT__IMP__AND__INTRO) ).
thf(374,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)],[45]) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EOR__ELIM__THM) ).
thf(355,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)],[43]) ).
thf(115,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub_2E2 @ ( c_2Einteger_2Eint__sub_2E2 @ A @ B ) @ A )
= ( c_2Einteger_2Eint__neg_2E1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__SUB) ).
thf(823,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub_2E2 @ ( c_2Einteger_2Eint__sub_2E2 @ A @ B ) @ A )
= ( c_2Einteger_2Eint__neg_2E1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(8,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ ( c_2Einteger_2Eint__neg_2E1 @ A ) @ ( c_2Einteger_2Eint__neg_2E1 @ B ) )
= ( c_2Einteger_2Eint__mul_2E2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__MUL2) ).
thf(194,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ ( c_2Einteger_2Eint__neg_2E1 @ A ) @ ( c_2Einteger_2Eint__neg_2E1 @ B ) )
= ( c_2Einteger_2Eint__mul_2E2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(141,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( p @ ( c_2Emarker_2EAC_2E2 @ A @ B ) )
<=> ( ( p @ A )
& ( p @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Emarker_2EAC__DEF) ).
thf(1049,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)],[141]) ).
thf(77,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
=> ( ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__add_2E2 @ C @ B ) )
= ( c_2Einteger_2Eint__divides_2E2 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RADD) ).
thf(525,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
=> ( ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__add_2E2 @ C @ B ) )
= ( c_2Einteger_2Eint__divides_2E2 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(29,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ ( c_2Einteger_2Eint__add_2E2 @ A @ B ) @ ( c_2Einteger_2Eint__sub_2E2 @ A @ B ) )
= ( c_2Einteger_2Eint__sub_2E2 @ ( c_2Einteger_2Eint__mul_2E2 @ A @ A ) @ ( c_2Einteger_2Eint__mul_2E2 @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIFFSQ) ).
thf(282,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ ( c_2Einteger_2Eint__add_2E2 @ A @ B ) @ ( c_2Einteger_2Eint__sub_2E2 @ A @ B ) )
= ( c_2Einteger_2Eint__sub_2E2 @ ( c_2Einteger_2Eint__mul_2E2 @ A @ A ) @ ( c_2Einteger_2Eint__mul_2E2 @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(54,axiom,
! [TA: $tType,A: tyop_2Elist_2Elist @ TA] : ( p @ ( c_2Erich__list_2EIS__SUFFIX_2E2 @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Erich__list_2EIS__SUFFIX__REFL) ).
thf(414,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)],[54]) ).
thf(52,axiom,
! [TA: $tType,A: tyop_2Elist_2Elist @ TA] : ( p @ ( c_2EEncode_2Ebiprefix_2E2 @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EEncode_2Ebiprefix__refl) ).
thf(409,plain,
! [TA: $tType,A: tyop_2Elist_2Elist @ TA] : ( p @ ( c_2EEncode_2Ebiprefix_2E2 @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(136,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/sandbox/benchmark/theBenchmark.p',thm_2EquantHeuristics_2ELEFT__IMP__OR__INTRO) ).
thf(993,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)],[136]) ).
thf(4,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub_2E2 @ A @ ( c_2Einteger_2Eint__add_2E2 @ A @ B ) )
= ( c_2Einteger_2Eint__neg_2E1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__SUB2) ).
thf(182,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub_2E2 @ A @ ( c_2Einteger_2Eint__add_2E2 @ A @ B ) )
= ( c_2Einteger_2Eint__neg_2E1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(133,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CONJ__THM) ).
thf(951,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)],[133]) ).
thf(168,axiom,
! [TA: $tType,A: tyop_2Elist_2Elist @ TA] : ( p @ ( c_2Esorting_2EPERM__SINGLE__SWAP_2E2 @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esorting_2EPERM__SINGLE__SWAP__REFL) ).
thf(1221,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)],[168]) ).
thf(152,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
<=> ( ~ ( p @ B )
=> ~ ( p @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EMONO__NOT__EQ) ).
thf(1140,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)],[152]) ).
thf(123,axiom,
! [TA: $tType,A: TA,B: TA,C: tyop_2Emin_2Ebool] :
( ( p @ ( c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL_2E3 @ TA @ A @ B @ C ) )
<=> ( ~ ( p @ C )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EquantHeuristics_2ESIMPLE__GUESS__FORALL__def) ).
thf(876,plain,
! [TA: $tType,A: TA,B: TA,C: tyop_2Emin_2Ebool] :
( ( ( p @ ( c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL_2E3 @ TA @ A @ B @ C ) )
=> ( ~ ( p @ C )
=> ( A = B ) ) )
& ( ( ~ ( p @ C )
=> ( A = B ) )
=> ( p @ ( c_2EquantHeuristics_2ESIMPLE__GUESS__FORALL_2E3 @ TA @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(44,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__AND__CONG) ).
thf(363,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)],[44]) ).
thf(109,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( ( p @ B )
=> ( p @ A ) )
=> ( p @ B ) )
=> ( p @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EPEIRCE) ).
thf(771,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)],[109]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,A: TB,B: tyop_2Elist_2Elist @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Eoption_2Eoption @ TA ) ),C: tyop_2Elist_2Elist @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Eoption_2Eoption @ TA ) )] :
( ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3 @ TB @ TA @ A @ B @ C )
= ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3 @ TB @ TA @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__is__equiv__2) ).
thf(250,plain,
! [TA: $tType,TB: $tType,A: TB,B: tyop_2Elist_2Elist @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Eoption_2Eoption @ TA ) ),C: tyop_2Elist_2Elist @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Eoption_2Eoption @ TA ) )] :
( ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3 @ TB @ TA @ A @ B @ C )
= ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3 @ TB @ TA @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(17,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg_2E1 @ ( c_2Einteger_2Eint__neg_2E1 @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEGNEG) ).
thf(231,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg_2E1 @ ( c_2Einteger_2Eint__neg_2E1 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(37,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ B )
=> ( p @ A ) )
=> ~ ( p @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Epth__ni2) ).
thf(319,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ B )
=> ( p @ A ) )
=> ~ ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(145,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EDISJ__IMP__THM) ).
thf(1062,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)],[145]) ).
thf(56,axiom,
! [TA: $tType,A: tyop_2Ellist_2Ellist @ TA,B: tyop_2Ellist_2Ellist @ TA,C: tyop_2Ellist_2Ellist @ TA] :
( ( ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ B @ A ) )
& ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ C @ A ) ) )
=> ( ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ B @ C ) )
| ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ellist_2Eprefixes__lprefix__total) ).
thf(418,plain,
! [TA: $tType,A: tyop_2Ellist_2Ellist @ TA,B: tyop_2Ellist_2Ellist @ TA,C: tyop_2Ellist_2Ellist @ TA] :
( ( ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ B @ A ) )
& ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ C @ A ) ) )
=> ( ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ B @ C ) )
| ( p @ ( c_2Ellist_2ELPREFIX_2E2 @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(101,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( A = B )
<=> ( ( ( p @ A )
=> ( p @ B ) )
& ( ( p @ B )
=> ( p @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__IMP__THM) ).
thf(667,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)],[101]) ).
thf(166,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/sandbox/benchmark/theBenchmark.p',thm_2Estring_2Estring__lt__trans) ).
thf(1212,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)],[166]) ).
thf(48,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/sandbox/benchmark/theBenchmark.p',thm_2Erelation_2EEQC__REFL) ).
thf(383,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)],[48]) ).
thf(13,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ B @ A )
= ( c_2Einteger_2Eint__mul_2E2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__SYM) ).
thf(214,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ B @ A )
= ( c_2Einteger_2Eint__mul_2E2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(149,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/sandbox/benchmark/theBenchmark.p',thm_2Emergesort_2Estable__trans) ).
thf(1116,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)],[149]) ).
thf(137,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/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__conj) ).
thf(999,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)],[137]) ).
thf(24,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add_2E2 @ ( c_2Einteger_2Eint__sub_2E2 @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__ADD) ).
thf(262,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add_2E2 @ ( c_2Einteger_2Eint__sub_2E2 @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(113,axiom,
! [A: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
~ ( p @ ( c_2Estring_2Estring__lt_2E2 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Estring_2Estring__lt__nonrefl) ).
thf(818,plain,
! [A: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
~ ( p @ ( c_2Estring_2Estring__lt_2E2 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(153,axiom,
! [A: tyop_2Emin_2Ebool] :
( ~ ~ ( p @ A )
=> ( p @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Epth__nn) ).
thf(1148,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(35,axiom,
! [A: tyop_2Emin_2Ebool] :
~ ( ( p @ A )
& ~ ( p @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__AND) ).
thf(305,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(19,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( A
= ( c_2Einteger_2Eint__sub_2E2 @ B @ C ) )
<=> ( ( c_2Einteger_2Eint__add_2E2 @ A @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__SUB__LADD) ).
thf(242,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( A
= ( c_2Einteger_2Eint__sub_2E2 @ B @ C ) )
=> ( ( c_2Einteger_2Eint__add_2E2 @ A @ C )
= B ) )
& ( ( ( c_2Einteger_2Eint__add_2E2 @ A @ C )
= B )
=> ( A
= ( c_2Einteger_2Eint__sub_2E2 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(26,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add_2E2 @ B @ ( c_2Einteger_2Eint__sub_2E2 @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__ADD2) ).
thf(268,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add_2E2 @ B @ ( c_2Einteger_2Eint__sub_2E2 @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(70,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
<=> ? [C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ C @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES) ).
thf(474,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
=> ? [C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ C @ A )
= B ) )
& ( ? [C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul_2E2 @ C @ A )
= B )
=> ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(100,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
=> ( ~ ( p @ B )
=> ~ ( p @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EMONO__NOT) ).
thf(664,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)],[100]) ).
thf(171,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/sandbox/benchmark/theBenchmark.p',thm_2Ecardinal_2ECONJ__ACI) ).
thf(1236,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)],[171]) ).
thf(84,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ A )
=> ( p @ B ) )
<=> ( ( p @ A )
& ~ ( p @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__IMP) ).
thf(575,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)],[84]) ).
thf(155,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B ) )
<=> ( ( p @ B )
& ( p @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECONJ__COMM) ).
thf(1152,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)],[155]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,A: TB,B: tyop_2Elist_2Elist @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Eoption_2Eoption @ TA ) ),C: tyop_2Elist_2Elist @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Eoption_2Eoption @ TA ) ),D: tyop_2Elist_2Elist @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Eoption_2Eoption @ TA ) )] :
( ( p @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3 @ TB @ TA @ A @ B @ C ) )
=> ( ( p @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3 @ TB @ TA @ A @ C @ D ) )
=> ( p @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3 @ TB @ TA @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__is__equiv__3) ).
thf(459,plain,
! [TA: $tType,TB: $tType,A: TB,B: tyop_2Elist_2Elist @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Eoption_2Eoption @ TA ) ),C: tyop_2Elist_2Elist @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Eoption_2Eoption @ TA ) ),D: tyop_2Elist_2Elist @ ( tyop_2Emin_2Efun @ TB @ ( tyop_2Eoption_2Eoption @ TA ) )] :
( ( p @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3 @ TB @ TA @ A @ B @ C ) )
=> ( ( p @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3 @ TB @ TA @ A @ C @ D ) )
=> ( p @ ( c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3 @ TB @ TA @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',thm_2Equotient_2ECONJ__IMPLIES) ).
thf(442,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)],[60]) ).
thf(73,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ B )
=> ( p @ A ) )
=> ( p @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Epth__ni1) ).
thf(501,plain,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ~ ( ( p @ B )
=> ( p @ A ) )
=> ( p @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(90,axiom,
! [A: tyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ A ) )
<=> ( p @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EAND__CLAUSES__XX) ).
thf(607,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EBOTH__FORALL__OR__THM) ).
thf(322,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(41,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
=> ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__mul_2E2 @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__LMUL) ).
thf(337,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ B ) )
=> ( p @ ( c_2Einteger_2Eint__divides_2E2 @ A @ ( c_2Einteger_2Eint__mul_2E2 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(67,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/sandbox/benchmark/theBenchmark.p',thm_2Efinite__map_2Efmap__EQ__UPTO______EQ) ).
thf(469,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)],[67]) ).
thf(129,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/sandbox/benchmark/theBenchmark.p',thm_2EquantHeuristics_2ERIGHT__IMP__OR__INTRO) ).
thf(935,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)],[129]) ).
thf(110,axiom,
! [A: tyop_2Emin_2Ebool,B: tyop_2Emin_2Ebool] :
( ( A = B )
<=> ( ( ( p @ A )
& ( p @ B ) )
| ( ~ ( p @ A )
& ~ ( p @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__EXPAND) ).
thf(775,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)],[110]) ).
thf(1316,plain,
$false,
inference(cvc4,[status(thm)],[892,629,760,1031,234,941,481,1083,468,408,217,379,614,597,1205,449,385,533,1164,814,340,174,1196,185,973,288,1265,1055,1264,1059,949,969,416,228,179,1183,821,211,646,253,687,866,411,428,265,452,512,529,1199,381,1057,1223,1042,302,598,392,630,197,329,583,461,285,874,615,188,1138,697,1234,420,1118,1160,225,554,1214,471,256,837,647,457,503,1202,633,205,530,586,926,856,745,279,689,296,191,826,259,1194,567,599,863,271,208,1080,758,535,323,1029,1149,626,932,848,700,1198,883,608,306,1113,299,922,505,438,473,490,1166,944,795,374,355,823,194,1049,525,282,414,409,993,182,951,1221,1140,876,363,771,250,231,319,1062,418,667,1212,383,214,1116,999,262,818,1148,305,242,268,474,664,1236,575,1152,459,442,501,607,322,337,469,935,775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP012_7 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n006.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 6 14:43:25 EDT 2024
% 0.14/0.36 % CPUTime :
% 1.02/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 5.59/2.34 % [INFO] Parsing done (1435ms).
% 5.59/2.35 % [INFO] Running in sequential loop mode.
% 6.01/2.57 % [INFO] eprover registered as external prover.
% 6.01/2.57 % [INFO] cvc4 registered as external prover.
% 6.01/2.58 % [INFO] Scanning for conjecture ...
% 9.92/3.54 % [INFO] Found a conjecture and 14071 axioms. Running axiom selection ...
% 11.31/3.99 % [INFO] Axiom selection finished. Selected 171 axioms (removed 13900 axioms).
% 11.99/4.12 % [INFO] Problem is typed first-order (TPTP TFF).
% 11.99/4.13 % [INFO] Type checking passed.
% 11.99/4.14 % [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 ...
% 19.42/5.85 % External prover 'cvc4' found a proof!
% 19.42/5.85 % [INFO] Killing All external provers ...
% 19.42/5.85 % Time passed: 5326ms (effective reasoning time: 3492ms)
% 19.42/5.85 % 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)>
% 19.42/5.85 % Axioms used in derivation (171): thm_2Ebool_2EDISJ__SYM, thm_2Ebool_2ERIGHT__AND__OVER__OR, thm_2Estring_2Estring__lt__cases, thm_2Ebag_2EPSUB__BAG__NOT__EQ, thm_2EConseqConv_2EIMP__CONG__conj__strengthen, thm_2Einteger_2EINT__NEG__RMUL, thm_2Ebool_2ELEFT__AND__CONG, thm_2Ebool_2EOR__IMP__THM, thm_2Einteger_2EINT__DIVIDES__MUL, thm_2Einteger_2Eint__sub, thm_2EConseqConv_2ENOT__CLAUSES__X, thm_2EquantHeuristics_2ESIMPLE__GUESS__FORALL__def, thm_2EConseqConv_2EIMP__CONG__conj__weaken, thm_2Eextra_2Dho_2Eboolext, thm_2Ecardinal_2ECONJ__EQ__IMP, thm_2Einteger_2EINT__ADD__ASSOC, thm_2Epath_2EfirstP__at__unique, thm_2Ebool_2EBOTH__FORALL__OR__THM, thm_2Esat_2Edc__conj, thm_2EquantHeuristics_2ERIGHT__IMP__AND__INTRO, thm_2Einteger_2EINT__NEG__SUB, thm_2Ebool_2EBOTH__FORALL__IMP__THM, thm_2Ebool_2EDISJ__COMM, thm_2Ebool_2EPEIRCE, thm_2Egcd_2EIS__GCD__UNIQUE, thm_2Ebool_2EEQ__IMP__THM, thm_2Equotient_2EEQ__IMPLIES, thm_2Eprim__rec_2ESIMP__REC__EXISTS, thm_2Ebool_2EIMP__ANTISYM__AX, thm_2Ebool_2EIMP__CONG, thm_2Einteger_2EINT__EQ__NEG, thm_2Ellist_2ELPREFIX__REFL, thm_2Ewellorder_2Eorderlt__TRANS, thm_2Einteger_2EINT__SUB__NEG2, thm_2Epred__set_2EUNIV__applied, thm_2Einteger_2EINT__DIVIDES__LSUB, thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__is__equiv__3, thm_2EConseqConv_2EIMP__CONG__disj__weaken, thm_2Einteger_2EINT__DIVIDES__REFL, thm_2Ebool_2ECONJ__ASSOC, thm_2Einteger_2ETINT__LT__TRANS, thm_2Ebool_2EMONO__OR, thm_2Efinite__map_2Efmap__EQ__UPTO______EQ, thm_2Esat_2Edc__eq, thm_2Einteger_2EINT__DIVIDES__RADD, thm_2Ebool_2EMONO__AND, thm_2Einteger_2EINT__SUB__TRIANGLE, thm_2Einteger_2EINT__MUL__SYM, thm_2Einteger_2EINT__SUB__SUB2, thm_2Ebool_2EMONO__NOT, thm_2Einteger_2EINT__ADD__SUB2, thm_2Einteger_2EINT__DIVIDES, thm_2Einteger_2EINT__MUL__COMM, thm_2Esat_2Edc__imp, thm_2Einteger_2EINT__DIVIDES__RMUL, thm_2Esat_2Epth__no1, thm_2EConseqConv_2EIMP__CONG__simple__imp__weaken, thm_2Erelation_2EEQC__TRANS, thm_2Ebool_2EOR__DEF, thm_2Ebool_2ELEFT__AND__OVER__OR, thm_2Einteger_2EINT__SUB__RNEG, thm_2Esat_2Epth__ni1, thm_2Esat_2Epth__an1, thm_2Ebool_2ERIGHT__OR__OVER__AND, thm_2Einteger_2EINT__DIVIDES__LMUL, thm_2EConseqConv_2EIMP__CONG__imp__weaken, thm_2Ebool_2EOR__CONG, thm_2Esat_2Epth__no2, thm_2Estring_2Estring__lt__trans, thm_2Emarker_2EAC__DEF, thm_2Ebool_2EOR__INTRO__THM2, thm_2Egcd_2EIS__GCD__REF, thm_2Einteger_2EINT__DIVIDES__NEG, thm_2Esat_2Edc__neg, thm_2Einteger_2ETINT__LT__REFL, thm_2Erelation_2EEQC__SYM, thm_2Einteger_2EINT__NEGNEG, thm_2EquantHeuristics_2ERIGHT__IMP__OR__INTRO, thm_2Ebag_2EPSUB__BAG__IRREFL, thm_2Ebool_2EAND__IMP__INTRO, thm_2EquantHeuristics_2ELEFT__IMP__AND__INTRO, thm_2Einteger_2EINT__NEG__EQ, thm_2Einteger_2EINT__DIVIDES__LADD, thm_2EquantHeuristics_2ELEFT__IMP__OR__INTRO, thm_2Einteger_2EINT__ADD__COMM, thm_2Einteger_2EINT__DIVIDES__TRANS, thm_2Ebool_2EAND__CONG, thm_2Ebool_2EEQ__EXPAND, thm_2Ellist_2Eprefixes__lprefix__total, thm_2Ebool_2ENOT__AND, thm_2Einteger_2EINT__ADD2__SUB2, thm_2Einteger_2EINT__NEG__MUL2, thm_2EEncode_2Ebiprefix__refl, thm_2Ebool_2EMONO__NOT__EQ, thm_2Einteger_2EINT__SUB__RDISTRIB, thm_2Ebool_2EDISJ__EQ__IMP, thm_2Einteger_2EINT__LDISTRIB, thm_2Ebool_2EAND2__THM, thm_2Ebool_2EIMP__CONJ__THM, thm_2EConseqConv_2EIMP__CONG__disj__strengthen, thm_2Einteger_2EINT__SUB__LDISTRIB, thm_2Einteger_2EINT__MUL__ASSOC, thm_2Erich__list_2EIS__SUFFIX__REFL, thm_2Esorting_2EPERM__SINGLE__SWAP__SYM, thm_2Ebool_2EEXCLUDED__MIDDLE, thm_2EConseqConv_2EIMP__CONG__imp__strengthen, thm_2Ebool_2EDISJ__ASSOC, thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__is__equiv__1, thm_2Ebool_2EBOTH__EXISTS__IMP__THM, thm_2Egcd_2EIS__GCD__SYM, thm_2Erelation_2EEQC__REFL, thm_2Esat_2Epth__ni2, thm_2Ebool_2EAND1__THM, thm_2Ebool_2EMONO__IMP, thm_2Ebool_2EDE__MORGAN__THM, thm_2Ebool_2EOR__INTRO__THM1, thm_2Ecardinal_2ECONJ__ACI, thm_2Equotient_2ECONJ__IMPLIES, thm_2Ebool_2ECONJ__COMM, thm_2Ebool_2EBOTH__EXISTS__AND__THM, thm_2Esat_2ENOT__NOT, thm_2Einteger_2EINT__RDISTRIB, thm_2Ebool_2ENOT__IMP, thm_2Einteger_2EINT__EQ__RADD, thm_2Ebool_2EFORALL__SIMP, thm_2Ebool_2EDISJ__IMP__THM, thm_2Emergesort_2Estable__trans, thm_2Einteger_2EINT__SUB__ADD, thm_2Esorting_2EPERM__SINGLE__SWAP__REFL, thm_2Ebool_2ELEFT__OR__OVER__AND, thm_2EConseqConv_2EOR__CLAUSES__XX, thm_2Einteger_2EINT__SUB__LNEG, thm_2Einteger_2EINT__NEG__LMUL, thm_2Ebool_2EIMP__DISJ__THM, thm_2Elbtree_2Emmindex__unique, thm_2Equotient_2EIMP__IMPLIES, thm_2Einteger_2EINT__NEG__ADD, thm_2Estring_2Estring__lt__nonrefl, thm_2EConseqConv_2EIMP__CONG__simple__imp__strengthen, thm_2Einteger_2EINT__ADD__SYM, thm_2Ebool_2EEXISTS__SIMP, thm_2Esat_2Epth__nn, thm_2Ebool_2EAND__DEF, thm_2Ebool_2EAND__INTRO__THM, thm_2Eind__type_2EINJN, thm_2Einteger_2EINT__EQ__SUB__RADD, thm_2Einteger_2EINT__ADD__SUB, thm_2Einteger_2EINT__EQ__SUB__LADD, thm_2Equotient_2EDISJ__IMPLIES, thm_2Eind__type_2EINJA, thm_2Esat_2EAND__IMP, thm_2Esat_2Epth__an2, thm_2Einteger_2EINT__SUB__SUB, thm_2Ebool_2EOR__ELIM__THM, thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__is__equiv__2, thm_2EEncode_2Ebiprefix__sym, thm_2Ebag_2EPSUB__BAG__ANTISYM, thm_2Einteger_2EINT__EQ__LADD, thm_2Equotient_2ENOT__IMPLIES, thm_2EquantHeuristics_2ECONJ__NOT__OR__THM, thm_2Ebag_2EPSUB__BAG__TRANS, thm_2Esat_2Edc__disj, thm_2Ebool_2ECONJ__SYM, thm_2Ellist_2ELPREFIX__ANTISYM, thm_2Ecardinal_2EIMP__CONJ__ALT, thm_2Estring_2Estring__lt__antisym, thm_2Ebool_2ELEFT__OR__CONG, thm_2EConseqConv_2EAND__CLAUSES__XX, thm_2Einteger_2EINT__SUB__ADD2, thm_2Ellist_2ELPREFIX__TRANS, thm_2Einteger_2EINT__DIFFSQ
% 19.42/5.85 % No. of inferences in proof: 346
% 19.42/5.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5326 ms resp. 3492 ms w/o parsing
% 19.87/5.95 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.87/5.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------