%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP015^7 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:22 AM UTC 2026
% Result : Theorem 42.63s 12.25s
% Output : Refutation 42.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 686
% Syntax : Number of formulae : 1442 ( 860 unt; 0 typ; 1 def)
% Number of atoms : 3970 (1972 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 13994 ( 429 ~; 229 |; 652 &;12074 @)
% ( 0 <=>; 610 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 79 ( 76 usr; 10 con; 0-5 aty)
% Number of variables : 3502 ( 4 ^;3411 !; 86 ?;3502 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Eind_type,type,
tyop_2Emin_2Eind: $tType ).
thf(tyop_2Enum_2Enum_type,type,
tyop_2Enum_2Enum: $tType ).
thf(tyop_2Eone_2Eone_type,type,
tyop_2Eone_2Eone: $tType ).
thf(tyop_2Estring_2Echar_type,type,
tyop_2Estring_2Echar: $tType ).
thf(tyop_2EternaryComparisons_2Eordering_type,type,
tyop_2EternaryComparisons_2Eordering: $tType ).
thf(tyop_2Ehrat_2Ehrat_type,type,
tyop_2Ehrat_2Ehrat: $tType ).
thf(tyop_2Einteger_2Eint_type,type,
tyop_2Einteger_2Eint: $tType ).
thf(tyop_2Equote_2Eindex_type,type,
tyop_2Equote_2Eindex: $tType ).
thf(tyop_2Etoto_2Enum__dt_type,type,
tyop_2Etoto_2Enum__dt: $tType ).
thf(tyop_2Ehreal_2Ehreal_type,type,
tyop_2Ehreal_2Ehreal: $tType ).
thf(tyop_2EDeepSyntax_2Edeep__form_type,type,
tyop_2EDeepSyntax_2Edeep__form: $tType ).
thf(skt1_type,type,
skt1: $tType ).
thf(c_2Ebool_2E_2F_5C_decl,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Ebool_2ECOND_decl,type,
c_2Ebool_2ECOND:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(c_2Ebool_2EF_decl,type,
c_2Ebool_2EF: $o ).
thf(c_2Ebool_2ET_decl,type,
c_2Ebool_2ET: $o ).
thf(c_2Enum_2E0_decl,type,
c_2Enum_2E0: tyop_2Enum_2Enum ).
thf(c_2Enum_2EABS__num_decl,type,
c_2Enum_2EABS__num: tyop_2Emin_2Eind > tyop_2Enum_2Enum ).
thf(c_2Enum_2EZERO__REP_decl,type,
c_2Enum_2EZERO__REP: tyop_2Emin_2Eind ).
thf(c_2Eprim__rec_2E_3C_decl,type,
c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Earithmetic_2E_2A_decl,type,
c_2Earithmetic_2E_2A: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2E_2D_decl,type,
c_2Earithmetic_2E_2D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2E_3C_3D_decl,type,
c_2Earithmetic_2E_3C_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Earithmetic_2EABS__DIFF_decl,type,
c_2Earithmetic_2EABS__DIFF: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EDIV_decl,type,
c_2Earithmetic_2EDIV: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EMOD_decl,type,
c_2Earithmetic_2EMOD: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EMODEQ_decl,type,
c_2Earithmetic_2EMODEQ: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Earithmetic_2ENRC_decl,type,
c_2Earithmetic_2ENRC:
!>[TA: $tType] : ( ( TA > TA > $o ) > tyop_2Enum_2Enum > TA > TA > $o ) ).
thf(c_2Earithmetic_2ENUMERAL_decl,type,
c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2EbasicSize_2Ebool__size_decl,type,
c_2EbasicSize_2Ebool__size: $o > tyop_2Enum_2Enum ).
thf(c_2EbasicSize_2Eone__size_decl,type,
c_2EbasicSize_2Eone__size: tyop_2Eone_2Eone > tyop_2Enum_2Enum ).
thf(c_2Egcd_2Egcd_decl,type,
c_2Egcd_2Egcd: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Egcd_2Eis__gcd_decl,type,
c_2Egcd_2Eis__gcd: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Egcd_2Elcm_decl,type,
c_2Egcd_2Elcm: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Enumpair_2Encons_decl,type,
c_2Enumpair_2Encons: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Estring_2Echar__size_decl,type,
c_2Estring_2Echar__size: tyop_2Estring_2Echar > tyop_2Enum_2Enum ).
thf(c_2EternaryComparisons_2Eordering__size_decl,type,
c_2EternaryComparisons_2Eordering__size: tyop_2EternaryComparisons_2Eordering > tyop_2Enum_2Enum ).
thf(c_2Einteger_2EABS_decl,type,
c_2Einteger_2EABS: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2ENum_decl,type,
c_2Einteger_2ENum: tyop_2Einteger_2Eint > tyop_2Enum_2Enum ).
thf(c_2Einteger_2Eint__0_decl,type,
c_2Einteger_2Eint__0: tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__add_decl,type,
c_2Einteger_2Eint__add: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__div_decl,type,
c_2Einteger_2Eint__div: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__divides_decl,type,
c_2Einteger_2Eint__divides: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).
thf(c_2Einteger_2Eint__exp_decl,type,
c_2Einteger_2Eint__exp: tyop_2Einteger_2Eint > tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__le_decl,type,
c_2Einteger_2Eint__le: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).
thf(c_2Einteger_2Eint__lt_decl,type,
c_2Einteger_2Eint__lt: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).
thf(c_2Einteger_2Eint__mod_decl,type,
c_2Einteger_2Eint__mod: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__mul_decl,type,
c_2Einteger_2Eint__mul: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__neg_decl,type,
c_2Einteger_2Eint__neg: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__of__num_decl,type,
c_2Einteger_2Eint__of__num: tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__quot_decl,type,
c_2Einteger_2Eint__quot: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__rem_decl,type,
c_2Einteger_2Eint__rem: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__sub_decl,type,
c_2Einteger_2Eint__sub: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Ewords_2Ebit__count_decl,type,
c_2Ewords_2Ebit__count:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > tyop_2Enum_2Enum ) ).
thf(c_2Ewords_2Ebit__count__upto_decl,type,
c_2Ewords_2Ebit__count__upto:
!>[TA: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TA ) > tyop_2Enum_2Enum ) ).
thf(c_2Ewords_2En2w_decl,type,
c_2Ewords_2En2w:
!>[TA: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Esw2sw_decl,type,
c_2Ewords_2Esw2sw:
!>[TA: $tType,TB: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TB ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Ew2n_decl,type,
c_2Ewords_2Ew2n:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > tyop_2Enum_2Enum ) ).
thf(c_2Ewords_2Ew2w_decl,type,
c_2Ewords_2Ew2w:
!>[TA: $tType,TB: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TB ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Eword__2comp_decl,type,
c_2Ewords_2Eword__2comp:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Eword__L_decl,type,
c_2Ewords_2Eword__L:
!>[TA: $tType] : ( tyop_2Efcp_2Ecart @ $o @ TA ) ).
thf(c_2Ewords_2Eword__abs_decl,type,
c_2Ewords_2Eword__abs:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Eword__add_decl,type,
c_2Ewords_2Eword__add:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Eword__bit_decl,type,
c_2Ewords_2Eword__bit:
!>[TA: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TA ) > $o ) ).
thf(c_2Ewords_2Eword__bits_decl,type,
c_2Ewords_2Eword__bits:
!>[TA: $tType] : ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Eword__concat_decl,type,
c_2Ewords_2Eword__concat:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TC ) > ( tyop_2Efcp_2Ecart @ $o @ TB ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Eword__extract_decl,type,
c_2Ewords_2Eword__extract:
!>[TA: $tType,TB: $tType] : ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TB ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Eword__le_decl,type,
c_2Ewords_2Eword__le:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > $o ) ).
thf(c_2Ewords_2Eword__lo_decl,type,
c_2Ewords_2Eword__lo:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > $o ) ).
thf(c_2Ewords_2Eword__ls_decl,type,
c_2Ewords_2Eword__ls:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > $o ) ).
thf(c_2Ewords_2Eword__lt_decl,type,
c_2Ewords_2Eword__lt:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > $o ) ).
thf(c_2Ewords_2Eword__msb_decl,type,
c_2Ewords_2Eword__msb:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > $o ) ).
thf(c_2Ewords_2Eword__mul_decl,type,
c_2Ewords_2Eword__mul:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Eword__reverse_decl,type,
c_2Ewords_2Eword__reverse:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Eword__slice_decl,type,
c_2Ewords_2Eword__slice:
!>[TA: $tType] : ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Eword__sub_decl,type,
c_2Ewords_2Eword__sub:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ealignment_2Ealign_decl,type,
c_2Ealignment_2Ealign:
!>[TA: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ealignment_2Ealigned_decl,type,
c_2Ealignment_2Ealigned:
!>[TA: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TA ) > $o ) ).
thf(c_2Ebitstring_2Eshiftr_decl,type,
c_2Ebitstring_2Eshiftr: ( tyop_2Elist_2Elist @ $o ) > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) ).
thf(c_2Ebitstring_2Ev2w_decl,type,
c_2Ebitstring_2Ev2w:
!>[TA: $tType] : ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Esptree_2Espt__acc_decl,type,
c_2Esptree_2Espt__acc: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Einteger__word_2Ei2w_decl,type,
c_2Einteger__word_2Ei2w:
!>[TA: $tType] : ( tyop_2Einteger_2Eint > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Einteger__word_2Ew2i_decl,type,
c_2Einteger__word_2Ew2i:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > tyop_2Einteger_2Eint ) ).
thf(c_2Einteger__word_2Eword__sdiv_decl,type,
c_2Einteger__word_2Eword__sdiv:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Einteger__word_2Eword__smod_decl,type,
c_2Einteger__word_2Eword__smod:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(sk32_decl,type,
sk32: $o ).
thf(sk32_def,definition,
( sk32
= ( @+[A: $o] : ~ A ) ) ).
thf(350,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__le @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__NEG) ).
thf(2452,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__le @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(248,axiom,
! [A: $o] :
( ( c_2Ebool_2ET
=> A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CLAUSES__TX) ).
thf(1879,plain,
! [A: $o] :
( ( c_2Ebool_2ET
=> A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(134,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__le @ TA @ A @ B )
= ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__OR__EQ) ).
thf(1190,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__le @ TA @ A @ B )
= ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(178,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__mul @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
= ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) @ ( c_2Ewords_2Eword__mul @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LEFT__SUB__DISTRIB) ).
thf(1454,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__mul @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
= ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) @ ( c_2Ewords_2Eword__mul @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(630,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Ewords_2En2w @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__nchotomy) ).
thf(3399,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Ewords_2En2w @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(230,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
=> ( ( ( c_2Earithmetic_2EMOD @ A @ B )
= A )
= ( c_2Eprim__rec_2E_3C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EX__MOD__Y__EQ__X) ).
thf(1729,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
=> ( ( ( c_2Earithmetic_2EMOD @ A @ B )
= A )
= ( c_2Eprim__rec_2E_3C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(650,axiom,
! [A: tyop_2Eone_2Eone] :
( ( c_2EbasicSize_2Eone__size @ A )
= c_2Enum_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EbasicSize_2Eone__size__def) ).
thf(3477,plain,
! [A: tyop_2Eone_2Eone] :
( ( c_2EbasicSize_2Eone__size @ A )
= c_2Enum_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(104,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B )
& ( c_2Ewords_2Eword__lt @ TA @ B @ A ) )
=> ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LT__SUB__UPPER) ).
thf(1083,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B )
& ( c_2Ewords_2Eword__lt @ TA @ B @ A ) )
=> ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(642,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD0) ).
thf(3449,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(382,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
& ( c_2Einteger_2Eint__lt @ A @ B )
& ( c_2Einteger_2Eint__lt @ C @ D ) )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__mul @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__MUL2) ).
thf(2544,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
& ( c_2Einteger_2Eint__lt @ A @ B )
& ( c_2Einteger_2Eint__lt @ C @ D ) )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__mul @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(201,axiom,
! [A: $o,B: $o,C: $o,D: $o,E: $o] :
( ( ( C
=> B )
& ( E
=> D ) )
=> ( ( c_2Ebool_2ECOND @ $o @ A @ C @ E )
=> ( c_2Ebool_2ECOND @ $o @ A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__cond__simple) ).
thf(1549,plain,
! [A: $o,B: $o,C: $o,D: $o,E: $o] :
( ( ( C
=> B )
& ( E
=> D ) )
=> ( ( c_2Ebool_2ECOND @ $o @ A @ C @ E )
=> ( c_2Ebool_2ECOND @ $o @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(112,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
& ( c_2Ewords_2Eword__le @ TA @ B @ C ) )
=> ( c_2Ewords_2Eword__le @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__EQ__TRANS) ).
thf(1110,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
& ( c_2Ewords_2Eword__le @ TA @ B @ C ) )
=> ( c_2Ewords_2Eword__le @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(220,axiom,
! [A: tyop_2Enum_2Enum] :
( ( A != c_2Enum_2E0 )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ENOT__ZERO__LT__ZERO) ).
thf(1686,plain,
! [A: tyop_2Enum_2Enum] :
( ( A != c_2Enum_2E0 )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(269,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Egcd_2Egcd @ A @ B )
= ( c_2Egcd_2Egcd @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__SYM) ).
thf(2163,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Egcd_2Egcd @ A @ B )
= ( c_2Egcd_2Egcd @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(55,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Earithmetic_2E_3C_3D @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE) ).
thf(892,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Earithmetic_2E_3C_3D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(91,axiom,
! [A: $o] :
( ( ( c_2Ebool_2ET
| A )
= c_2Ebool_2ET )
& ( ( A
| c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
| A )
= A )
& ( ( A
| c_2Ebool_2EF )
= A )
& ( ( A
| A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EOR__CLAUSES) ).
thf(1036,plain,
! [A: $o] :
( ( ( c_2Ebool_2ET
| A )
= c_2Ebool_2ET )
& ( ( A
| c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
| A )
= A )
& ( ( A
| c_2Ebool_2EF )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(462,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2En2w @ TA @ ( c_2Ewords_2Ew2n @ TA @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2En2w__w2n) ).
thf(2822,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2En2w @ TA @ ( c_2Ewords_2Ew2n @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(58,axiom,
! [A: $o,B: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2ET @ B )
= ( ~ A
=> B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ECOND__CLAUSES__TT) ).
thf(901,plain,
! [A: $o,B: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2ET @ B )
= ( ~ A
=> B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(906,plain,
( ( c_2Ebool_2ECOND @ $o @ $false @ c_2Ebool_2ET @ $true )
= ( ~ $false
=> $true ) ),
inference(instance,[status(thm)],[901]) ).
thf(907,plain,
c_2Ebool_2ECOND @ $o @ $false @ c_2Ebool_2ET @ $true,
inference(simp,[status(thm)],[906]) ).
thf(52,axiom,
! [A: $o] :
( ( A
& c_2Ebool_2ET )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EAND__CLAUSES__XT) ).
thf(881,plain,
! [A: $o] :
( ( A
& c_2Ebool_2ET )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(882,plain,
( ( $true
& c_2Ebool_2ET )
= $true ),
inference(instance,[status(thm)],[881]) ).
thf(883,plain,
c_2Ebool_2ET,
inference(simp,[status(thm)],[882]) ).
thf(3873,plain,
c_2Ebool_2ECOND @ $o @ $false @ $true @ $true,
inference(rewrite,[status(thm)],[907,883]) ).
thf(260,axiom,
! [A: $o] :
( ( c_2Ebool_2EF
& A )
= c_2Ebool_2EF ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EAND__CLAUSES__FX) ).
thf(2094,plain,
! [A: $o] :
( ( c_2Ebool_2EF
& A )
= c_2Ebool_2EF ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(169,axiom,
! [A: tyop_2Enum_2Enum > $o] :
( ? [B: tyop_2Enum_2Enum] : ( A @ B )
=> ? [B: tyop_2Enum_2Enum] :
( ( A @ B )
& ! [C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ C @ B )
=> ~ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EWOP) ).
thf(1411,plain,
! [A: tyop_2Enum_2Enum > $o] :
( ? [B: tyop_2Enum_2Enum] : ( A @ B )
=> ? [B: tyop_2Enum_2Enum] :
( ( A @ B )
& ! [C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ C @ B )
=> ~ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(129,axiom,
! [A: $o] :
( ( ~ A
& A )
= c_2Ebool_2EF ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EAND__INV) ).
thf(1168,plain,
~ c_2Ebool_2EF,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(305,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ B ) )
=> ( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__neg @ A ) )
=> ( ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ C ) @ A ) )
= c_2Ebool_2EF ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ele__context__rwt4) ).
thf(2306,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ B ) )
=> ( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__neg @ A ) )
=> ( ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ C ) @ A ) )
= c_2Ebool_2EF ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(354,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__sub @ A @ B ) @ C )
= ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__add @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__SUB__RADD) ).
thf(2463,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__sub @ A @ B ) @ C )
= ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__add @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(629,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__0__LS) ).
thf(3397,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(131,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2EWORD__LTi) ).
thf(1179,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(313,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ B ) @ C )
= ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__sub @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADD__SUB) ).
thf(2331,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ B ) @ C )
= ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__sub @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(27,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__mod @ A @ B ) ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__mod @ A @ B ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mod @ A @ B ) ) @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mod @ A @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__BOUNDS) ).
thf(777,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__mod @ A @ B ) ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__mod @ A @ B ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mod @ A @ B ) ) @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mod @ A @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(677,axiom,
( c_2Einteger_2Eint__0
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__0) ).
thf(3565,plain,
( c_2Einteger_2Eint__0
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(3566,plain,
( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
= c_2Einteger_2Eint__0 ),
inference(lifteq,[status(thm)],[3565]) ).
thf(235,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( A = B )
| ( c_2Ewords_2Eword__lt @ TA @ A @ B )
| ( c_2Ewords_2Eword__lt @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__LESS__CASES) ).
thf(1750,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( A = B )
| ( c_2Ewords_2Eword__lt @ TA @ A @ B )
| ( c_2Ewords_2Eword__lt @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(306,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( A
= ( c_2Einteger_2Eint__add @ B @ C ) )
= ( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ C ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__move__right__left) ).
thf(2309,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( A
= ( c_2Einteger_2Eint__add @ B @ C ) )
= ( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ C ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(283,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ B )
=> ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__mul @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__LMUL) ).
thf(2210,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ B )
=> ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__mul @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(15,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__mul @ TA @ A @ B )
= ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2A @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__mul__def) ).
thf(730,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__mul @ TA @ A @ B )
= ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2A @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(101,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B != c_2Enum_2E0 )
=> ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EMOD @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM) ).
thf(1068,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B != c_2Enum_2E0 )
=> ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EMOD @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(253,axiom,
! [A: $o] :
( ( c_2Ebool_2ET
& A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EAND__CLAUSES__TX) ).
thf(2062,plain,
! [A: $o] :
( ( c_2Ebool_2ET
& A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(504,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ C ) )
= ( c_2Einteger_2Eint__lt @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__RADD) ).
thf(2947,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ C ) )
= ( c_2Einteger_2Eint__lt @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(555,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ B ) )
= ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
| ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__SIGN__CASES) ).
thf(3108,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ B ) )
= ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
| ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(261,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ B @ A )
=> ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB) ).
thf(2099,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ B @ A )
=> ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(656,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__RZERO) ).
thf(3498,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(631,axiom,
! [A: tyop_2Einteger_2Eint] :
( ? [B: tyop_2Enum_2Enum] :
( ( A
= ( c_2Einteger_2Eint__of__num @ B ) )
& ( B != c_2Enum_2E0 ) )
| ? [B: tyop_2Enum_2Enum] :
( ( A
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
& ( B != c_2Enum_2E0 ) )
| ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NUM__CASES) ).
thf(3402,plain,
! [A: tyop_2Einteger_2Eint] :
( ? [B: tyop_2Enum_2Enum] :
( ( A
= ( c_2Einteger_2Eint__of__num @ B ) )
& ( B != c_2Enum_2E0 ) )
| ? [B: tyop_2Enum_2Enum] :
( ( A
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
& ( B != c_2Enum_2E0 ) )
| ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(176,axiom,
! [A: $o > $o] :
( ( ( A @ c_2Ebool_2ET )
& ( A @ c_2Ebool_2EF ) )
=> ! [B: $o] : ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__INDUCT) ).
thf(1437,plain,
! [A: $o > $o] :
( ( ( A @ c_2Ebool_2ET )
& ( A @ c_2Ebool_2EF ) )
=> ! [B: $o] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(92,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ECOND__CLAUSES__CF) ).
thf(1041,plain,
! [TA: $tType,A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(137,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__LESS__EQ) ).
thf(1200,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(667,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
=> ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__POS__NZ) ).
thf(3534,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
=> ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(193,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2ENUMERAL @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ENUMERAL__DEF) ).
thf(1522,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2ENUMERAL @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(412,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__2comp @ TA @ B )
= A )
= ( B
= ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__EQ) ).
thf(2644,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__2comp @ TA @ B )
= A )
= ( B
= ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(364,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ C ) )
= ( c_2Einteger_2Eint__le @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__RADD) ).
thf(2495,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ C ) )
= ( c_2Einteger_2Eint__le @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(587,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__sub @ A @ B ) )
= ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mul @ A @ A ) @ ( c_2Einteger_2Eint__mul @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIFFSQ) ).
thf(3230,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__sub @ A @ B ) )
= ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mul @ A @ A ) @ ( c_2Einteger_2Eint__mul @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(449,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
= ( c_2Ewords_2Eword__add @ TA @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EQ__ADD__RCANCEL) ).
thf(2776,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
= ( c_2Ewords_2Eword__add @ TA @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(416,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ B )
=> ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
= ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__LSUB) ).
thf(2659,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ B )
=> ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
= ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(622,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EABS__DIFF @ A @ A )
= c_2Enum_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EABS__DIFF__EQS) ).
thf(3377,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EABS__DIFF @ A @ A )
= c_2Enum_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(81,axiom,
! [A: $o] :
( ( ( c_2Ebool_2ET
=> A )
= A )
& ( ( A
=> c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
=> A )
= c_2Ebool_2ET )
& ( ( A
=> A )
= c_2Ebool_2ET )
& ( ( A
=> c_2Ebool_2EF )
= ( ~ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).
thf(994,plain,
! [A: $o] :
( ( ( c_2Ebool_2ET
=> A )
= A )
& ( ( A
=> c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
=> A )
= c_2Ebool_2ET )
& c_2Ebool_2ET
& ( ( A
=> c_2Ebool_2EF )
= ( ~ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(506,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
=> ( ( c_2Einteger_2Eint__lt @ B @ C )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Elt__justify__multiplication) ).
thf(2953,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
=> ( ( c_2Einteger_2Eint__lt @ B @ C )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(394,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( A
= ( c_2Einteger_2Eint__sub @ B @ C ) )
= ( ( c_2Einteger_2Eint__add @ A @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__SUB__LADD) ).
thf(2590,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( A
= ( c_2Einteger_2Eint__sub @ B @ C ) )
= ( ( c_2Einteger_2Eint__add @ A @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(167,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B )
& ( c_2Ewords_2Eword__le @ TA @ B @ A ) )
=> ( ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
& ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__LE) ).
thf(1401,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B )
& ( c_2Ewords_2Eword__le @ TA @ B @ A ) )
=> ( ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
& ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(425,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ~ ( c_2Ewords_2Eword__msb @ TA @ A )
=> ( ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
| ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2ETWO__COMP__POS) ).
thf(2686,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ~ ( c_2Ewords_2Eword__msb @ TA @ A )
=> ( ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
| ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(237,axiom,
! [A: $o] :
( ( A
| c_2Ebool_2EF )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EOR__CLAUSES__XF) ).
thf(1756,plain,
! [A: $o] :
( ( A
| c_2Ebool_2EF )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(617,axiom,
! [A: $o] :
( ( c_2EbasicSize_2Ebool__size @ A )
= c_2Enum_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EbasicSize_2Ebool__size__def) ).
thf(3361,plain,
! [A: $o] :
( ( c_2EbasicSize_2Ebool__size @ A )
= c_2Enum_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(3363,plain,
( ( c_2EbasicSize_2Ebool__size @ $false )
= c_2Enum_2E0 ),
inference(instance,[status(thm)],[3361]) ).
thf(3365,plain,
( ( c_2EbasicSize_2Ebool__size @ $false )
= c_2Enum_2E0 ),
inference(lifteq,[status(thm)],[3363]) ).
thf(232,axiom,
( c_2Ebool_2EF
= ( ! [A: $o] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EF__DEF) ).
thf(1735,plain,
( c_2Ebool_2EF
= ( ! [A: $o] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(143,axiom,
! [A: $o] :
( ( ~ A
=> c_2Ebool_2EF )
=> ( ( A
=> c_2Ebool_2EF )
=> c_2Ebool_2EF ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EAND__INV2) ).
thf(1233,plain,
! [A: $o] :
( ( ~ A
=> c_2Ebool_2EF )
=> ( ( A
=> c_2Ebool_2EF )
=> c_2Ebool_2EF ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(39,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) )
=> ! [C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2EDIV @ C @ A ) @ B )
= ( c_2Earithmetic_2EDIV @ C @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EDIV__DIV__DIV__MULT) ).
thf(814,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) )
=> ! [C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2EDIV @ C @ A ) @ B )
= ( c_2Earithmetic_2EDIV @ C @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(186,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A )
& ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CLAUSES) ).
thf(1497,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A )
& ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(278,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Eword__smod @ TA @ A @ B )
= ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__mod @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__smod__def) ).
thf(2195,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Eword__smod @ TA @ A @ B )
= ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__mod @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(526,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) )
= ( c_2Ewords_2Eword__mul @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__mul__i2w) ).
thf(3017,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) )
= ( c_2Ewords_2Eword__mul @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(522,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
= ( c_2Einteger_2Eint__neg @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LZERO) ).
thf(3004,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
= ( c_2Einteger_2Eint__neg @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(611,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
= A )
= ( B
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__INV__0__EQ) ).
thf(3332,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
= A )
= ( B
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(308,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__add @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) )
= ( c_2Ewords_2Eword__add @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__add__i2w) ).
thf(2316,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__add @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) )
= ( c_2Ewords_2Eword__add @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(641,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__RZERO) ).
thf(3446,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(10,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ B ) )
= ( ( B = c_2Enum_2E0 )
| ( c_2Earithmetic_2E_3C_3D @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELE__MULT__RCANCEL) ).
thf(715,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ B ) )
= ( ( B = c_2Enum_2E0 )
| ( c_2Earithmetic_2E_3C_3D @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(613,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ A @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__REFL) ).
thf(3338,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ A @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(271,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Eword__sdiv @ TA @ A @ B )
= ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__div @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__sdiv__def) ).
thf(2168,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Eword__sdiv @ TA @ A @ B )
= ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__div @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(6,axiom,
! [A: $o,B: $o] :
( ( c_2Ebool_2E_2F_5C @ A @ B )
= ( A
& B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_2F_5C) ).
thf(698,plain,
! [A: $o,B: $o] :
( ( c_2Ebool_2E_2F_5C @ A @ B )
= ( A
& B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(238,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ A @ B )
| ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__EQ__CASES) ).
thf(1761,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ A @ B )
| ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(60,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2D @ A @ B )
= c_2Enum_2E0 )
= ( c_2Earithmetic_2E_3C_3D @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__EQ__0) ).
thf(913,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2D @ A @ B )
= c_2Enum_2E0 )
= ( c_2Earithmetic_2E_3C_3D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(676,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__extract @ TA @ TB @ A @ B @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EXTRACT__ZERO2) ).
thf(3562,plain,
! [TA: $tType,TB: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__extract @ TA @ TB @ A @ B @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(207,axiom,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2D @ c_2Enum_2E0 @ A )
= c_2Enum_2E0 )
& ( ( c_2Earithmetic_2E_2D @ A @ c_2Enum_2E0 )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__0) ).
thf(1640,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2D @ c_2Enum_2E0 @ A )
= c_2Enum_2E0 )
& ( ( c_2Earithmetic_2E_2D @ A @ c_2Enum_2E0 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(156,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
& ( c_2Ewords_2Eword__le @ TA @ B @ C ) )
=> ( c_2Ewords_2Eword__lt @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__LESS__EQ__TRANS) ).
thf(1354,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
& ( c_2Ewords_2Eword__le @ TA @ B @ C ) )
=> ( c_2Ewords_2Eword__lt @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(266,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Enum_2E0 = A )
| ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__0__CASES) ).
thf(2146,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Enum_2E0 = A )
| ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(188,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
~ ( ( c_2Eprim__rec_2E_3C @ A @ B )
& ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__EQ__ANTISYM) ).
thf(1507,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
~ ( ( c_2Eprim__rec_2E_3C @ A @ B )
& ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(140,axiom,
! [A: $o] :
( ( c_2Ebool_2EF
| A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EOR__CLAUSES__FX) ).
thf(1222,plain,
! [A: $o] :
( ( c_2Ebool_2EF
| A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(612,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__neg @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__EQ0) ).
thf(3335,plain,
! [A: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__neg @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(512,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__sub @ A @ B ) @ C )
= ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__mul @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__RDISTRIB) ).
thf(2972,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__sub @ A @ B ) @ C )
= ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__mul @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(7,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) )
=> ( ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2E_2D @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) @ B )
= ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2EDIV @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EDIV__SUB) ).
thf(707,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) )
=> ( ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2E_2D @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) @ B )
= ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2EDIV @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(708,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
| ~ ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C )
| ( ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2E_2D @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) @ B )
= ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2EDIV @ C @ B ) @ A ) ) ),
inference(cnf,[status(esa)],[707]) ).
thf(709,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2E_2D @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) @ B )
= ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2EDIV @ C @ B ) @ A ) )
| ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
| ~ ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) ),
inference(lifteq,[status(thm)],[708]) ).
thf(94,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ELESS__NOT__EQ) ).
thf(1046,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(603,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ A )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__REFL) ).
thf(3308,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ A )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(158,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2D @ B @ A ) @ ( c_2Earithmetic_2E_2D @ C @ A ) )
= ( ( c_2Eprim__rec_2E_3C @ B @ C )
& ( c_2Eprim__rec_2E_3C @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELT__SUB__RCANCEL) ).
thf(1359,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2D @ B @ A ) @ ( c_2Earithmetic_2E_2D @ C @ A ) )
= ( ( c_2Eprim__rec_2E_3C @ B @ C )
& ( c_2Eprim__rec_2E_3C @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(162,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Egcd_2Egcd @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__REF) ).
thf(1386,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Egcd_2Egcd @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(257,axiom,
! [A: $o] :
( ( A
& c_2Ebool_2EF )
= c_2Ebool_2EF ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EAND__CLAUSES__XF) ).
thf(2082,plain,
! [A: $o] :
( ( A
& c_2Ebool_2EF )
= c_2Ebool_2EF ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(227,axiom,
( ( ~ c_2Ebool_2EF ) = c_2Ebool_2ET ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ENOT__CLAUSES__F) ).
thf(1724,plain,
( ( ~ c_2Ebool_2EF ) = c_2Ebool_2ET ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(461,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__add @ A @ C ) )
= ( c_2Einteger_2Eint__lt @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__LADD) ).
thf(2819,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__add @ A @ C ) )
= ( c_2Einteger_2Eint__lt @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(191,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
=> ( c_2Ewords_2Eword__le @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__IMP__LESS__OR__EQ) ).
thf(1518,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
=> ( c_2Ewords_2Eword__le @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(334,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__NEG) ).
thf(2405,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(507,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ A ) @ ( c_2Einteger_2Eint__mul @ B @ B ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( B
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUMSQ) ).
thf(2957,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ A ) @ ( c_2Einteger_2Eint__mul @ B @ B ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( B
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(553,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LET__ADD) ).
thf(3103,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(57,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ B @ A ) @ ( c_2Earithmetic_2E_2D @ C @ A ) )
= ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
| ( c_2Earithmetic_2E_3C_3D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELE__SUB__RCANCEL) ).
thf(898,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ B @ A ) @ ( c_2Earithmetic_2E_2D @ C @ A ) )
= ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
| ( c_2Earithmetic_2E_3C_3D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(146,axiom,
! [A: $o,B: $o,C: $o,D: $o,E: $o] :
( ( C
=> B )
=> ( ( A
=> D )
=> ( ( c_2Ebool_2ECOND @ $o @ E @ C @ A )
=> ( c_2Ebool_2ECOND @ $o @ E @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EMONO__COND) ).
thf(1243,plain,
! [A: $o,B: $o,C: $o,D: $o,E: $o] :
( ( C
=> B )
=> ( ( A
=> D )
=> ( ( c_2Ebool_2ECOND @ $o @ E @ C @ A )
=> ( c_2Ebool_2ECOND @ $o @ E @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(116,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__le @ TA @ A @ B )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2EWORD__LEi) ).
thf(1127,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__le @ TA @ A @ B )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(516,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( ( c_2Einteger_2Eint__mod @ A @ B )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
=> ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__mul @ C @ A ) @ B )
= ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__div @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__DIV) ).
thf(2985,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( ( c_2Einteger_2Eint__mod @ A @ B )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
=> ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__mul @ C @ A ) @ B )
= ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__div @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(289,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ! [B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__mul @ B @ A ) @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__COMMON__FACTOR) ).
thf(2227,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ! [B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__mul @ B @ A ) @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType] :
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__mul @ TB @ ( c_2Ewords_2En2w @ TB @ A ) @ ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ B ) ) )
= ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ A ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ B ) ) )
= ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LITERAL__MULT) ).
thf(841,plain,
! [TA: $tType,TB: $tType] :
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__mul @ TB @ ( c_2Ewords_2En2w @ TB @ A ) @ ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ B ) ) )
= ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ A ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ B ) ) )
= ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(661,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__mod @ B @ A ) @ A )
= ( c_2Einteger_2Eint__mod @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__MOD) ).
thf(3513,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__mod @ B @ A ) @ A )
= ( c_2Einteger_2Eint__mod @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(254,axiom,
! [A: $o,B: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2EF @ B )
= ( ~ A
& B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ECOND__CLAUSES__TF) ).
thf(2067,plain,
! [A: $o,B: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2EF @ B )
= ( ~ A
& B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(463,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__neg @ A ) )
= ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__GE0) ).
thf(2825,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__neg @ A ) )
= ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(13,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Earithmetic_2E_3C_3D @ C @ A ) )
=> ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) @ A )
= ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ A @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__TIMES__SUB) ).
thf(724,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Earithmetic_2E_3C_3D @ C @ A ) )
=> ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) @ A )
= ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ A @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(584,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ B )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Elt__move__all__left) ).
thf(3221,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ B )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(530,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
=> ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__ADD) ).
thf(3029,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
=> ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(556,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
= ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__ASSOC) ).
thf(3116,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
= ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(316,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__LT0) ).
thf(2339,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(655,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__mul @ A @ B )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
| ( B
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ENTIRE) ).
thf(3495,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__mul @ A @ B )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
| ( B
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(680,axiom,
! [TA: $tType] :
~ ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__0__POS) ).
thf(3573,plain,
! [TA: $tType] :
~ ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(3574,plain,
! [TA: $tType] :
~ ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(cnf,[status(esa)],[3573]) ).
thf(366,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
| ( c_2Ewords_2Eword__ls @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__EQ__CASES) ).
thf(2501,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
| ( c_2Ewords_2Eword__ls @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(285,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ealignment_2Ealign @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealigned__align) ).
thf(2217,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ealignment_2Ealign @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(149,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ~ ( c_2Ewords_2Eword__lt @ TA @ A @ B ) )
= ( c_2Ewords_2Eword__le @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NOT__LESS) ).
thf(1323,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ~ ( c_2Ewords_2Eword__lt @ TA @ A @ B ) )
= ( c_2Ewords_2Eword__le @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(701,plain,
( ( c_2Ebool_2E_2F_5C @ $true @ $false )
= ( $true
& $false ) ),
inference(instance,[status(thm)],[698]) ).
thf(702,plain,
~ ( c_2Ebool_2E_2F_5C @ $true @ $false ),
inference(simp,[status(thm)],[701]) ).
thf(35,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ A @ B )
= c_2Enum_2E0 )
= ( ( A = c_2Enum_2E0 )
| ( B = c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__EQ__0) ).
thf(802,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ A @ B )
= c_2Enum_2E0 )
= ( ( A = c_2Enum_2E0 )
| ( B = c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(548,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
=> ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__MUL) ).
thf(3089,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
=> ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(487,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ A ) )
= ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__POASQ) ).
thf(2897,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ A ) )
= ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(355,axiom,
! [TA: $tType] :
( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__L @ TA ) )
= ( c_2Ewords_2Eword__L @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__L) ).
thf(2466,plain,
! [TA: $tType] :
( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__L @ TA ) )
= ( c_2Ewords_2Eword__L @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(398,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__neg @ A ) @ B )
= ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__sub @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__NEG__NUMERATOR) ).
thf(2603,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__neg @ A ) @ B )
= ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__sub @ B @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(493,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__SUB) ).
thf(2916,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(429,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( C
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( ( ( c_2Einteger_2Eint__mod @ A @ C )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
| ( ( c_2Einteger_2Eint__mod @ B @ C )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) )
=> ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__add @ A @ B ) @ C )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__div @ A @ C ) @ ( c_2Einteger_2Eint__div @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__DIV) ).
thf(2698,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( C
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( ( ( c_2Einteger_2Eint__mod @ A @ C )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
| ( ( c_2Einteger_2Eint__mod @ B @ C )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) )
=> ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__add @ A @ B ) @ C )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__div @ A @ C ) @ ( c_2Einteger_2Eint__div @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(212,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B != c_2Enum_2E0 )
=> ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV) ).
thf(1660,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B != c_2Enum_2E0 )
=> ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(67,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMODEQ @ A @ C @ B )
= ( ( ( A = c_2Enum_2E0 )
& ( C = B ) )
| ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( ( c_2Earithmetic_2EMOD @ C @ A )
= ( c_2Earithmetic_2EMOD @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__THM) ).
thf(949,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMODEQ @ A @ C @ B )
= ( ( ( A = c_2Enum_2E0 )
& ( C = B ) )
| ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( ( c_2Earithmetic_2EMOD @ C @ A )
= ( c_2Earithmetic_2EMOD @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(438,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
= ( ( ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2Eword__L @ TA ) @ A )
& ( ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__L @ TA ) )
| ( c_2Ewords_2Eword__lo @ TA @ A @ B ) ) )
| ( ( c_2Ewords_2Eword__lo @ TA @ A @ ( c_2Ewords_2Eword__L @ TA ) )
& ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__L @ TA ) )
& ( c_2Ewords_2Eword__lo @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LT__LO) ).
thf(2745,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
= ( ( ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2Eword__L @ TA ) @ A )
& ( ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__L @ TA ) )
| ( c_2Ewords_2Eword__lo @ TA @ A @ B ) ) )
| ( ( c_2Ewords_2Eword__lo @ TA @ A @ ( c_2Ewords_2Eword__L @ TA ) )
& ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__L @ TA ) )
& ( c_2Ewords_2Eword__lo @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(389,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) )
= ( c_2Ewords_2Eword__mul @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__mul__i2w__w2n) ).
thf(2571,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) )
= ( c_2Ewords_2Eword__mul @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(40,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ B @ A ) @ B )
= ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( A = c_2Enum_2E0 ) ) )
& ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ B @ A ) @ A )
= ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( B = c_2Enum_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELT__MULT__CANCEL__RBARE) ).
thf(817,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ B @ A ) @ B )
= ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( A = c_2Enum_2E0 ) ) )
& ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ B @ A ) @ A )
= ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( B = c_2Enum_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(662,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__bits @ TA @ A @ B @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__BITS__ZERO2) ).
thf(3517,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__bits @ TA @ A @ B @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(620,axiom,
! [TA: $tType] :
( ( c_2Ewords_2Eword__L @ TA )
!= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2ENOT__INT__MIN__ZERO) ).
thf(3372,plain,
! [TA: $tType] :
( ( c_2Ewords_2Eword__L @ TA )
!= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(3373,plain,
! [TA: $tType] :
( ( c_2Ewords_2Eword__L @ TA )
!= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(cnf,[status(esa)],[3372]) ).
thf(3374,plain,
! [TA: $tType] :
( ( c_2Ewords_2Eword__L @ TA )
!= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(lifteq,[status(thm)],[3373]) ).
thf(225,axiom,
! [A: $o,B: $o,C: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ B @ C )
= ( ( ~ A
| B )
& ( A
| C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__EXPAND) ).
thf(1704,plain,
! [A: $o,B: $o,C: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ B @ C )
= ( ( ~ A
| B )
& ( A
| C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(446,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) @ C )
= ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADDNEG2) ).
thf(2767,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) @ C )
= ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(76,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Egcd_2Egcd @ A @ B )
= c_2Enum_2E0 )
= ( ( A = c_2Enum_2E0 )
& ( B = c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__EQ__0) ).
thf(969,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Egcd_2Egcd @ A @ B )
= c_2Enum_2E0 )
= ( ( A = c_2Enum_2E0 )
& ( B = c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(86,axiom,
! [A: $o,B: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ B @ c_2Ebool_2EF )
= ( A
& B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ECOND__CLAUSES__FF) ).
thf(1017,plain,
! [A: $o,B: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ B @ c_2Ebool_2EF )
= ( A
& B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(1024,plain,
( ( c_2Ebool_2ECOND @ $o @ $false @ $false @ c_2Ebool_2EF )
= ( $false
& $false ) ),
inference(instance,[status(thm)],[1017]) ).
thf(1025,plain,
~ ( c_2Ebool_2ECOND @ $o @ $false @ $false @ c_2Ebool_2EF ),
inference(simp,[status(thm)],[1024]) ).
thf(78,axiom,
! [A: $o] :
( c_2Ebool_2EF
=> A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2Efalse__imp) ).
thf(981,plain,
! [A: $o] :
( c_2Ebool_2EF
=> A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(984,plain,
( c_2Ebool_2EF
=> $false ),
inference(instance,[status(thm)],[981]) ).
thf(985,plain,
~ c_2Ebool_2EF,
inference(simp,[status(thm)],[984]) ).
thf(3951,plain,
~ ( c_2Ebool_2ECOND @ $o @ $false @ $false @ $false ),
inference(rewrite,[status(thm)],[1025,985]) ).
thf(472,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Efcp_2Ecart @ $o @ TB] :
( ( c_2Ewords_2Ew2w @ TB @ TA @ A )
= ( c_2Ewords_2En2w @ TA @ ( c_2Ewords_2Ew2n @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Ew2w__def) ).
thf(2852,plain,
! [TA: $tType,TB: $tType,A: tyop_2Efcp_2Ecart @ $o @ TB] :
( ( c_2Ewords_2Ew2w @ TB @ TA @ A )
= ( c_2Ewords_2En2w @ TA @ ( c_2Ewords_2Ew2n @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(593,axiom,
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B != c_2Enum_2E0 )
=> ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ) )
& ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__div @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__of__num @ A )
= ( c_2Einteger_2Eint__of__num @ B ) )
= ( A = B ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__neg @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__CALCULATE) ).
thf(3258,plain,
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B != c_2Enum_2E0 )
=> ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ) )
& ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__div @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__of__num @ A )
= ( c_2Einteger_2Eint__of__num @ B ) )
= ( A = B ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__neg @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(464,axiom,
! [TA: $tType] : ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2Eword__L @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__L__NEG) ).
thf(2828,plain,
! [TA: $tType] : ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2Eword__L @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(2829,plain,
! [TA: $tType] : ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2Eword__L @ TA ) ),
inference(cnf,[status(esa)],[2828]) ).
thf(199,axiom,
( c_2Ebool_2ET
= ( ( ^ [A: $o] : A )
= ( ^ [A: $o] : A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ET__DEF) ).
thf(1545,plain,
c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(339,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ A @ B )
& ( c_2Einteger_2Eint__le @ C @ D ) )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LTE__ADD2) ).
thf(2420,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ A @ B )
& ( c_2Einteger_2Eint__le @ C @ D ) )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(166,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
= ( c_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LS) ).
thf(1398,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
= ( c_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(114,axiom,
! [TA: $tType,A: TA > $o,B: TA > TA] :
? [C: TA > TA] :
! [D: TA] :
( ( C @ D )
= ( c_2Ebool_2ECOND @ TA @ ( A @ D ) @ D @ ( C @ ( B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewhile_2EITERATION) ).
thf(1115,plain,
! [TA: $tType,A: TA > $o,B: TA > TA] :
? [C: TA > TA] :
! [D: TA] :
( ( C @ D )
= ( c_2Ebool_2ECOND @ TA @ ( A @ D ) @ D @ ( C @ ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(409,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ B ) )
=> ( ( c_2Einteger_2Eint__lt @ B @ A )
=> ( ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
= ( c_2Einteger_2Eint__add @ C @ A ) )
= c_2Ebool_2EF ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ele__context__rwt3) ).
thf(2635,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ B ) )
=> ( ( c_2Einteger_2Eint__lt @ B @ A )
=> ( ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
= ( c_2Einteger_2Eint__add @ C @ A ) )
= c_2Ebool_2EF ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(373,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__div @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__NEG) ).
thf(2520,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__div @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(433,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
~ ( ( c_2Einteger_2Eint__le @ A @ B )
& ( c_2Einteger_2Eint__lt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LTE__ANTSYM) ).
thf(2730,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
~ ( ( c_2Einteger_2Eint__le @ A @ B )
& ( c_2Einteger_2Eint__lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(517,axiom,
! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( C
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( A @ ( c_2Einteger_2Eint__mod @ B @ C ) )
= ( ! [D: tyop_2Einteger_2Eint,E: tyop_2Einteger_2Eint] :
( ( ( B
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ C ) @ E ) )
& ( ( ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__lt @ C @ E )
& ( c_2Einteger_2Eint__le @ E @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ( ~ ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ E )
& ( c_2Einteger_2Eint__lt @ E @ C ) ) ) )
=> ( A @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__FORALL__P) ).
thf(2989,plain,
! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( C
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( A @ ( c_2Einteger_2Eint__mod @ B @ C ) )
= ( ! [D: tyop_2Einteger_2Eint,E: tyop_2Einteger_2Eint] :
( ( ( B
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ C ) @ E ) )
& ( ( ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__lt @ C @ E )
& ( c_2Einteger_2Eint__le @ E @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ( ~ ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ E )
& ( c_2Einteger_2Eint__lt @ E @ C ) ) ) )
=> ( A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(159,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__quot @ A @ B )
= ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) @ ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ ( c_2Einteger_2ENum @ A ) @ ( c_2Einteger_2ENum @ B ) ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ A ) ) @ ( c_2Einteger_2ENum @ B ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ ( c_2Einteger_2ENum @ A ) @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ B ) ) ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ A ) ) @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2Eint__quot) ).
thf(1362,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__quot @ A @ B )
= ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) @ ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ ( c_2Einteger_2ENum @ A ) @ ( c_2Einteger_2ENum @ B ) ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ A ) ) @ ( c_2Einteger_2ENum @ B ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ ( c_2Einteger_2ENum @ A ) @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ B ) ) ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ A ) ) @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(329,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( C
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ B @ C ) @ A ) @ C )
= ( c_2Einteger_2Eint__mod @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__ADD__MULTIPLES) ).
thf(2388,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( C
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ B @ C ) @ A ) @ C )
= ( c_2Einteger_2Eint__mod @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(378,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) )
= ( c_2Ewords_2Eword__add @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__add__i2w__w2n) ).
thf(2533,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) )
= ( c_2Ewords_2Eword__add @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(287,axiom,
! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__REFL) ).
thf(2222,plain,
! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(607,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ A @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__ID) ).
thf(3322,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ A @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(130,axiom,
! [A: $o,B: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ B @ c_2Ebool_2ET )
= ( A
=> B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ECOND__CLAUSES__FT) ).
thf(1170,plain,
! [A: $o,B: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ B @ c_2Ebool_2ET )
= ( A
=> B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(1173,plain,
( ( c_2Ebool_2ECOND @ $o @ $true @ $false @ c_2Ebool_2ET )
= ( $true
=> $false ) ),
inference(instance,[status(thm)],[1170]) ).
thf(1174,plain,
~ ( c_2Ebool_2ECOND @ $o @ $true @ $false @ c_2Ebool_2ET ),
inference(simp,[status(thm)],[1173]) ).
thf(3966,plain,
~ ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $true ),
inference(rewrite,[status(thm)],[1174,883]) ).
thf(31,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ B ) )
= ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Eprim__rec_2E_3C @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELT__MULT__RCANCEL) ).
thf(789,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ B ) )
= ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Eprim__rec_2E_3C @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(259,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( A = B )
=> ~ ( c_2Eprim__rec_2E_3C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ENOT__LESS__EQ) ).
thf(2090,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( A = B )
=> ~ ( c_2Eprim__rec_2E_3C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(598,axiom,
( c_2Enum_2E0
= ( c_2Enum_2EABS__num @ c_2Enum_2EZERO__REP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enum_2EZERO__DEF) ).
thf(3294,plain,
( c_2Enum_2E0
= ( c_2Enum_2EABS__num @ c_2Enum_2EZERO__REP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(3295,plain,
( ( c_2Enum_2EABS__num @ c_2Enum_2EZERO__REP )
= c_2Enum_2E0 ),
inference(lifteq,[status(thm)],[3294]) ).
thf(171,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A )
& ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B ) )
=> ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
= ( c_2Ewords_2Eword__lo @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LT__EQ__LO) ).
thf(1418,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A )
& ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B ) )
=> ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
= ( c_2Ewords_2Eword__lo @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(664,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__LZERO) ).
thf(3525,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(496,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__add @ A @ B ) @ C )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__mul @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__RDISTRIB) ).
thf(2925,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__add @ A @ B ) @ C )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__mul @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(74,axiom,
! [A: $o] :
( ( A
=> A )
= c_2Ebool_2ET ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CLAUSES__XX) ).
thf(966,plain,
c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(184,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
=> ( ( c_2Earithmetic_2EDIV @ A @ B )
= c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__DIV__EQ__ZERO) ).
thf(1489,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
=> ( ( c_2Earithmetic_2EDIV @ A @ B )
= c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(505,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__add @ B @ C ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ C ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ele__move__right__left) ).
thf(2950,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__add @ B @ C ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(293,axiom,
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B != c_2Enum_2E0 )
=> ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EMOD @ A @ B ) ) ) )
& ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__neg @ A ) @ B )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__rem @ A @ B ) ) )
& ( ( c_2Einteger_2Eint__rem @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__rem @ A @ B ) ) ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
= A )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__of__num @ A )
= ( c_2Einteger_2Eint__of__num @ B ) )
= ( A = B ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__neg @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM__CALCULATE) ).
thf(2237,plain,
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B != c_2Enum_2E0 )
=> ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EMOD @ A @ B ) ) ) )
& ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__neg @ A ) @ B )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__rem @ A @ B ) ) )
& ( ( c_2Einteger_2Eint__rem @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__rem @ A @ B ) ) ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
= A )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__of__num @ A )
= ( c_2Einteger_2Eint__of__num @ B ) )
= ( A = B ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__neg @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(170,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ A @ B )
=> ? [C: tyop_2Enum_2Enum] :
( A
= ( c_2Earithmetic_2E_2D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__EQUAL__DIFF) ).
thf(1415,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ A @ B )
=> ? [C: tyop_2Enum_2Enum] :
( A
= ( c_2Earithmetic_2E_2D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(486,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__mul @ A @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__LMUL) ).
thf(2893,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__mul @ A @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(204,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
& ( c_2Earithmetic_2E_3C_3D @ A @ C ) )
=> ( ( ( c_2Earithmetic_2E_2D @ B @ A )
= ( c_2Earithmetic_2E_2D @ C @ A ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ECANCEL__SUB) ).
thf(1632,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
& ( c_2Earithmetic_2E_3C_3D @ A @ C ) )
=> ( ( ( c_2Earithmetic_2E_2D @ B @ A )
= ( c_2Earithmetic_2E_2D @ C @ A ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(356,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2EABS @ B )
= ( c_2Einteger_2EABS @ A ) )
= ( ( B = A )
| ( B
= ( c_2Einteger_2Eint__neg @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__EQ__ABS) ).
thf(2469,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2EABS @ B )
= ( c_2Einteger_2EABS @ A ) )
= ( ( B = A )
| ( B
= ( c_2Einteger_2Eint__neg @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(119,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ? [D: tyop_2Einteger_2Eint] :
( ( A
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ B ) @ C ) )
& ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ B @ C ) @ ( c_2Einteger_2Eint__le @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C ) @ ( c_2Einteger_2Eint__lt @ C @ B ) ) ) )
=> ( ( c_2Einteger_2Eint__mod @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__UNIQUE) ).
thf(1136,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ? [D: tyop_2Einteger_2Eint] :
( ( A
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ B ) @ C ) )
& ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ B @ C ) @ ( c_2Einteger_2Eint__le @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C ) @ ( c_2Einteger_2Eint__lt @ C @ B ) ) ) )
=> ( ( c_2Einteger_2Eint__mod @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(44,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) )
=> ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__MULT2) ).
thf(834,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) )
=> ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(252,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( A = B )
=> ~ ( c_2Ewords_2Eword__lt @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NOT__LESS__EQ) ).
thf(2058,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( A = B )
=> ~ ( c_2Ewords_2Eword__lt @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(1,conjecture,
! [TA: $tType] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__0) ).
thf(2,negated_conjecture,
~ ! [TA: $tType] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(687,plain,
~ ! [TA: $tType] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(541,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ A @ C )
= ( c_2Einteger_2Eint__add @ B @ C ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__RADD) ).
thf(3068,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ A @ C )
= ( c_2Einteger_2Eint__add @ B @ C ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(475,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__neg @ A )
= B )
= ( A
= ( c_2Einteger_2Eint__neg @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__EQ) ).
thf(2861,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__neg @ A )
= B )
= ( A
= ( c_2Einteger_2Eint__neg @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(70,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ B @ A )
=> ( ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ A @ B ) )
= ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2En2w @ TA @ A ) @ ( c_2Ewords_2En2w @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2En2w__sub) ).
thf(956,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ B @ A )
=> ( ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ A @ B ) )
= ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2En2w @ TA @ A ) @ ( c_2Ewords_2En2w @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(26,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__exp @ ( c_2Einteger_2Eint__exp @ C @ B ) @ A )
= ( c_2Einteger_2Eint__exp @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EXP__MULTIPLY__EXPONENTS) ).
thf(774,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__exp @ ( c_2Einteger_2Eint__exp @ C @ B ) @ A )
= ( c_2Einteger_2Eint__exp @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(569,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
= ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LDISTRIB) ).
thf(3157,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
= ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(155,axiom,
! [TA: $tType,TB: $tType,A: $o,B: TB > TA,C: TB > TA] :
( ( ^ [D: TB] : ( c_2Ebool_2ECOND @ TA @ A @ ( B @ D ) @ ( C @ D ) ) )
= ( c_2Ebool_2ECOND @ ( TB > TA ) @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__ABS) ).
thf(1351,plain,
! [TA: $tType,TB: $tType,A: $o,B: TB > TA,C: TB > TA] :
( ( ^ [D: TB] : ( c_2Ebool_2ECOND @ TA @ A @ ( B @ D ) @ ( C @ D ) ) )
= ( c_2Ebool_2ECOND @ ( TB > TA ) @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(299,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( A != c_2Enum_2E0 )
=> ( ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ A ) @ B )
= C )
= ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ A ) @ C )
& ( B
= ( c_2Einteger_2Eint__div @ C @ ( c_2Einteger_2Eint__of__num @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eelim__eq__coeffs) ).
thf(2286,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( A != c_2Enum_2E0 )
=> ( ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ A ) @ B )
= C )
= ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ A ) @ C )
& ( B
= ( c_2Einteger_2Eint__div @ C @ ( c_2Einteger_2Eint__of__num @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(455,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
~ ( c_2Ewords_2Eword__lo @ TA @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__REFL) ).
thf(2804,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
~ ( c_2Ewords_2Eword__lo @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(483,axiom,
! [A: tyop_2Einteger_2Eint] :
( ~ ( c_2Einteger_2Eint__lt @ A @ c_2Einteger_2Eint__0 )
=> ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Einteger_2Eint__of__num @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__POSINT__EX) ).
thf(2884,plain,
! [A: tyop_2Einteger_2Eint] :
( ~ ( c_2Einteger_2Eint__lt @ A @ c_2Einteger_2Eint__0 )
=> ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Einteger_2Eint__of__num @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(660,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__ls @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LS__word__0) ).
thf(3510,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__ls @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(444,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ A ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__RINV) ).
thf(2762,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ A ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(626,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__mul @ A @ C )
= ( c_2Einteger_2Eint__mul @ B @ C ) )
= ( ( C
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__RMUL) ).
thf(3389,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__mul @ A @ C )
= ( c_2Einteger_2Eint__mul @ B @ C ) )
= ( ( C
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(403,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__sub @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__ADD2) ).
thf(2618,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__sub @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(466,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ A ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__DOUBLE) ).
thf(2833,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ A ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(4,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ! [B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ B @ A ) @ A )
= c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__EQ__0) ).
thf(692,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ! [B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ B @ A ) @ A )
= c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(276,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
& ( c_2Ewords_2Eword__ls @ TA @ B @ C ) )
=> ( c_2Ewords_2Eword__ls @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__EQ__TRANS) ).
thf(2190,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
& ( c_2Ewords_2Eword__ls @ TA @ B @ C ) )
=> ( c_2Ewords_2Eword__ls @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(635,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__LID) ).
thf(3421,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(688,plain,
( ( c_2Einteger__word_2Ei2w @ skt1 @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
!= ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) ),
inference(cnf,[status(esa)],[687]) ).
thf(689,plain,
( ( c_2Einteger__word_2Ei2w @ skt1 @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
!= ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) ),
inference(lifteq,[status(thm)],[688]) ).
thf(3808,plain,
( ( c_2Einteger__word_2Ei2w @ skt1 @ c_2Einteger_2Eint__0 )
!= ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) ),
inference(rewrite,[status(thm)],[689,3566]) ).
thf(374,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ A )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__LINV) ).
thf(2523,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ A )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(377,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__rem @ A @ B )
= ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__quot @ A @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2Eint__rem) ).
thf(2530,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__rem @ A @ B )
= ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__quot @ A @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(457,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ A @ C )
& ( c_2Einteger_2Eint__le @ C @ ( c_2Einteger_2Eint__add @ A @ B ) ) )
= ( ? [D: tyop_2Einteger_2Eint] :
( ( C
= ( c_2Einteger_2Eint__add @ A @ D ) )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
& ( c_2Einteger_2Eint__le @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ein__additive__range) ).
thf(2809,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ A @ C )
& ( c_2Einteger_2Eint__le @ C @ ( c_2Einteger_2Eint__add @ A @ B ) ) )
= ( ? [D: tyop_2Einteger_2Eint] :
( ( C
= ( c_2Einteger_2Eint__add @ A @ D ) )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
& ( c_2Einteger_2Eint__le @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(440,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__L @ TA ) ) )
= ( ~ ( c_2Ewords_2Eword__msb @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__msb__add__word__L) ).
thf(2750,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__L @ TA ) ) )
= ( ~ ( c_2Ewords_2Eword__msb @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(168,axiom,
( ( c_2Ebool_2ET != c_2Ebool_2EF )
& ( c_2Ebool_2EF != c_2Ebool_2ET ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EBOOL__EQ__DISTINCT) ).
thf(1405,plain,
( ( c_2Ebool_2ET != c_2Ebool_2EF )
& ( c_2Ebool_2EF != c_2Ebool_2ET ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(223,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ( ( c_2Earithmetic_2EMODEQ @ A @ C @ B )
= ( ( c_2Earithmetic_2EMOD @ C @ A )
= ( c_2Earithmetic_2EMOD @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__NONZERO__MODEQUALITY) ).
thf(1697,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ( ( c_2Earithmetic_2EMODEQ @ A @ C @ B )
= ( ( c_2Earithmetic_2EMOD @ C @ A )
= ( c_2Earithmetic_2EMOD @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(675,axiom,
! [TA: $tType] :
( ( c_2Ewords_2Eword__reverse @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__reverse__0) ).
thf(3559,plain,
! [TA: $tType] :
( ( c_2Ewords_2Eword__reverse @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(209,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ A @ B )
| ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecardinal_2ELE__CASES) ).
thf(1651,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ A @ B )
| ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(495,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__sub @ A @ B ) )
= ( c_2Einteger_2Eint__le @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LE) ).
thf(2922,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__sub @ A @ B ) )
= ( c_2Einteger_2Eint__le @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(524,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ? [D: tyop_2Einteger_2Eint] :
( ( A
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ C @ B ) @ D ) )
& ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D ) @ ( c_2Einteger_2Eint__le @ D @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ D ) @ ( c_2Einteger_2EABS @ B ) ) )
=> ( ( c_2Einteger_2Eint__quot @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__QUOT__UNIQUE) ).
thf(3011,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ? [D: tyop_2Einteger_2Eint] :
( ( A
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ C @ B ) @ D ) )
& ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D ) @ ( c_2Einteger_2Eint__le @ D @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ D ) @ ( c_2Einteger_2EABS @ B ) ) )
=> ( ( c_2Einteger_2Eint__quot @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(281,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A )
= ( c_2Ewords_2Eword__2comp @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__LZERO) ).
thf(2204,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A )
= ( c_2Ewords_2Eword__2comp @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(678,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMODEQ @ c_2Enum_2E0 @ B @ A )
= ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__0__CONG) ).
thf(3567,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMODEQ @ c_2Enum_2E0 @ B @ A )
= ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(390,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
=> ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) )
= ( c_2Einteger_2Eint__lt @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__MONO) ).
thf(2574,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
=> ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) )
= ( c_2Einteger_2Eint__lt @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(22,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ( ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2E_2A @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__DIV) ).
thf(761,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ( ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2E_2A @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(152,axiom,
! [A: $o] :
( A
=> ( A = c_2Ebool_2ET ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EEQT__Imp1) ).
thf(1338,plain,
! [A: $o] :
( A
=> ( A = c_2Ebool_2ET ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(242,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ A ) @ B )
=> ( c_2Earithmetic_2E_3C_3D @ A @ ( c_2Einteger_2ENum @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ELE__NUM__OF__INT) ).
thf(1783,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ A ) @ B )
=> ( c_2Earithmetic_2E_3C_3D @ A @ ( c_2Einteger_2ENum @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(411,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lo @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) )
= ( ( B
!= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
& ( ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
| ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__NEG__RIGHT) ).
thf(2641,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lo @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) )
= ( ( B
!= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
& ( ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
| ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(404,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADD) ).
thf(2621,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(634,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA] :
( ( c_2Earithmetic_2ENRC @ TA @ A @ c_2Enum_2E0 @ B @ C )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ENRC__0) ).
thf(3418,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA] :
( ( c_2Earithmetic_2ENRC @ TA @ A @ c_2Enum_2E0 @ B @ C )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(567,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( A
!= ( c_2Ewords_2Eword__L @ TA ) )
=> ( ( c_2Einteger__word_2Ew2i @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger__word_2Ew2i @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ew2i__neg) ).
thf(3151,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( A
!= ( c_2Ewords_2Eword__L @ TA ) )
=> ( ( c_2Einteger__word_2Ew2i @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger__word_2Ew2i @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(551,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ealignment_2Ealigned @ TA @ A @ B )
= ( ( c_2Ealignment_2Ealign @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealigned__def) ).
thf(3097,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ealignment_2Ealigned @ TA @ A @ B )
= ( ( c_2Ealignment_2Ealign @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(64,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
=> ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2EMOD @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__LESS) ).
thf(942,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
=> ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2EMOD @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(685,axiom,
! [A: tyop_2Einteger_2Eint > $o] :
( ( ! [B: tyop_2Enum_2Enum] : ( A @ ( c_2Einteger_2Eint__of__num @ B ) ) )
= ( ! [B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2EINT__NUM__FORALL) ).
thf(3591,plain,
! [A: tyop_2Einteger_2Eint > $o] :
( ( ! [B: tyop_2Enum_2Enum] : ( A @ ( c_2Einteger_2Eint__of__num @ B ) ) )
= ( ! [B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(491,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
~ ( ( c_2Einteger_2Eint__lt @ A @ B )
& ( c_2Einteger_2Eint__lt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ANTISYM) ).
thf(2910,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
~ ( ( c_2Einteger_2Eint__lt @ A @ B )
& ( c_2Einteger_2Eint__lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(666,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Ebit__count @ TA @ A )
= c_2Enum_2E0 )
= ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Ebit__count__is__zero) ).
thf(3531,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Ebit__count @ TA @ A )
= c_2Enum_2E0 )
= ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(325,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__divides @ A @ B )
& ( c_2Einteger_2Eint__divides @ B @ C ) )
=> ( c_2Einteger_2Eint__divides @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__TRANS) ).
thf(2364,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__divides @ A @ B )
& ( c_2Einteger_2Eint__divides @ B @ C ) )
=> ( c_2Einteger_2Eint__divides @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(291,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__SUB2) ).
thf(2232,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(302,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( A = B )
= ( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__move__all__left) ).
thf(2296,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( A = B )
= ( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(9,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ A @ C )
& ( c_2Eprim__rec_2E_3C @ B @ D ) )
=> ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2ELESS__MULT__MONO2) ).
thf(713,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ A @ C )
& ( c_2Eprim__rec_2E_3C @ B @ D ) )
=> ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(714,plain,
! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ A @ C )
| ~ ( c_2Eprim__rec_2E_3C @ B @ D )
| ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ D ) ) ),
inference(cnf,[status(esa)],[713]) ).
thf(245,axiom,
c_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(1868,plain,
c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(672,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( ( c_2Einteger_2Eint__mul @ A @ B )
= ( c_2Einteger_2Eint__mul @ A @ C ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__LMUL__IMP) ).
thf(3550,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( ( c_2Einteger_2Eint__mul @ A @ B )
= ( c_2Einteger_2Eint__mul @ A @ C ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(448,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__add @ B @ A ) )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ C @ B ) @ ( c_2Einteger_2Eint__mul @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LDISTRIB) ).
thf(2773,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__add @ B @ A ) )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ C @ B ) @ ( c_2Einteger_2Eint__mul @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(533,axiom,
! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ! [D: tyop_2Einteger_2Eint] :
( ( A @ D )
=> ( A @ ( c_2Einteger_2Eint__sub @ D @ B ) ) )
& ( A @ C ) )
=> ! [D: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
=> ( A @ ( c_2Einteger_2Eint__sub @ C @ ( c_2Einteger_2Eint__mul @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Etop__and__lessers) ).
thf(3037,plain,
! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ! [D: tyop_2Einteger_2Eint] :
( ( A @ D )
=> ( A @ ( c_2Einteger_2Eint__sub @ D @ B ) ) )
& ( A @ C ) )
=> ! [D: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
=> ( A @ ( c_2Einteger_2Eint__sub @ C @ ( c_2Einteger_2Eint__mul @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(127,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) )
= ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__LMUL) ).
thf(1163,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) )
= ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(421,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ealignment_2Ealigned @ TA @ A @ B )
& ( c_2Ealignment_2Ealigned @ TA @ A @ C ) )
=> ( ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
& ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealigned__add__sub__cor) ).
thf(2673,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ealignment_2Ealigned @ TA @ A @ B )
& ( c_2Ealignment_2Ealigned @ TA @ A @ C ) )
=> ( ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
& ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(297,axiom,
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B != c_2Enum_2E0 )
=> ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ) )
& ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__neg @ A ) @ B )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__quot @ A @ B ) ) )
& ( ( c_2Einteger_2Eint__quot @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__quot @ A @ B ) ) ) ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__of__num @ A )
= ( c_2Einteger_2Eint__of__num @ B ) )
= ( A = B ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__neg @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__QUOT__CALCULATE) ).
thf(2264,plain,
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B != c_2Enum_2E0 )
=> ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ) )
& ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__neg @ A ) @ B )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__quot @ A @ B ) ) )
& ( ( c_2Einteger_2Eint__quot @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__quot @ A @ B ) ) ) ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__of__num @ A )
= ( c_2Einteger_2Eint__of__num @ B ) )
= ( A = B ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__neg @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(59,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
& ( c_2Earithmetic_2E_3C_3D @ C @ A ) )
=> ( ( ( c_2Earithmetic_2E_2D @ A @ B )
= ( c_2Earithmetic_2E_2D @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__CANCEL) ).
thf(910,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
& ( c_2Earithmetic_2E_3C_3D @ C @ A ) )
=> ( ( ( c_2Earithmetic_2E_2D @ A @ B )
= ( c_2Earithmetic_2E_2D @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(107,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
= ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecardinal_2ELT__LE) ).
thf(1091,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
= ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(342,axiom,
! [TA: $tType] : ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__L @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EZERO__LO__INT__MIN) ).
thf(2428,plain,
! [TA: $tType] : ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__L @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(528,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ B )
=> ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__add @ B @ C ) )
= ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__LADD) ).
thf(3022,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ B )
=> ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__add @ B @ C ) )
= ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(214,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) @ A )
= ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__mul @ TA @ B @ A ) @ ( c_2Ewords_2Eword__mul @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__RIGHT__SUB__DISTRIB) ).
thf(1666,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) @ A )
= ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__mul @ TA @ B @ A ) @ ( c_2Ewords_2Eword__mul @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(511,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ B ) @ C )
= ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Elt__move__left__right) ).
thf(2969,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ B ) @ C )
= ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(588,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ! [B: tyop_2Einteger_2Eint] :
( ( B
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__quot @ B @ A ) @ A ) @ ( c_2Einteger_2Eint__rem @ B @ A ) ) )
& ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__rem @ B @ A ) ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__rem @ B @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__rem @ B @ A ) ) @ ( c_2Einteger_2EABS @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REMQUOT) ).
thf(3233,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ! [B: tyop_2Einteger_2Eint] :
( ( B
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__quot @ B @ A ) @ A ) @ ( c_2Einteger_2Eint__rem @ B @ A ) ) )
& ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__rem @ B @ A ) ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__rem @ B @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__rem @ B @ A ) ) @ ( c_2Einteger_2EABS @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(399,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Egcd_2Elcm @ B @ A )
= ( c_2Egcd_2Elcm @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2ELCM__COMM) ).
thf(2606,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Egcd_2Elcm @ B @ A )
= ( c_2Egcd_2Elcm @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(568,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
= ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2EINT__SUB__SUB3) ).
thf(3154,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
= ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(376,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ewords_2Eword__ls @ TA @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__EQ__REFL) ).
thf(2528,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ewords_2Eword__ls @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(144,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
& ( c_2Ewords_2Eword__lt @ TA @ B @ C ) )
=> ( c_2Ewords_2Eword__lt @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__EQ__LESS__TRANS) ).
thf(1238,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
& ( c_2Ewords_2Eword__lt @ TA @ B @ C ) )
=> ( c_2Ewords_2Eword__lt @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(648,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Esptree_2Espt__acc @ c_2Enum_2E0 @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esptree_2Espt__acc__0) ).
thf(3471,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Esptree_2Espt__acc @ c_2Enum_2E0 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(434,axiom,
! [TA: $tType,A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Ewords_2Eword__add @ TA @ ( c_2Einteger__word_2Ei2w @ TA @ A ) @ ( c_2Einteger__word_2Ei2w @ TA @ B ) )
= ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__i2w__add) ).
thf(2733,plain,
! [TA: $tType,A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Ewords_2Eword__add @ TA @ ( c_2Einteger__word_2Ei2w @ TA @ A ) @ ( c_2Einteger__word_2Ei2w @ TA @ B ) )
= ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(41,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2D @ A @ B ) )
= ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2EINT__NUM__SUB) ).
thf(825,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2D @ A @ B ) )
= ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(153,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
? [B: tyop_2Elist_2Elist @ $o] :
( A
= ( c_2Ebitstring_2Ev2w @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebitstring_2Ebitstring__nchotomy) ).
thf(1343,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
? [B: tyop_2Elist_2Elist @ $o] :
( A
= ( c_2Ebitstring_2Ev2w @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(386,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__NOT__EQ) ).
thf(2560,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(68,axiom,
! [A: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ c_2Enum_2E0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EZERO__LESS__EQ) ).
thf(952,plain,
! [A: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ c_2Enum_2E0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(381,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ C ) ) )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADDNEG) ).
thf(2541,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ C ) ) )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(485,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) )
= ( c_2Ewords_2Eword__sub @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__sub__i2w__w2n) ).
thf(2890,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) )
= ( c_2Ewords_2Eword__sub @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(337,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ A @ B )
= ( c_2Ewords_2Eword__add @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__COMM) ).
thf(2414,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ A @ B )
= ( c_2Ewords_2Eword__add @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(61,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum > $o] :
( ( ( C @ B )
& ! [D: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ D @ B )
=> ~ ( C @ D ) )
& ( C @ A )
& ! [D: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ D @ A )
=> ~ ( C @ D ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2ETemporal__Logic_2EWELL__ORDER__UNIQUE) ).
thf(916,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum > $o] :
( ( ( C @ B )
& ! [D: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ D @ B )
=> ~ ( C @ D ) )
& ( C @ A )
& ! [D: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ D @ A )
=> ~ ( C @ D ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(344,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ ( c_2Ewords_2Eword__2comp @ TA @ B ) )
= ( c_2Ewords_2Eword__sub @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__NEG) ).
thf(2433,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ ( c_2Ewords_2Eword__2comp @ TA @ B ) )
= ( c_2Ewords_2Eword__sub @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(51,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ A @ B )
& ( c_2Eprim__rec_2E_3C @ B @ C ) )
=> ( c_2Eprim__rec_2E_3C @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__TRANS) ).
thf(879,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ A @ B )
& ( c_2Eprim__rec_2E_3C @ B @ C ) )
=> ( c_2Eprim__rec_2E_3C @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(417,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ B )
= ( ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
| ( ( B
!= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
& ( ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B )
| ( B
= ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__LEFT__LS2) ).
thf(2663,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ B )
= ( ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
| ( ( B
!= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
& ( ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B )
| ( B
= ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(682,axiom,
! [A: tyop_2Enum_2Enum] : ( c_2Egcd_2Eis__gcd @ A @ c_2Enum_2E0 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__0R) ).
thf(3578,plain,
! [A: tyop_2Enum_2Enum] : ( c_2Egcd_2Eis__gcd @ A @ c_2Enum_2E0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(479,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Esw2sw @ TA @ TA @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Esw2sw__id) ).
thf(2872,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Esw2sw @ TA @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(179,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
= ( c_2Eprim__rec_2E_3C @ B @ A ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( ( A != c_2Enum_2E0 )
| ( B != c_2Enum_2E0 ) ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
= c_2Ebool_2EF ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__CALCULATE) ).
thf(1457,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
= ( c_2Eprim__rec_2E_3C @ B @ A ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( ( A != c_2Enum_2E0 )
| ( B != c_2Enum_2E0 ) ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
= c_2Ebool_2EF ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(202,axiom,
! [A: $o] :
( ( ( c_2Ebool_2ET
& A )
= A )
& ( ( A
& c_2Ebool_2ET )
= A )
& ( ( c_2Ebool_2EF
& A )
= c_2Ebool_2EF )
& ( ( A
& c_2Ebool_2EF )
= c_2Ebool_2EF )
& ( ( A
& A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EAND__CLAUSES) ).
thf(1624,plain,
! [A: $o] :
( ( ( c_2Ebool_2ET
& A )
= A )
& ( ( A
& c_2Ebool_2ET )
= A )
& ( ( c_2Ebool_2EF
& A )
= c_2Ebool_2EF )
& ( ( A
& c_2Ebool_2EF )
= c_2Ebool_2EF ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(400,axiom,
! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__SQUARE) ).
thf(2609,plain,
! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(54,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
= ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LO) ).
thf(889,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
= ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(125,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] : ( c_2Egcd_2Eis__gcd @ A @ B @ ( c_2Egcd_2Egcd @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__IS__GCD) ).
thf(1159,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] : ( c_2Egcd_2Eis__gcd @ A @ B @ ( c_2Egcd_2Egcd @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(211,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ? [D: tyop_2Einteger_2Eint] :
( ( A
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ C @ B ) @ D ) )
& ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ B @ D ) @ ( c_2Einteger_2Eint__le @ D @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D ) @ ( c_2Einteger_2Eint__lt @ D @ B ) ) ) )
=> ( ( c_2Einteger_2Eint__div @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__UNIQUE) ).
thf(1656,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ? [D: tyop_2Einteger_2Eint] :
( ( A
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ C @ B ) @ D ) )
& ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ B @ D ) @ ( c_2Einteger_2Eint__le @ D @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D ) @ ( c_2Einteger_2Eint__lt @ D @ B ) ) ) )
=> ( ( c_2Einteger_2Eint__div @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(535,axiom,
! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2EABS @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__POS) ).
thf(3050,plain,
! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2EABS @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(164,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( A = B )
| ( c_2Eprim__rec_2E_3C @ A @ B )
| ( c_2Eprim__rec_2E_3C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__LESS__CASES) ).
thf(1392,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( A = B )
| ( c_2Eprim__rec_2E_3C @ A @ B )
| ( c_2Eprim__rec_2E_3C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(8,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Eprim__rec_2E_3C @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) )
=> ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) @ A )
= ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ A @ ( c_2Earithmetic_2EMOD @ C @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EMOD__COMPLEMENT) ).
thf(710,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Eprim__rec_2E_3C @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) )
=> ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) @ A )
= ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ A @ ( c_2Earithmetic_2EMOD @ C @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(84,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
& ( c_2Earithmetic_2E_3C_3D @ B @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__EQUAL__ANTISYM) ).
thf(1012,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
& ( c_2Earithmetic_2E_3C_3D @ B @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(414,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ! [B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__rem @ B @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ? [C: tyop_2Einteger_2Eint] :
( B
= ( c_2Einteger_2Eint__mul @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM__EQ0) ).
thf(2653,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ! [B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__rem @ B @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ? [C: tyop_2Einteger_2Eint] :
( B
= ( c_2Einteger_2Eint__mul @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(160,axiom,
! [A: $o,B: $o,C: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ B @ C )
= ( ( A
& B )
| ( ~ A
& C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__EXPAND__OR) ).
thf(1365,plain,
! [A: $o,B: $o,C: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ B @ C )
= ( ( A
& B )
| ( ~ A
& C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(420,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
= ( c_2Einteger_2Eint__add @ C @ B ) )
=> ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ A ) )
= ( c_2Einteger_2Eint__le @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__context__rwt1) ).
thf(2670,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
= ( c_2Einteger_2Eint__add @ C @ B ) )
=> ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ A ) )
= ( c_2Einteger_2Eint__le @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(540,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Ewords_2Eword__lt @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ew2i__lt__0) ).
thf(3065,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Ewords_2Eword__lt @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(674,axiom,
! [TA: $tType,TB: $tType] :
( ( c_2Ewords_2Ew2w @ TA @ TB @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Ew2w__0) ).
thf(3556,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Ewords_2Ew2w @ TA @ TB @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(87,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2Eword__L @ TA ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__L__LESS__EQ) ).
thf(1026,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2Eword__L @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1027,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2Eword__L @ TA ) @ A ),
inference(cnf,[status(esa)],[1026]) ).
thf(312,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( A = B )
=> ( c_2Einteger_2Eint__le @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__IMP__LE) ).
thf(2327,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( A = B )
=> ( c_2Einteger_2Eint__le @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(284,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mod @ C @ A ) @ ( c_2Einteger_2Eint__mod @ B @ A ) ) @ A )
= ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__sub @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__SUB) ).
thf(2213,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mod @ C @ A ) @ ( c_2Einteger_2Eint__mod @ B @ A ) ) @ A )
= ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__sub @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(318,axiom,
! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint] :
( ( ? [C: tyop_2Einteger_2Eint] : ( A @ ( c_2Einteger_2Eint__mul @ B @ C ) ) )
= ( ? [C: tyop_2Einteger_2Eint] :
( ( A @ C )
& ( c_2Einteger_2Eint__divides @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Elcm__eliminate) ).
thf(2344,plain,
! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint] :
( ( ? [C: tyop_2Einteger_2Eint] : ( A @ ( c_2Einteger_2Eint__mul @ B @ C ) ) )
= ( ? [C: tyop_2Einteger_2Eint] :
( ( A @ C )
& ( c_2Einteger_2Eint__divides @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(363,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__le @ TA @ A @ B )
= ( ( ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2Eword__L @ TA ) @ A )
& ( ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__L @ TA ) )
| ( c_2Ewords_2Eword__ls @ TA @ A @ B ) ) )
| ( ( c_2Ewords_2Eword__lo @ TA @ A @ ( c_2Ewords_2Eword__L @ TA ) )
& ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__L @ TA ) )
& ( c_2Ewords_2Eword__ls @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LE__LS) ).
thf(2492,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__le @ TA @ A @ B )
= ( ( ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2Eword__L @ TA ) @ A )
& ( ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__L @ TA ) )
| ( c_2Ewords_2Eword__ls @ TA @ A @ B ) ) )
| ( ( c_2Ewords_2Eword__lo @ TA @ A @ ( c_2Ewords_2Eword__L @ TA ) )
& ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__L @ TA ) )
& ( c_2Ewords_2Eword__ls @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(554,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
= ( c_2Ewords_2Eword__sub @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__TRIANGLE) ).
thf(3105,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
= ( c_2Ewords_2Eword__sub @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(558,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ c_2Einteger_2Eint__0 @ A )
& ( c_2Einteger_2Eint__lt @ c_2Einteger_2Eint__0 @ B ) )
=> ( c_2Einteger_2Eint__lt @ c_2Einteger_2Eint__0 @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__MUL) ).
thf(3122,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ c_2Einteger_2Eint__0 @ A )
& ( c_2Einteger_2Eint__lt @ c_2Einteger_2Eint__0 @ B ) )
=> ( c_2Einteger_2Eint__lt @ c_2Einteger_2Eint__0 @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(454,axiom,
! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( C
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( A @ ( c_2Einteger_2Eint__div @ B @ C ) )
= ( ! [D: tyop_2Einteger_2Eint,E: tyop_2Einteger_2Eint] :
( ( ( B
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ C ) @ E ) )
& ( ( ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__lt @ C @ E )
& ( c_2Einteger_2Eint__le @ E @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ( ~ ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ E )
& ( c_2Einteger_2Eint__lt @ E @ C ) ) ) )
=> ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__FORALL__P) ).
thf(2801,plain,
! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( C
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( A @ ( c_2Einteger_2Eint__div @ B @ C ) )
= ( ! [D: tyop_2Einteger_2Eint,E: tyop_2Einteger_2Eint] :
( ( ( B
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ C ) @ E ) )
& ( ( ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__lt @ C @ E )
& ( c_2Einteger_2Eint__le @ E @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ( ~ ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ E )
& ( c_2Einteger_2Eint__lt @ E @ C ) ) ) )
=> ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(141,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ~ ( c_2Ewords_2Eword__le @ TA @ A @ B ) )
= ( c_2Ewords_2Eword__lt @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NOT__LESS__EQUAL) ).
thf(1227,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ~ ( c_2Ewords_2Eword__le @ TA @ A @ B ) )
= ( c_2Ewords_2Eword__lt @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(583,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__neg @ A )
= ( c_2Einteger_2Eint__neg @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__NEG) ).
thf(3218,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__neg @ A )
= ( c_2Einteger_2Eint__neg @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(427,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2EABS @ A ) )
= ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__0LT) ).
thf(2692,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2EABS @ A ) )
= ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(82,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__abs @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) )
= ( c_2Ewords_2Eword__abs @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__abs__neg) ).
thf(1006,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__abs @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) )
= ( c_2Ewords_2Eword__abs @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(625,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__sub @ TA @ B @ A )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EQ__SUB__ZERO) ).
thf(3386,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__sub @ TA @ B @ A )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(557,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2EABS @ A )
= A )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__EQ__ID) ).
thf(3119,plain,
! [A: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2EABS @ A )
= A )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(639,axiom,
! [A: tyop_2Enum_2Enum] :
( ( A = c_2Enum_2E0 )
| ? [B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( A
= ( c_2Enumpair_2Encons @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Enlist__cases) ).
thf(3440,plain,
! [A: tyop_2Enum_2Enum] :
( ( A = c_2Enum_2E0 )
| ? [B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( A
= ( c_2Enumpair_2Encons @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(5,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ B )
= ( c_2Earithmetic_2E_2A @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__SYM) ).
thf(695,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ B )
= ( c_2Earithmetic_2E_2A @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(696,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ B )
= ( c_2Earithmetic_2E_2A @ B @ A ) ),
inference(cnf,[status(esa)],[695]) ).
thf(697,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ B )
= ( c_2Earithmetic_2E_2A @ B @ A ) ),
inference(lifteq,[status(thm)],[696]) ).
thf(365,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__SUB) ).
thf(2498,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(268,axiom,
( ! [A: $o] :
( ( ~ ~ A )
= A )
& ( ( ~ c_2Ebool_2ET ) = c_2Ebool_2EF )
& ( ( ~ c_2Ebool_2EF ) = c_2Ebool_2ET ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__CLAUSES) ).
thf(2157,plain,
( ( ( ~ c_2Ebool_2ET ) = c_2Ebool_2EF )
& ( ( ~ c_2Ebool_2EF ) = c_2Ebool_2ET ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(468,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ealignment_2Ealigned @ TA @ A @ B )
=> ( ( c_2Ealignment_2Ealign @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealign__aligned) ).
thf(2840,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ealignment_2Ealigned @ TA @ A @ B )
=> ( ( c_2Ealignment_2Ealign @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(121,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__msb @ TA @ A )
= ( c_2Ewords_2Eword__lt @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__msb__neg) ).
thf(1143,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__msb @ TA @ A )
= ( c_2Ewords_2Eword__lt @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(109,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Egcd_2Egcd @ c_2Enum_2E0 @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__0L) ).
thf(1096,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Egcd_2Egcd @ c_2Enum_2E0 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(369,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ B )
| ( c_2Einteger_2Eint__le @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__TOTAL) ).
thf(2509,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ B )
| ( c_2Einteger_2Eint__le @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(431,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__lt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__NEG) ).
thf(2724,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(474,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__bits @ TA @ A @ B @ ( c_2Ewords_2Eword__slice @ TA @ A @ B @ C ) )
= ( c_2Ewords_2Eword__bits @ TA @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__BITS__SLICE__THM) ).
thf(2858,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__bits @ TA @ A @ B @ ( c_2Ewords_2Eword__slice @ TA @ A @ B @ C ) )
= ( c_2Ewords_2Eword__bits @ TA @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(29,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2En2w @ TA @ A ) @ ( c_2Ewords_2En2w @ TA @ B ) )
= ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__mul__n2w) ).
thf(783,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2En2w @ TA @ A ) @ ( c_2Ewords_2En2w @ TA @ B ) )
= ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(410,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ A ) @ A )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__NEGL) ).
thf(2638,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ A ) @ A )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(115,axiom,
! [A: $o,B: $o] :
( ( ~ ( B
| A )
=> c_2Ebool_2EF )
= ( ( B
=> c_2Ebool_2EF )
=> ( ~ A
=> c_2Ebool_2EF ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL2) ).
thf(1118,plain,
! [A: $o,B: $o] :
( ( ~ ( B
| A )
=> c_2Ebool_2EF )
= ( ( B
=> c_2Ebool_2EF )
=> ( ~ A
=> c_2Ebool_2EF ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(521,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2EABS @ ( c_2Einteger_2EABS @ A ) )
= ( c_2Einteger_2EABS @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__ABS) ).
thf(3001,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2EABS @ ( c_2Einteger_2EABS @ A ) )
= ( c_2Einteger_2EABS @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(80,axiom,
! [A: $o] :
( ( c_2Ebool_2ET
| A )
= c_2Ebool_2ET ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EOR__CLAUSES__TX) ).
thf(989,plain,
! [A: $o] :
( ( c_2Ebool_2ET
| A )
= c_2Ebool_2ET ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(604,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Enumpair_2Encons @ B @ A )
!= c_2Enum_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Encons__not__nnil) ).
thf(3311,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Enumpair_2Encons @ B @ A )
!= c_2Enum_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(88,axiom,
! [A: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__EQ__REFL) ).
thf(1028,plain,
! [A: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(580,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ B )
| ( c_2Einteger_2Eint__le @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LTE__TOTAL) ).
thf(3210,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ B )
| ( c_2Einteger_2Eint__le @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(550,axiom,
! [A: tyop_2Einteger_2Eint] :
~ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__LT0) ).
thf(3094,plain,
! [A: tyop_2Einteger_2Eint] :
~ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(577,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) )
= ( c_2Ewords_2Eword__sub @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__sub__i2w) ).
thf(3194,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) )
= ( c_2Ewords_2Eword__sub @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(418,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ A @ B )
& ( c_2Einteger_2Eint__le @ C @ D ) )
=> ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__ADD2) ).
thf(2666,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ A @ B )
& ( c_2Einteger_2Eint__le @ C @ D ) )
=> ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(451,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__sub @ A @ B ) )
= ( c_2Einteger_2Eint__sub @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__SUB) ).
thf(2781,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__sub @ A @ B ) )
= ( c_2Einteger_2Eint__sub @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(453,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__bits @ TA @ A @ B @ C )
= ( c_2Ewords_2Eword__extract @ TA @ TA @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__BITS__EXTRACT) ).
thf(2798,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__bits @ TA @ A @ B @ C )
= ( c_2Ewords_2Eword__extract @ TA @ TA @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(219,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ B @ A )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2E_2D @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__LESS__0) ).
thf(1683,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ B @ A )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2E_2D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(465,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Einteger__word_2Ew2i @ TA @ A )
= ( c_2Einteger__word_2Ew2i @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ew2i__11) ).
thf(2830,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Einteger__word_2Ew2i @ TA @ A )
= ( c_2Einteger__word_2Ew2i @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(132,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
=> ( ( c_2Ewords_2Eword__bits @ TA @ A @ B @ C )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__BITS__ZERO) ).
thf(1182,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
=> ( ( c_2Ewords_2Eword__bits @ TA @ A @ B @ C )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(173,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__le @ TA @ A @ B )
= ( ( ( ( c_2Ewords_2Eword__msb @ TA @ A )
= ( c_2Ewords_2Eword__msb @ TA @ B ) )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) )
| ( ( c_2Ewords_2Eword__msb @ TA @ A )
& ~ ( c_2Ewords_2Eword__msb @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LE) ).
thf(1424,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__le @ TA @ A @ B )
= ( ( ( ( c_2Ewords_2Eword__msb @ TA @ A )
= ( c_2Ewords_2Eword__msb @ TA @ B ) )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) )
| ( ( c_2Ewords_2Eword__msb @ TA @ A )
& ~ ( c_2Ewords_2Eword__msb @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(307,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ B )
=> ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__sub @ C @ B ) )
= ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RSUB) ).
thf(2312,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ B )
=> ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__sub @ C @ B ) )
= ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(351,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( ( c_2Einteger_2Eint__mod @ A @ B )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
=> ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__div @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__MUL__ID) ).
thf(2455,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( ( c_2Einteger_2Eint__mod @ A @ B )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
=> ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__div @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(514,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMODEQ @ C @ B @ A )
= ( c_2Earithmetic_2EMODEQ @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__SYM) ).
thf(2978,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMODEQ @ C @ B @ A )
= ( c_2Earithmetic_2EMODEQ @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(357,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
= ( c_2Ewords_2Eword__sub @ TA @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LCANCEL__SUB) ).
thf(2472,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
= ( c_2Ewords_2Eword__sub @ TA @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(124,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Einteger_2Eint,E: tyop_2Enum_2Enum,F: tyop_2Einteger_2Eint,G: tyop_2Einteger_2Eint,H: tyop_2Einteger_2Eint,I: tyop_2Einteger_2Eint,J: tyop_2Enum_2Enum] :
( ( ( J
= ( c_2Egcd_2Egcd @ ( c_2Earithmetic_2E_2A @ E @ A ) @ ( c_2Earithmetic_2E_2A @ C @ B ) ) )
& ( ( c_2Einteger_2Eint__of__num @ J )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ G @ ( c_2Einteger_2Eint__of__num @ E ) ) @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ H @ ( c_2Einteger_2Eint__of__num @ C ) ) @ ( c_2Einteger_2Eint__of__num @ B ) ) ) )
& ( A != c_2Enum_2E0 )
& ( B != c_2Enum_2E0 )
& ( C != c_2Enum_2E0 )
& ( E != c_2Enum_2E0 ) )
=> ( ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ C ) @ I ) @ D ) )
& ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ B ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ E ) @ I ) @ F ) ) )
= ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ J ) @ I ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ F @ ( c_2Einteger_2Eint__of__num @ A ) ) @ G ) ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ D @ ( c_2Einteger_2Eint__of__num @ B ) ) @ H ) ) )
& ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ J ) @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ C ) @ F ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ E ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ecooper__lemma__1) ).
thf(1155,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Einteger_2Eint,E: tyop_2Enum_2Enum,F: tyop_2Einteger_2Eint,G: tyop_2Einteger_2Eint,H: tyop_2Einteger_2Eint,I: tyop_2Einteger_2Eint,J: tyop_2Enum_2Enum] :
( ( ( J
= ( c_2Egcd_2Egcd @ ( c_2Earithmetic_2E_2A @ E @ A ) @ ( c_2Earithmetic_2E_2A @ C @ B ) ) )
& ( ( c_2Einteger_2Eint__of__num @ J )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ G @ ( c_2Einteger_2Eint__of__num @ E ) ) @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ H @ ( c_2Einteger_2Eint__of__num @ C ) ) @ ( c_2Einteger_2Eint__of__num @ B ) ) ) )
& ( A != c_2Enum_2E0 )
& ( B != c_2Enum_2E0 )
& ( C != c_2Enum_2E0 )
& ( E != c_2Enum_2E0 ) )
=> ( ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ C ) @ I ) @ D ) )
& ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ B ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ E ) @ I ) @ F ) ) )
= ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ J ) @ I ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ F @ ( c_2Einteger_2Eint__of__num @ A ) ) @ G ) ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ D @ ( c_2Einteger_2Eint__of__num @ B ) ) @ H ) ) )
& ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ J ) @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ C ) @ F ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ E ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(705,plain,
( ( c_2Ebool_2E_2F_5C @ $false @ $false )
= ( $false
& $false ) ),
inference(instance,[status(thm)],[698]) ).
thf(706,plain,
~ ( c_2Ebool_2E_2F_5C @ $false @ $false ),
inference(simp,[status(thm)],[705]) ).
thf(538,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2EABS @ A ) @ ( c_2Einteger_2EABS @ B ) )
= ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__MUL) ).
thf(3059,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2EABS @ A ) @ ( c_2Einteger_2EABS @ B ) )
= ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(488,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( ( c_2Einteger_2Eint__rem @ A @ B )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
=> ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__mul @ C @ A ) @ B )
= ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__quot @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__QUOT) ).
thf(2900,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( ( c_2Einteger_2Eint__rem @ A @ B )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
=> ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__mul @ C @ A ) @ B )
= ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__quot @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(322,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ C )
= ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__SUB__ASSOC) ).
thf(2355,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ C )
= ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(12,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C ) )
=> ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2EMOD @ B @ C ) )
= ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__COMMON__FACTOR) ).
thf(721,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C ) )
=> ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2EMOD @ B @ C ) )
= ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1020,plain,
( ( c_2Ebool_2ECOND @ $o @ $true @ $false @ c_2Ebool_2EF )
= ( $true
& $false ) ),
inference(instance,[status(thm)],[1017]) ).
thf(1021,plain,
~ ( c_2Ebool_2ECOND @ $o @ $true @ $false @ c_2Ebool_2EF ),
inference(simp,[status(thm)],[1020]) ).
thf(3937,plain,
~ ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $false ),
inference(rewrite,[status(thm)],[1021,985]) ).
thf(590,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mod @ C @ A ) @ ( c_2Einteger_2Eint__mod @ B @ A ) ) @ A )
= ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__add @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__PLUS) ).
thf(3247,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mod @ C @ A ) @ ( c_2Einteger_2Eint__mod @ B @ A ) ) @ A )
= ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__add @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(543,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ A @ B )
& ( c_2Einteger_2Eint__le @ B @ A ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__ANTISYM) ).
thf(3074,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ A @ B )
& ( c_2Einteger_2Eint__le @ B @ A ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(3362,plain,
( ( c_2EbasicSize_2Ebool__size @ $true )
= c_2Enum_2E0 ),
inference(instance,[status(thm)],[3361]) ).
thf(3364,plain,
( ( c_2EbasicSize_2Ebool__size @ $true )
= c_2Enum_2E0 ),
inference(lifteq,[status(thm)],[3362]) ).
thf(499,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
~ ( ( c_2Einteger_2Eint__lt @ A @ B )
& ( c_2Einteger_2Eint__le @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LET__ANTISYM) ).
thf(2932,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
~ ( ( c_2Einteger_2Eint__lt @ A @ B )
& ( c_2Einteger_2Eint__le @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(653,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Ebit__count__upto @ TA @ c_2Enum_2E0 @ A )
= c_2Enum_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Ebit__count__upto__0) ).
thf(3486,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Ebit__count__upto @ TA @ c_2Enum_2E0 @ A )
= c_2Enum_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(110,axiom,
! [A: $o,B: $o] :
( ( ~ ( B
| A )
=> c_2Ebool_2EF )
= ( ~ B
=> ( ~ A
=> c_2Ebool_2EF ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL) ).
thf(1099,plain,
! [A: $o,B: $o] :
( ( ~ ( B
| A )
=> c_2Ebool_2EF )
= ( ~ B
=> ( ~ A
=> c_2Ebool_2EF ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(123,axiom,
! [A: $o] :
( ~ A
=> ( A = c_2Ebool_2EF ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__F) ).
thf(1150,plain,
! [A: $o] :
( ~ A
=> ( A = c_2Ebool_2EF ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(182,axiom,
! [TA: $tType,A: TA,B: TA] :
? [C: $o > TA] :
( ( ( C @ c_2Ebool_2ET )
= A )
& ( ( C @ c_2Ebool_2EF )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EboolAxiom) ).
thf(1478,plain,
! [TA: $tType,A: TA,B: TA] :
? [C: $o > TA] :
( ( ( C @ c_2Ebool_2ET )
= A )
& ( ( C @ c_2Ebool_2EF )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(379,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__sub @ A @ B ) )
= ( c_2Einteger_2Eint__lt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LT) ).
thf(2536,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__sub @ A @ B ) )
= ( c_2Einteger_2Eint__lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(560,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__of__num @ A ) )
= ( c_2Einteger_2Eint__of__num @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__NUM) ).
thf(3126,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__of__num @ A ) )
= ( c_2Einteger_2Eint__of__num @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(669,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__mul @ A @ B )
= ( c_2Einteger_2Eint__mul @ A @ C ) )
= ( ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__LMUL) ).
thf(3541,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__mul @ A @ B )
= ( c_2Einteger_2Eint__mul @ A @ C ) )
= ( ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(195,axiom,
! [TA: $tType,A: TA] :
( ( A = A )
= c_2Ebool_2ET ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).
thf(1530,plain,
c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(197,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: $o,C: TB,D: TB] :
( ( A @ ( c_2Ebool_2ECOND @ TB @ B @ C @ D ) )
= ( c_2Ebool_2ECOND @ TA @ B @ ( A @ C ) @ ( A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__RAND) ).
thf(1539,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: $o,C: TB,D: TB] :
( ( A @ ( c_2Ebool_2ECOND @ TB @ B @ C @ D ) )
= ( c_2Ebool_2ECOND @ TA @ B @ ( A @ C ) @ ( A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(467,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( A = B )
=> ~ ( c_2Ewords_2Eword__lo @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NOT__LOWER__EQ) ).
thf(2836,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( A = B )
=> ~ ( c_2Ewords_2Eword__lo @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(161,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ( ( c_2Earithmetic_2EMODEQ @ A @ C @ B )
=> ( ( c_2Earithmetic_2EMOD @ C @ A )
= ( c_2Earithmetic_2EMOD @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__INTRO__CONG) ).
thf(1382,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ( ( c_2Earithmetic_2EMODEQ @ A @ C @ B )
=> ( ( c_2Earithmetic_2EMOD @ C @ A )
= ( c_2Earithmetic_2EMOD @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(392,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__sub @ A @ B ) @ C )
= ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__SUB__RADD) ).
thf(2581,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__sub @ A @ B ) @ C )
= ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(99,axiom,
! [A: $o] :
( ~ A
=> ( A = c_2Ebool_2EF ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EEQF__Imp1) ).
thf(1060,plain,
! [A: $o] :
( ~ A
=> ( A = c_2Ebool_2EF ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(95,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ A @ c_2Enum_2E0 )
= ( A = c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__EQ__0) ).
thf(1050,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ A @ c_2Enum_2E0 )
= ( A = c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(264,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__abs @ TA @ A )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ TA ) @ ( c_2Ewords_2Eword__lt @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__abs__def) ).
thf(2140,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__abs @ TA @ A )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ TA ) @ ( c_2Ewords_2Eword__lt @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(442,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__2comp @ TA @ A )
= ( c_2Ewords_2Eword__2comp @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EQ__NEG) ).
thf(2756,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__2comp @ TA @ A )
= ( c_2Ewords_2Eword__2comp @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(546,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ B ) )
=> ( ( c_2Einteger_2Eint__le @ B @ A )
=> ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ A ) )
= c_2Ebool_2ET ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ele__context__rwt1) ).
thf(3083,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ B ) )
=> ( ( c_2Einteger_2Eint__le @ B @ A )
=> ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ A ) )
= c_2Ebool_2ET ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(571,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ B )
= ( ( B
!= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
& ( ( ( A
!= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
& ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B ) )
| ( B
= ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__LEFT__LO2) ).
thf(3162,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ B )
= ( ( B
!= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
& ( ( ( A
!= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
& ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B ) )
| ( B
= ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(582,axiom,
! [A: tyop_2Einteger_2Eint] :
~ ( c_2Einteger_2Eint__lt @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__REFL) ).
thf(3215,plain,
! [A: tyop_2Einteger_2Eint] :
~ ( c_2Einteger_2Eint__lt @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(194,axiom,
! [A: $o] :
( ~ A
=> ( A
=> c_2Ebool_2EF ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EF__IMP) ).
thf(1525,plain,
! [A: $o] :
( ~ A
=> ( A
=> c_2Ebool_2EF ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(151,axiom,
! [A: $o] :
( ( A
=> c_2Ebool_2EF )
= ( ~ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CLAUSES__XF) ).
thf(1333,plain,
! [A: $o] :
( ( A
=> c_2Ebool_2EF )
= ( ~ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(175,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B != c_2Enum_2E0 )
=> ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EMOD @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD) ).
thf(1434,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B != c_2Enum_2E0 )
=> ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EMOD @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(147,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
~ ( c_2Ewords_2Eword__lt @ TA @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__REFL) ).
thf(1318,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
~ ( c_2Ewords_2Eword__lt @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(383,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( ( c_2Einteger_2EABS @ A )
= B )
= ( ( ( A = B )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
| ( ( A
= ( c_2Einteger_2Eint__neg @ B ) )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ) ) )
& ( ( B
= ( c_2Einteger_2EABS @ A ) )
= ( ( ( A = B )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
| ( ( A
= ( c_2Einteger_2Eint__neg @ B ) )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__EQ) ).
thf(2546,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( ( c_2Einteger_2EABS @ A )
= B )
= ( ( ( A = B )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
| ( ( A
= ( c_2Einteger_2Eint__neg @ B ) )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ) ) )
& ( ( B
= ( c_2Einteger_2EABS @ A ) )
= ( ( ( A = B )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
| ( ( A
= ( c_2Einteger_2Eint__neg @ B ) )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(36,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2E_2D @ A @ B ) @ C )
= ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ A @ C ) @ ( c_2Earithmetic_2E_2A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ERIGHT__SUB__DISTRIB) ).
thf(805,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2E_2D @ A @ B ) @ C )
= ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ A @ C ) @ ( c_2Earithmetic_2E_2A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(596,axiom,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Egcd_2Elcm @ c_2Enum_2E0 @ A )
= c_2Enum_2E0 )
& ( ( c_2Egcd_2Elcm @ A @ c_2Enum_2E0 )
= c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2ELCM__0) ).
thf(3279,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Egcd_2Elcm @ c_2Enum_2E0 @ A )
= c_2Enum_2E0 )
& ( ( c_2Egcd_2Elcm @ A @ c_2Enum_2E0 )
= c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(23,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ! [B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2EMOD @ B @ A ) @ ( c_2Earithmetic_2EMOD @ C @ A ) ) @ A )
= ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__TIMES2) ).
thf(765,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ! [B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2EMOD @ B @ A ) @ ( c_2Earithmetic_2EMOD @ C @ A ) ) @ A )
= ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(509,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__NEGINT__EXISTS) ).
thf(2963,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(102,axiom,
! [A: $o > $o] :
( ( ! [B: $o] : ( A @ B ) )
= ( ( A @ c_2Ebool_2ET )
& ( A @ c_2Ebool_2EF ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EFORALL__BOOL) ).
thf(1071,plain,
! [A: $o > $o] :
( ( ! [B: $o] : ( A @ B ) )
= ( ( A @ c_2Ebool_2ET )
& ( A @ c_2Ebool_2EF ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(346,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mul @ A @ B ) )
= ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__LMUL) ).
thf(2440,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mul @ A @ B ) )
= ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(190,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
& ( C
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
=> ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__exp @ C @ A ) @ ( c_2Einteger_2Eint__exp @ C @ B ) )
= ( c_2Einteger_2Eint__exp @ C @ ( c_2Earithmetic_2E_2D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EXP__SUBTRACT__EXPONENTS) ).
thf(1515,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
& ( C
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
=> ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__exp @ C @ A ) @ ( c_2Einteger_2Eint__exp @ C @ B ) )
= ( c_2Einteger_2Eint__exp @ C @ ( c_2Earithmetic_2E_2D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(519,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ A @ B )
= ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2Eint__sub) ).
thf(2995,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ A @ B )
= ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(11,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ c_2Enum_2E0 )
= c_2Enum_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__0) ).
thf(718,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ c_2Enum_2E0 )
= c_2Enum_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(231,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) )
= ( c_2Ewords_2Eword__mul @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__RMUL) ).
thf(1732,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) )
= ( c_2Ewords_2Eword__mul @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(138,axiom,
! [A: $o,B: $o,C: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ B @ C )
= ( ( A
=> B )
& ( ~ A
=> C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__EXPAND__IMP) ).
thf(1202,plain,
! [A: $o,B: $o,C: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ B @ C )
= ( ( A
=> B )
& ( ~ A
=> C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(32,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2E_2D @ A @ B ) )
= ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ C @ A ) @ ( c_2Earithmetic_2E_2A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELEFT__SUB__DISTRIB) ).
thf(792,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2E_2D @ A @ B ) )
= ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ C @ A ) @ ( c_2Earithmetic_2E_2A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(255,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__ls @ TA @ B @ A )
=> ( ( c_2Ewords_2Ew2n @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
= ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__sub__w2n) ).
thf(2076,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__ls @ TA @ B @ A )
=> ( ( c_2Ewords_2Ew2n @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
= ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(439,axiom,
! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__divides @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__REFL) ).
thf(2748,plain,
! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__divides @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(335,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
= C )
= ( A
= ( c_2Ewords_2Eword__add @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EQ__SUB__RADD) ).
thf(2408,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
= C )
= ( A
= ( c_2Ewords_2Eword__add @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(213,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ C @ B ) @ ( c_2Earithmetic_2E_2D @ C @ A ) )
= ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
| ( c_2Earithmetic_2E_3C_3D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELE__SUB__LCANCEL) ).
thf(1663,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ C @ B ) @ ( c_2Earithmetic_2E_2D @ C @ A ) )
= ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
| ( c_2Earithmetic_2E_3C_3D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(953,plain,
! [A: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ c_2Enum_2E0 @ A ),
inference(cnf,[status(esa)],[952]) ).
thf(133,axiom,
! [A: $o] :
( ( A
=> c_2Ebool_2EF )
=> ~ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__F) ).
thf(1185,plain,
! [A: $o] :
( ( A
=> c_2Ebool_2EF )
=> ~ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(292,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
& ( c_2Ewords_2Eword__lo @ TA @ B @ C ) )
=> ( c_2Ewords_2Eword__lo @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__TRANS) ).
thf(2235,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
& ( c_2Ewords_2Eword__lo @ TA @ B @ C ) )
=> ( c_2Ewords_2Eword__lo @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(208,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__mul @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
= ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) @ ( c_2Ewords_2Eword__mul @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LEFT__ADD__DISTRIB) ).
thf(1648,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__mul @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
= ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) @ ( c_2Ewords_2Eword__mul @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(422,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__mul @ B @ A ) )
= ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__ASSOC) ).
thf(2677,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__mul @ B @ A ) )
= ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(122,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__NOT__EQ) ).
thf(1146,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(139,axiom,
! [A: tyop_2Enum_2Enum] :
( ( ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) )
= ( A = c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ENOT__LT__ZERO__EQ__ZERO) ).
thf(1219,plain,
! [A: tyop_2Enum_2Enum] :
( ( ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) )
= ( A = c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(502,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ A @ B )
= ( c_2Einteger_2Eint__add @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__LADD) ).
thf(2941,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ A @ B )
= ( c_2Einteger_2Eint__add @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(621,axiom,
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__0) ).
thf(3375,plain,
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(594,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( A = B )
| ( c_2Einteger_2Eint__lt @ A @ B )
| ( c_2Einteger_2Eint__lt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__TOTAL) ).
thf(3274,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( A = B )
| ( c_2Einteger_2Eint__lt @ A @ B )
| ( c_2Einteger_2Eint__lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(16,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2E_2A @ A @ B ) )
= ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EZERO__LESS__MULT) ).
thf(733,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2E_2A @ A @ B ) )
= ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(229,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
& ( c_2Egcd_2Eis__gcd @ ( c_2Earithmetic_2E_2D @ A @ B ) @ B @ C ) )
=> ( c_2Egcd_2Eis__gcd @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__MINUS__L) ).
thf(1727,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
& ( c_2Egcd_2Eis__gcd @ ( c_2Earithmetic_2E_2D @ A @ B ) @ B @ C ) )
=> ( c_2Egcd_2Eis__gcd @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(189,axiom,
! [A: $o] :
( ( ~ A
=> c_2Ebool_2EF )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2ENOT__ELIM2) ).
thf(1510,plain,
! [A: $o] :
( ( ~ A
=> c_2Ebool_2EF )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(330,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( A = B )
| ( c_2Ewords_2Eword__lo @ TA @ A @ B )
| ( c_2Ewords_2Eword__lo @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__LOWER__CASES) ).
thf(2391,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( A = B )
| ( c_2Ewords_2Eword__lo @ TA @ A @ B )
| ( c_2Ewords_2Eword__lo @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(489,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ! [B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__mod @ B @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ? [C: tyop_2Einteger_2Eint] :
( B
= ( c_2Einteger_2Eint__mul @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__EQ0) ).
thf(2904,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ! [B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__mod @ B @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ? [C: tyop_2Einteger_2Eint] :
( B
= ( c_2Einteger_2Eint__mul @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(218,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B != c_2Enum_2E0 )
=> ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__QUOT) ).
thf(1680,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B != c_2Enum_2E0 )
=> ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(616,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ealignment_2Ealign @ TA @ c_2Enum_2E0 @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealign__0) ).
thf(3358,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ealignment_2Ealign @ TA @ c_2Enum_2E0 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(902,plain,
( ( c_2Ebool_2ECOND @ $o @ $true @ c_2Ebool_2ET @ $true )
= ( ~ $true
=> $true ) ),
inference(instance,[status(thm)],[901]) ).
thf(903,plain,
c_2Ebool_2ECOND @ $o @ $true @ c_2Ebool_2ET @ $true,
inference(simp,[status(thm)],[902]) ).
thf(3871,plain,
c_2Ebool_2ECOND @ $o @ $true @ $true @ $true,
inference(rewrite,[status(thm)],[903,883]) ).
thf(267,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ! [B: tyop_2Einteger_2Eint] :
( ( B
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__div @ B @ A ) @ A ) @ ( c_2Einteger_2Eint__mod @ B @ A ) ) )
& ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__mod @ B @ A ) ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__mod @ B @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mod @ B @ A ) ) @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mod @ B @ A ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVISION) ).
thf(2149,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ! [B: tyop_2Einteger_2Eint] :
( ( B
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__div @ B @ A ) @ A ) @ ( c_2Einteger_2Eint__mod @ B @ A ) ) )
& ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__mod @ B @ A ) ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__mod @ B @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mod @ B @ A ) ) @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mod @ B @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(671,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__RZERO) ).
thf(3547,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(432,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) )
= ( c_2Ewords_2Eword__2comp @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__SUB3) ).
thf(2727,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) )
= ( c_2Ewords_2Eword__2comp @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(501,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__ls @ TA @ B @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) )
= ( ( B
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
| ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
| ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__RIGHT__LS2) ).
thf(2938,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__ls @ TA @ B @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) )
= ( ( B
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
| ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
| ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(471,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EABS__DIFF @ A @ B )
= ( c_2Earithmetic_2EABS__DIFF @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EABS__DIFF__SYM) ).
thf(2849,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EABS__DIFF @ A @ B )
= ( c_2Earithmetic_2EABS__DIFF @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(515,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
=> ? [C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eadd__to__great) ).
thf(2981,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
=> ? [C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(547,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__add @ B @ A ) )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__add @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__ASSOC) ).
thf(3086,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__add @ B @ A ) )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__add @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(456,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__add @ A @ B ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__ADDR) ).
thf(2806,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__add @ A @ B ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(428,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__SUB__LADD) ).
thf(2695,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(693,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
| ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ B @ A ) @ A )
= c_2Enum_2E0 ) ),
inference(cnf,[status(esa)],[692]) ).
thf(694,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ B @ A ) @ A )
= c_2Enum_2E0 )
| ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ),
inference(lifteq,[status(thm)],[693]) ).
thf(606,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2EABS @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__EQ0) ).
thf(3319,plain,
! [A: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2EABS @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(658,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__rem @ A @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM__ID) ).
thf(3504,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__rem @ A @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(249,axiom,
! [A: $o > $o > $o] :
( ( ( A @ c_2Ebool_2ET @ c_2Ebool_2ET )
& ( A @ c_2Ebool_2EF @ c_2Ebool_2EF )
& ( A @ c_2Ebool_2ET @ c_2Ebool_2EF )
& ( A @ c_2Ebool_2EF @ c_2Ebool_2ET ) )
=> ! [B: $o,C: $o] : ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EternaryComparisons_2Ebool__compare__ind) ).
thf(1884,plain,
! [A: $o > $o > $o] :
( ( ( A @ c_2Ebool_2ET @ c_2Ebool_2ET )
& ( A @ c_2Ebool_2EF @ c_2Ebool_2EF )
& ( A @ c_2Ebool_2ET @ c_2Ebool_2EF )
& ( A @ c_2Ebool_2EF @ c_2Ebool_2ET ) )
=> ! [B: $o,C: $o] : ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(163,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ! [B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2EMOD @ B @ A ) @ A )
= ( c_2Earithmetic_2EMOD @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__MOD) ).
thf(1389,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ! [B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2EMOD @ B @ A ) @ A )
= ( c_2Earithmetic_2EMOD @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(592,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__sub @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__SUB2) ).
thf(3255,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__sub @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(371,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
| ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
| ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__neg @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__NEGTOTAL) ).
thf(2514,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
| ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
| ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__neg @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(388,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ~ ( c_2Ewords_2Eword__lo @ TA @ A @ B )
& ( A != B ) )
=> ( c_2Ewords_2Eword__lo @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__CASES__IMP) ).
thf(2568,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ~ ( c_2Ewords_2Eword__lo @ TA @ A @ B )
& ( A != B ) )
=> ( c_2Ewords_2Eword__lo @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(224,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
= ( ( ( ( c_2Ewords_2Eword__msb @ TA @ A )
= ( c_2Ewords_2Eword__msb @ TA @ B ) )
& ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) )
| ( ( c_2Ewords_2Eword__msb @ TA @ A )
& ~ ( c_2Ewords_2Eword__msb @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LT) ).
thf(1701,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
= ( ( ( ( c_2Ewords_2Eword__msb @ TA @ A )
= ( c_2Ewords_2Eword__msb @ TA @ B ) )
& ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) )
| ( ( c_2Ewords_2Eword__msb @ TA @ A )
& ~ ( c_2Ewords_2Eword__msb @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(332,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ B @ A ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__SUB2) ).
thf(2398,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ B @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(192,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) )
=> ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2EDIV__GT0) ).
thf(1520,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) )
=> ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(460,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMODEQ @ A @ B @ C )
& ( c_2Earithmetic_2EMODEQ @ A @ C @ D ) )
=> ( c_2Earithmetic_2EMODEQ @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__TRANS) ).
thf(2817,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMODEQ @ A @ B @ C )
& ( c_2Earithmetic_2EMODEQ @ A @ C @ D ) )
=> ( c_2Earithmetic_2EMODEQ @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(187,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) )
=> ( ( c_2Earithmetic_2E_3C_3D @ B @ ( c_2Egcd_2Elcm @ B @ A ) )
& ( c_2Earithmetic_2E_3C_3D @ B @ ( c_2Egcd_2Elcm @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2ELCM__LE) ).
thf(1503,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) )
=> ( ( c_2Earithmetic_2E_3C_3D @ B @ ( c_2Egcd_2Elcm @ B @ A ) )
& ( c_2Earithmetic_2E_3C_3D @ B @ ( c_2Egcd_2Elcm @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(215,axiom,
! [A: $o] :
( ( c_2Ebool_2EF
=> A )
= c_2Ebool_2ET ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CLAUSES__FX) ).
thf(1669,plain,
! [A: $o] :
( ( c_2Ebool_2EF
=> A )
= c_2Ebool_2ET ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(62,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ A @ B )
=> ( ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ A @ B ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2En2w__sub__eq__0) ).
thf(936,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ A @ B )
=> ( ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ A @ B ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(301,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( A
= ( c_2Einteger_2Eint__add @ B @ C ) )
= ( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__move__left__left) ).
thf(2293,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( A
= ( c_2Einteger_2Eint__add @ B @ C ) )
= ( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(544,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__neg @ A ) )
= ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__NEGR) ).
thf(3077,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__neg @ A ) )
= ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(610,axiom,
! [A: tyop_2Enum_2Enum] : ( c_2Egcd_2Eis__gcd @ c_2Enum_2E0 @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__0L) ).
thf(3330,plain,
! [A: tyop_2Enum_2Enum] : ( c_2Egcd_2Eis__gcd @ c_2Enum_2E0 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(98,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
& ( c_2Earithmetic_2E_3C_3D @ B @ C ) )
=> ( c_2Earithmetic_2E_3C_3D @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__EQ__TRANS) ).
thf(1058,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
& ( c_2Earithmetic_2E_3C_3D @ B @ C ) )
=> ( c_2Earithmetic_2E_3C_3D @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(686,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
= A )
= ( B
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__RID__UNIQ) ).
thf(3594,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
= A )
= ( B
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(270,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
=> ( c_2Earithmetic_2E_3C_3D @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__IMP__LESS__OR__EQ) ).
thf(2166,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
=> ( c_2Earithmetic_2E_3C_3D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(385,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ B )
= ( ( ( ( c_2Einteger_2Eint__mod @ B @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ( ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( B
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__MOD0) ).
thf(2557,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ B )
= ( ( ( ( c_2Einteger_2Eint__mod @ B @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ( ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( B
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(341,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__mul @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__MUL2) ).
thf(2425,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__mul @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(703,plain,
( ( c_2Ebool_2E_2F_5C @ $false @ $true )
= ( $false
& $true ) ),
inference(instance,[status(thm)],[698]) ).
thf(704,plain,
~ ( c_2Ebool_2E_2F_5C @ $false @ $true ),
inference(simp,[status(thm)],[703]) ).
thf(549,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ B @ ( c_2Einteger_2Eint__add @ A @ B ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__ADDL) ).
thf(3091,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ B @ ( c_2Einteger_2Eint__add @ A @ B ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(601,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger__word_2Ew2i @ TA @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__w2i) ).
thf(3302,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger__word_2Ew2i @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(216,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ~ ( c_2Earithmetic_2E_3C_3D @ A @ B ) )
= ( c_2Eprim__rec_2E_3C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ENOT__LESS__EQUAL) ).
thf(1675,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ~ ( c_2Earithmetic_2E_3C_3D @ A @ B ) )
= ( c_2Eprim__rec_2E_3C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(205,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Earithmetic_2E_3C_3D @ B @ A ) )
=> ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ A @ B ) @ B )
= ( c_2Earithmetic_2EMOD @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__MOD) ).
thf(1635,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Earithmetic_2E_3C_3D @ B @ A ) )
=> ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ A @ B ) @ B )
= ( c_2Earithmetic_2EMOD @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(500,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__slice @ TA @ A @ c_2Enum_2E0 @ B )
= ( c_2Ewords_2Eword__bits @ TA @ A @ c_2Enum_2E0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SLICE__BITS__THM) ).
thf(2935,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__slice @ TA @ A @ c_2Enum_2E0 @ B )
= ( c_2Ewords_2Eword__bits @ TA @ A @ c_2Enum_2E0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(443,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__neg @ A ) )
= ( c_2Einteger_2EABS @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__NEG) ).
thf(2759,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__neg @ A ) )
= ( c_2Einteger_2EABS @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(441,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B )
= ( ( B
!= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
& ( ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
| ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__NEG__LEFT) ).
thf(2753,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B )
= ( ( B
!= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
& ( ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
| ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(206,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ A @ B )
& ( c_2Earithmetic_2E_3C_3D @ B @ C ) )
=> ( c_2Eprim__rec_2E_3C @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__LESS__EQ__TRANS) ).
thf(1638,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ A @ B )
& ( c_2Earithmetic_2E_3C_3D @ B @ C ) )
=> ( c_2Eprim__rec_2E_3C @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(615,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Ew2n @ TA @ A )
= c_2Enum_2E0 )
= ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Ew2n__eq__0) ).
thf(3355,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Ew2n @ TA @ A )
= c_2Enum_2E0 )
= ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(323,axiom,
! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( C
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( A @ ( c_2Einteger_2Eint__div @ B @ C ) )
= ( ? [D: tyop_2Einteger_2Eint,E: tyop_2Einteger_2Eint] :
( ( B
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ C ) @ E ) )
& ( ( ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__lt @ C @ E )
& ( c_2Einteger_2Eint__le @ E @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ( ~ ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ E )
& ( c_2Einteger_2Eint__lt @ E @ C ) ) )
& ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__P) ).
thf(2358,plain,
! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( C
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( A @ ( c_2Einteger_2Eint__div @ B @ C ) )
= ( ? [D: tyop_2Einteger_2Eint,E: tyop_2Einteger_2Eint] :
( ( B
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ C ) @ E ) )
& ( ( ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__lt @ C @ E )
& ( c_2Einteger_2Eint__le @ E @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ( ~ ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ E )
& ( c_2Einteger_2Eint__lt @ E @ C ) ) )
& ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(309,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__neg @ A ) @ B )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LNEG) ).
thf(2319,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__neg @ A ) @ B )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(157,axiom,
! [TA: $tType,A: tyop_2Einteger_2Eint] :
( ( c_2Einteger__word_2Ei2w @ TA @ A )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ TA ) @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ A ) ) ) ) @ ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__def) ).
thf(1356,plain,
! [TA: $tType,A: tyop_2Einteger_2Eint] :
( ( c_2Einteger__word_2Ei2w @ TA @ A )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ TA ) @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ A ) ) ) ) @ ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(43,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C ) )
=> ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2EDIV @ A @ B ) @ C )
= ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2EMOD @ A @ ( c_2Earithmetic_2E_2A @ B @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EDIV__MOD__MOD__DIV) ).
thf(831,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C ) )
=> ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2EDIV @ A @ B ) @ C )
= ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2EMOD @ A @ ( c_2Earithmetic_2E_2A @ B @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(328,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint,E: tyop_2Enum_2Enum,F: tyop_2Einteger_2Eint,G: tyop_2Einteger_2Eint] :
( ( ( E
= ( c_2Egcd_2Egcd @ B @ A ) )
& ( ( c_2Einteger_2Eint__of__num @ E )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ F @ ( c_2Einteger_2Eint__of__num @ B ) ) @ ( c_2Einteger_2Eint__mul @ G @ ( c_2Einteger_2Eint__of__num @ A ) ) ) )
& ( E != c_2Enum_2E0 )
& ( A != c_2Enum_2E0 )
& ( B != c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ B ) @ C ) @ D ) )
= ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ E ) @ D )
& ? [H: tyop_2Einteger_2Eint] :
( C
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ F ) @ ( c_2Einteger_2Eint__div @ D @ ( c_2Einteger_2Eint__of__num @ E ) ) ) @ ( c_2Einteger_2Eint__mul @ H @ ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Egcdthm2) ).
thf(2383,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint,E: tyop_2Enum_2Enum,F: tyop_2Einteger_2Eint,G: tyop_2Einteger_2Eint] :
( ( ( E
= ( c_2Egcd_2Egcd @ B @ A ) )
& ( ( c_2Einteger_2Eint__of__num @ E )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ F @ ( c_2Einteger_2Eint__of__num @ B ) ) @ ( c_2Einteger_2Eint__mul @ G @ ( c_2Einteger_2Eint__of__num @ A ) ) ) )
& ( E != c_2Enum_2E0 )
& ( A != c_2Enum_2E0 )
& ( B != c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ B ) @ C ) @ D ) )
= ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ E ) @ D )
& ? [H: tyop_2Einteger_2Eint] :
( C
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ F ) @ ( c_2Einteger_2Eint__div @ D @ ( c_2Einteger_2Eint__of__num @ E ) ) ) @ ( c_2Einteger_2Eint__mul @ H @ ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(340,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__sub @ A @ B ) @ ( c_2Einteger_2Eint__sub @ B @ C ) )
= ( c_2Einteger_2Eint__sub @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__TRIANGLE) ).
thf(2422,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__sub @ A @ B ) @ ( c_2Einteger_2Eint__sub @ B @ C ) )
= ( c_2Einteger_2Eint__sub @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(597,axiom,
! [TA: $tType] :
( ! [A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= A )
& ! [A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__0) ).
thf(3287,plain,
! [TA: $tType] :
( ! [A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= A )
& ! [A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(17,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ A @ C ) )
= ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( c_2Eprim__rec_2E_3C @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELT__MULT__LCANCEL) ).
thf(736,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ A @ C ) )
= ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( c_2Eprim__rec_2E_3C @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(578,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
= ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__PLUS) ).
thf(3197,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
= ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(570,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
& ( c_2Ewords_2Eword__ls @ TA @ B @ C ) )
=> ( c_2Ewords_2Eword__lo @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__LOWER__EQ__TRANS) ).
thf(3160,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
& ( c_2Ewords_2Eword__ls @ TA @ B @ C ) )
=> ( c_2Ewords_2Eword__lo @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(256,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
=> ( ( c_2Ewords_2Eword__slice @ TA @ A @ B @ C )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SLICE__ZERO) ).
thf(2079,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
=> ( ( c_2Ewords_2Eword__slice @ TA @ A @ B @ C )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(324,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__sub @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__ADD) ).
thf(2361,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__sub @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(359,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ A ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__RINV) ).
thf(2478,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ A ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(591,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ C @ B ) )
= ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2EINT__DIVIDES__LRMUL) ).
thf(3251,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ C @ B ) )
= ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(185,axiom,
! [A: $o] :
( ( A
=> c_2Ebool_2ET )
= c_2Ebool_2ET ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CLAUSES__XT) ).
thf(1492,plain,
! [A: $o] :
( ( A
=> c_2Ebool_2ET )
= c_2Ebool_2ET ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(303,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__sub @ C @ A ) @ B )
= ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Emove__sub) ).
thf(2299,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__sub @ C @ A ) @ B )
= ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(647,axiom,
! [A: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Eshiftr @ A @ c_2Enum_2E0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebitstring_2Eshiftr__0) ).
thf(3468,plain,
! [A: tyop_2Elist_2Elist @ $o] :
( ( c_2Ebitstring_2Eshiftr @ A @ c_2Enum_2E0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(198,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ~ ( c_2Ewords_2Eword__lt @ TA @ A @ B )
& ( A != B ) )
=> ( c_2Ewords_2Eword__lt @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__CASES__IMP) ).
thf(1542,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ~ ( c_2Ewords_2Eword__lt @ TA @ A @ B )
& ( A != B ) )
=> ( c_2Ewords_2Eword__lt @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(38,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C )
=> ( ( c_2Earithmetic_2E_3C_3D @ A @ ( c_2Earithmetic_2EDIV @ B @ C ) )
= ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EX__LE__DIV) ).
thf(811,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C )
=> ( ( c_2Earithmetic_2E_3C_3D @ A @ ( c_2Earithmetic_2EDIV @ B @ C ) )
= ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(180,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2D @ C @ B ) @ ( c_2Earithmetic_2E_2D @ C @ A ) )
= ( ( c_2Eprim__rec_2E_3C @ A @ B )
& ( c_2Eprim__rec_2E_3C @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELT__SUB__LCANCEL) ).
thf(1471,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2D @ C @ B ) @ ( c_2Earithmetic_2E_2D @ C @ A ) )
= ( ( c_2Eprim__rec_2E_3C @ A @ B )
& ( c_2Eprim__rec_2E_3C @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(437,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ~ ( c_2Ewords_2Eword__lo @ TA @ A @ B ) )
= ( c_2Ewords_2Eword__ls @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NOT__LOWER) ).
thf(2742,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ~ ( c_2Ewords_2Eword__lo @ TA @ A @ B ) )
= ( c_2Ewords_2Eword__ls @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(21,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C )
=> ( ( ( c_2Earithmetic_2E_2A @ C @ B )
= A )
= ( ( B
= ( c_2Earithmetic_2EDIV @ A @ C ) )
& ( ( c_2Earithmetic_2EMOD @ A @ C )
= c_2Enum_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__EQ__DIV) ).
thf(758,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C )
=> ( ( ( c_2Earithmetic_2E_2A @ C @ B )
= A )
= ( ( B
= ( c_2Earithmetic_2EDIV @ A @ C ) )
& ( ( c_2Earithmetic_2EMOD @ A @ C )
= c_2Enum_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(562,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) )
= ( c_2Ewords_2Eword__add @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__RNEG) ).
thf(3133,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) )
= ( c_2Ewords_2Eword__add @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(296,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2EABS @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__LE0) ).
thf(2261,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2EABS @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(34,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ B )
= ( c_2Earithmetic_2E_2A @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__COMM) ).
thf(799,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ B )
= ( c_2Earithmetic_2E_2A @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(348,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ B )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ele__move__all__right) ).
thf(2446,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ B )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(572,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ealignment_2Ealign @ TA @ A @ ( c_2Ealignment_2Ealign @ TA @ A @ B ) )
= ( c_2Ealignment_2Ealign @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealign__align) ).
thf(3165,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ealignment_2Ealign @ TA @ A @ ( c_2Ealignment_2Ealign @ TA @ A @ B ) )
= ( c_2Ealignment_2Ealign @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(532,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ B @ A )
= ( c_2Einteger_2Eint__mul @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__SYM) ).
thf(3034,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ B @ A )
= ( c_2Einteger_2Eint__mul @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(413,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__neg @ A ) @ B )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__quot @ A @ B ) ) )
& ( ( c_2Einteger_2Eint__quot @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__quot @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__QUOT__NEG) ).
thf(2647,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__neg @ A ) @ B )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__quot @ A @ B ) ) )
& ( ( c_2Einteger_2Eint__quot @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__quot @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(497,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ B @ C )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__add @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__LADD__IMP) ).
thf(2928,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ B @ C )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__add @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(353,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Enum_2Enum] :
( ( ~ ( c_2Ewords_2Eword__msb @ TA @ A )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) )
=> ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ TA @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ew2i__w2n__pos) ).
thf(2461,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Enum_2Enum] :
( ( ~ ( c_2Ewords_2Eword__msb @ TA @ A )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) )
=> ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ TA @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(458,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
= C )
= ( A
= ( c_2Ewords_2Eword__sub @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__EQ__SUB) ).
thf(2812,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
= C )
= ( A
= ( c_2Ewords_2Eword__sub @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(103,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A )
& ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B ) )
=> ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
= ( c_2Ewords_2Eword__ls @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LE__EQ__LS) ).
thf(1080,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A )
& ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B ) )
=> ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
= ( c_2Ewords_2Eword__ls @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(408,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
( ( ( c_2Egcd_2Eis__gcd @ A @ B @ C )
& ( c_2Egcd_2Eis__gcd @ A @ B @ D ) )
=> ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__UNIQUE) ).
thf(2632,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
( ( ( c_2Egcd_2Eis__gcd @ A @ B @ C )
& ( c_2Egcd_2Eis__gcd @ A @ B @ D ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(48,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) )
& ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ) )
& ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ) )
& ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__REDUCE) ).
thf(848,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) )
& ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ) )
& ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ) )
& ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(699,plain,
( ( c_2Ebool_2E_2F_5C @ $true @ $true )
= ( $true
& $true ) ),
inference(instance,[status(thm)],[698]) ).
thf(700,plain,
c_2Ebool_2E_2F_5C @ $true @ $true,
inference(simp,[status(thm)],[699]) ).
thf(395,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
=> ? [C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Esubtract__to__small) ).
thf(2593,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
=> ? [C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(56,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ( ( c_2Earithmetic_2EDIV @ c_2Enum_2E0 @ A )
= c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EZERO__DIV) ).
thf(895,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ( ( c_2Earithmetic_2EDIV @ c_2Enum_2E0 @ A )
= c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(652,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__0) ).
thf(3483,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(684,axiom,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EABS__DIFF @ A @ c_2Enum_2E0 )
= A )
& ( ( c_2Earithmetic_2EABS__DIFF @ c_2Enum_2E0 @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EABS__DIFF__ZERO) ).
thf(3583,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EABS__DIFF @ A @ c_2Enum_2E0 )
= A )
& ( ( c_2Earithmetic_2EABS__DIFF @ c_2Enum_2E0 @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(113,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__mul @ TA @ A @ ( c_2Ewords_2Eword__mul @ TA @ B @ C ) )
= ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__MULT__ASSOC) ).
thf(1112,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__mul @ TA @ A @ ( c_2Ewords_2Eword__mul @ TA @ B @ C ) )
= ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(391,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__add @ A @ B ) )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__ADD) ).
thf(2578,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__add @ A @ B ) )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(651,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
? [B: tyop_2Einteger_2Eint] :
( A
= ( c_2Einteger__word_2Ei2w @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eint__word__nchotomy) ).
thf(3480,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
? [B: tyop_2Einteger_2Eint] :
( A
= ( c_2Einteger__word_2Ei2w @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(447,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
= ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__sub__def) ).
thf(2770,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
= ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(136,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Eprim__rec_2E_3C @ A @ B )
& ( c_2Ealignment_2Ealigned @ TA @ B @ C ) )
=> ( c_2Ealignment_2Ealigned @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealigned__imp) ).
thf(1198,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Eprim__rec_2E_3C @ A @ B )
& ( c_2Ealignment_2Ealigned @ TA @ B @ C ) )
=> ( c_2Ealignment_2Ealigned @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(333,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__IMP__NE) ).
thf(2401,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(24,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ A @ B )
=> ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ C ) @ ( c_2Earithmetic_2E_2A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__MONO__MULT) ).
thf(768,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ A @ B )
=> ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ C ) @ ( c_2Earithmetic_2E_2A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(49,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ B @ ( c_2Earithmetic_2E_2A @ B @ A ) )
= ( ( B = c_2Enum_2E0 )
| ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ) )
& ( ( c_2Earithmetic_2E_3C_3D @ B @ ( c_2Earithmetic_2E_2A @ A @ B ) )
= ( ( B = c_2Enum_2E0 )
| ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELE__MULT__CANCEL__LBARE) ).
thf(868,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ B @ ( c_2Earithmetic_2E_2A @ B @ A ) )
= ( ( B = c_2Enum_2E0 )
| ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ) )
& ( ( c_2Earithmetic_2E_3C_3D @ B @ ( c_2Earithmetic_2E_2A @ A @ B ) )
= ( ( B = c_2Enum_2E0 )
| ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(28,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2E_2A @ B @ C ) )
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2E_2A @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__ASSOC) ).
thf(780,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2E_2A @ B @ C ) )
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2E_2A @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(79,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2D @ A @ B )
= A )
= ( ( A = c_2Enum_2E0 )
| ( B = c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__EQ__EQ__0) ).
thf(986,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2D @ A @ B )
= A )
= ( ( A = c_2Enum_2E0 )
| ( B = c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(228,axiom,
c_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebag_2Emlt__UNION__EMPTY__EQN) ).
thf(1726,plain,
c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(576,axiom,
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B != c_2Enum_2E0 )
=> ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EMOD @ A @ B ) ) ) )
& ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ) ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
= A )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__of__num @ A )
= ( c_2Einteger_2Eint__of__num @ B ) )
= ( A = B ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__neg @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__CALCULATE) ).
thf(3178,plain,
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( B != c_2Enum_2E0 )
=> ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EMOD @ A @ B ) ) ) )
& ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ) ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
= A )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__of__num @ A )
= ( c_2Einteger_2Eint__of__num @ B ) )
= ( A = B ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__neg @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(282,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) )
= ( ( A
!= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
& ( ( B
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
| ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__RIGHT__LO2) ).
thf(2207,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) )
= ( ( A
!= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
& ( ( B
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
| ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(222,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__abs @ TA @ ( c_2Ewords_2Eword__abs @ TA @ A ) )
= ( c_2Ewords_2Eword__abs @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__abs__word__abs) ).
thf(1694,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__abs @ TA @ ( c_2Ewords_2Eword__abs @ TA @ A ) )
= ( c_2Ewords_2Eword__abs @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(477,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Egcd_2Eis__gcd @ A @ B @ C )
= ( c_2Egcd_2Eis__gcd @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__SYM) ).
thf(2867,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Egcd_2Eis__gcd @ A @ B @ C )
= ( c_2Egcd_2Eis__gcd @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(181,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B )
& ( c_2Ewords_2Eword__lt @ TA @ B @ A ) )
=> ( ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
& ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__LT) ).
thf(1474,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B )
& ( c_2Ewords_2Eword__lt @ TA @ B @ A ) )
=> ( ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
& ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(320,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__add @ A @ B ) )
= ( c_2Einteger_2Eint__neg @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__SUB2) ).
thf(2350,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__add @ A @ B ) )
= ( c_2Einteger_2Eint__neg @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(71,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
| ( c_2Ewords_2Eword__le @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__CASES) ).
thf(959,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
| ( c_2Ewords_2Eword__le @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(272,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) )
= ( c_2Einteger_2Eint__divides @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__MUL__BOTH) ).
thf(2171,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) )
= ( c_2Einteger_2Eint__divides @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(445,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ A @ B )
& ( c_2Einteger_2Eint__lt @ B @ C ) )
=> ( c_2Einteger_2Eint__lt @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LET__TRANS) ).
thf(2765,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ A @ B )
& ( c_2Einteger_2Eint__lt @ B @ C ) )
=> ( c_2Einteger_2Eint__lt @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(93,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
& ( c_2Egcd_2Eis__gcd @ A @ ( c_2Earithmetic_2E_2D @ B @ A ) @ C ) )
=> ( c_2Egcd_2Eis__gcd @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__MINUS__R) ).
thf(1044,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
& ( c_2Egcd_2Eis__gcd @ A @ ( c_2Earithmetic_2E_2D @ B @ A ) @ C ) )
=> ( c_2Egcd_2Eis__gcd @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(360,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
& ( C
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
=> ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__exp @ C @ A ) @ ( c_2Einteger_2Eint__exp @ C @ B ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EXP__MOD) ).
thf(2481,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
& ( C
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
=> ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__exp @ C @ A ) @ ( c_2Einteger_2Eint__exp @ C @ B ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(327,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2EABS @ A ) @ B )
= ( ( c_2Einteger_2Eint__le @ A @ B )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ B ) @ A ) ) )
& ( ( c_2Einteger_2Eint__le @ B @ ( c_2Einteger_2EABS @ A ) )
= ( ( c_2Einteger_2Eint__le @ B @ A )
| ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ) )
& ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2EABS @ A ) ) @ B )
= ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ B ) @ A )
| ( c_2Einteger_2Eint__le @ A @ B ) ) )
& ( ( c_2Einteger_2Eint__le @ B @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2EABS @ A ) ) )
= ( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__neg @ B ) )
& ( c_2Einteger_2Eint__le @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__LE) ).
thf(2369,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2EABS @ A ) @ B )
= ( ( c_2Einteger_2Eint__le @ A @ B )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ B ) @ A ) ) )
& ( ( c_2Einteger_2Eint__le @ B @ ( c_2Einteger_2EABS @ A ) )
= ( ( c_2Einteger_2Eint__le @ B @ A )
| ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ) )
& ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2EABS @ A ) ) @ B )
= ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ B ) @ A )
| ( c_2Einteger_2Eint__le @ A @ B ) ) )
& ( ( c_2Einteger_2Eint__le @ B @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2EABS @ A ) ) )
= ( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__neg @ B ) )
& ( c_2Einteger_2Eint__le @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(85,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ( c_2Earithmetic_2EMODEQ @ A @ A @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__0) ).
thf(1015,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ( c_2Earithmetic_2EMODEQ @ A @ A @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(608,axiom,
! [A: tyop_2EternaryComparisons_2Eordering] :
( ( c_2EternaryComparisons_2Eordering__size @ A )
= c_2Enum_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EternaryComparisons_2Eordering__size__def) ).
thf(3325,plain,
! [A: tyop_2EternaryComparisons_2Eordering] :
( ( c_2EternaryComparisons_2Eordering__size @ A )
= c_2Enum_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(565,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ B )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Elt__move__all__right) ).
thf(3142,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ B )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(368,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__sub @ A @ B ) @ A )
= ( c_2Einteger_2Eint__neg @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__SUB) ).
thf(2506,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__sub @ A @ B ) @ A )
= ( c_2Einteger_2Eint__neg @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(623,axiom,
! [A: tyop_2Einteger_2Eint > $o] :
( ( ? [B: tyop_2Enum_2Enum] : ( A @ ( c_2Einteger_2Eint__of__num @ B ) ) )
= ( ? [B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
& ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2EINT__NUM__EXISTS) ).
thf(3380,plain,
! [A: tyop_2Einteger_2Eint > $o] :
( ( ? [B: tyop_2Enum_2Enum] : ( A @ ( c_2Einteger_2Eint__of__num @ B ) ) )
= ( ? [B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
& ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(531,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__add @ C @ D ) )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__sub @ A @ C ) @ ( c_2Einteger_2Eint__sub @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD2__SUB2) ).
thf(3031,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__add @ C @ D ) )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__sub @ A @ C ) @ ( c_2Einteger_2Eint__sub @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(402,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
( ( B != c_2Enum_2E0 )
=> ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ B ) @ C ) )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eelim__lt__coeffs1) ).
thf(2614,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
( ( B != c_2Enum_2E0 )
=> ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ B ) @ C ) )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(637,axiom,
! [A: tyop_2Enum_2Enum > $o] :
( ( ( A @ c_2Enum_2E0 )
& ! [B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( A @ C )
=> ( A @ ( c_2Enumpair_2Encons @ B @ C ) ) ) )
=> ! [B: tyop_2Enum_2Enum] : ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Enlist__ind) ).
thf(3427,plain,
! [A: tyop_2Enum_2Enum > $o] :
( ( ( A @ c_2Enum_2E0 )
& ! [B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( A @ C )
=> ( A @ ( c_2Enumpair_2Encons @ B @ C ) ) ) )
=> ! [B: tyop_2Enum_2Enum] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(128,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
=> ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EMOD @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2EMOD__LEQ) ).
thf(1166,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
=> ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EMOD @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(65,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ! [B: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EDIV @ B @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EDIV__LESS__EQ) ).
thf(944,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ! [B: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EDIV @ B @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(349,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ B @ A )
= ( c_2Einteger_2Eint__add @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__SYM) ).
thf(2449,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ B @ A )
= ( c_2Einteger_2Eint__add @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(407,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Ew2n @ TA @ A )
= ( c_2Ewords_2Ew2n @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Ew2n__11) ).
thf(2629,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Ew2n @ TA @ A )
= ( c_2Ewords_2Ew2n @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(63,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ECOND__CLAUSES__CT) ).
thf(939,plain,
! [TA: $tType,A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(644,axiom,
! [TA: $tType,TB: $tType] :
( ! [A: tyop_2Efcp_2Ecart @ $o @ TB] :
( ( c_2Ewords_2Eword__lo @ TB @ ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) @ A )
= ( A
!= ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) ) )
& ! [A: tyop_2Efcp_2Ecart @ $o @ TA] :
~ ( c_2Ewords_2Eword__lo @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LO__word__0) ).
thf(3455,plain,
! [TA: $tType,TB: $tType] :
( ! [A: tyop_2Efcp_2Ecart @ $o @ TB] :
( ( c_2Ewords_2Eword__lo @ TB @ ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) @ A )
= ( A
!= ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) ) )
& ! [A: tyop_2Efcp_2Ecart @ $o @ TA] :
~ ( c_2Ewords_2Eword__lo @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(396,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ B @ A )
= ( c_2Einteger_2Eint__mul @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__COMM) ).
thf(2597,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ B @ A )
= ( c_2Einteger_2Eint__mul @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(45,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2EABS @ A )
= ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Einteger_2Eint__neg @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS) ).
thf(836,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2EABS @ A )
= ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Einteger_2Eint__neg @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(33,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ( ( ( c_2Earithmetic_2EMOD @ B @ A )
= c_2Enum_2E0 )
= ( ? [C: tyop_2Enum_2Enum] :
( B
= ( c_2Earithmetic_2E_2A @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__EQ__0__DIVISOR) ).
thf(795,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ( ( ( c_2Earithmetic_2EMOD @ B @ A )
= c_2Enum_2E0 )
= ( ? [C: tyop_2Enum_2Enum] :
( B
= ( c_2Earithmetic_2E_2A @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(628,axiom,
! [A: tyop_2Enum_2Enum] : ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__of__num @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__POS) ).
thf(3395,plain,
! [A: tyop_2Enum_2Enum] : ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__of__num @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(452,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ A ) @ B )
= ( ( c_2Einteger_2Eint__lt @ A @ B )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ B ) @ A ) ) )
& ( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2EABS @ A ) )
= ( ( c_2Einteger_2Eint__lt @ B @ A )
| ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2EABS @ A ) ) @ B )
= ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ B ) @ A )
| ( c_2Einteger_2Eint__lt @ A @ B ) ) )
& ( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2EABS @ A ) ) )
= ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__neg @ B ) )
& ( c_2Einteger_2Eint__lt @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__LT) ).
thf(2784,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ A ) @ B )
= ( ( c_2Einteger_2Eint__lt @ A @ B )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ B ) @ A ) ) )
& ( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2EABS @ A ) )
= ( ( c_2Einteger_2Eint__lt @ B @ A )
| ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ) )
& ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2EABS @ A ) ) @ B )
= ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ B ) @ A )
| ( c_2Einteger_2Eint__lt @ A @ B ) ) )
& ( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2EABS @ A ) ) )
= ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__neg @ B ) )
& ( c_2Einteger_2Eint__lt @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(481,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mul @ A @ B ) )
= ( c_2Einteger_2Eint__mul @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__RMUL) ).
thf(2878,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mul @ A @ B ) )
= ( c_2Einteger_2Eint__mul @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(367,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( c_2Einteger_2Eint__le @ ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__quot @ A @ B ) @ B ) ) @ ( c_2Einteger_2EABS @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__QUOT) ).
thf(2503,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( c_2Einteger_2Eint__le @ ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__quot @ A @ B ) @ B ) ) @ ( c_2Einteger_2EABS @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(470,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__of__num @ ( c_2Einteger_2ENum @ A ) )
= A )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__OF__NUM) ).
thf(2846,plain,
! [A: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__of__num @ ( c_2Einteger_2ENum @ A ) )
= A )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(294,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
| ( c_2Ewords_2Eword__ls @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__CASES) ).
thf(2256,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
| ( c_2Ewords_2Eword__ls @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(387,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
=> ? [D: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__sub @ B @ ( c_2Einteger_2Eint__mul @ D @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ecan__get__small) ).
thf(2564,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
=> ? [D: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__sub @ B @ ( c_2Einteger_2Eint__mul @ D @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(234,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( c_2Earithmetic_2E_3C_3D @ B @ C ) )
=> ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EDIV @ B @ A ) @ ( c_2Earithmetic_2EDIV @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EDIV__LE__MONOTONE) ).
thf(1748,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
& ( c_2Earithmetic_2E_3C_3D @ B @ C ) )
=> ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EDIV @ B @ A ) @ ( c_2Earithmetic_2EDIV @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(711,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
| ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
| ~ ( c_2Eprim__rec_2E_3C @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) )
| ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) @ A )
= ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ A @ ( c_2Earithmetic_2EMOD @ C @ A ) ) @ A ) ) ),
inference(cnf,[status(esa)],[710]) ).
thf(712,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) @ A )
= ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ A @ ( c_2Earithmetic_2EMOD @ C @ A ) ) @ A ) )
| ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
| ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
| ~ ( c_2Eprim__rec_2E_3C @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) ),
inference(lifteq,[status(thm)],[711]) ).
thf(659,axiom,
! [TA: $tType] :
( ( c_2Einteger__word_2Ew2i @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__0__w2i) ).
thf(3507,plain,
! [TA: $tType] :
( ( c_2Einteger__word_2Ew2i @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(277,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) )
= ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__ADD) ).
thf(2192,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) )
= ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(265,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EMOD @ B @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__LESS__EQ) ).
thf(2143,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EMOD @ B @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(69,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ewords_2Eword__le @ TA @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__EQ__REFL) ).
thf(954,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ewords_2Eword__le @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(561,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
=> ? [D: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
& ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__mul @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ecan__get__big) ).
thf(3129,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
=> ? [D: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
& ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__mul @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(18,axiom,
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2A @ A @ B ) ) )
& ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ A ) @ B )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mul @ A @ B ) ) )
& ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mul @ A @ B ) ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__CALCULATE) ).
thf(739,plain,
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2A @ A @ B ) ) )
& ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ A ) @ B )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mul @ A @ B ) ) )
& ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mul @ A @ B ) ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(273,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__divides @ A @ B ) )
& ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__neg @ A ) @ B )
= ( c_2Einteger_2Eint__divides @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__NEG) ).
thf(2175,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__divides @ A @ B ) )
& ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__neg @ A ) @ B )
= ( c_2Einteger_2Eint__divides @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(241,axiom,
! [TA: $tType,A: $o,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ A @ B @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__ID) ).
thf(1780,plain,
! [TA: $tType,A: $o,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ A @ B @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(236,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
~ ( ( c_2Eprim__rec_2E_3C @ A @ B )
& ( c_2Eprim__rec_2E_3C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__ANTISYM) ).
thf(1753,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
~ ( ( c_2Eprim__rec_2E_3C @ A @ B )
& ( c_2Eprim__rec_2E_3C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(904,plain,
( ( c_2Ebool_2ECOND @ $o @ $true @ c_2Ebool_2ET @ $false )
= ( ~ $true
=> $false ) ),
inference(instance,[status(thm)],[901]) ).
thf(905,plain,
c_2Ebool_2ECOND @ $o @ $true @ c_2Ebool_2ET @ $false,
inference(simp,[status(thm)],[904]) ).
thf(3872,plain,
c_2Ebool_2ECOND @ $o @ $true @ $true @ $false,
inference(rewrite,[status(thm)],[905,883]) ).
thf(196,axiom,
! [A: tyop_2Enum_2Enum > $o] :
( ! [B: tyop_2Enum_2Enum] :
( ! [C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ C @ B )
=> ( A @ C ) )
=> ( A @ B ) )
=> ! [B: tyop_2Enum_2Enum] : ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ECOMPLETE__INDUCTION) ).
thf(1531,plain,
! [A: tyop_2Enum_2Enum > $o] :
( ! [B: tyop_2Enum_2Enum] :
( ! [C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ C @ B )
=> ( A @ C ) )
=> ( A @ B ) )
=> ! [B: tyop_2Enum_2Enum] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(426,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
= ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__OR__EQ) ).
thf(2689,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
= ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(3,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ A @ C )
& ( c_2Earithmetic_2E_3C_3D @ B @ D ) )
=> ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__MONO__MULT2) ).
thf(690,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ A @ C )
& ( c_2Earithmetic_2E_3C_3D @ B @ D ) )
=> ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(605,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( C
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( ( c_2Einteger_2Eint__mul @ A @ C )
= ( c_2Einteger_2Eint__mul @ B @ C ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__RMUL__IMP) ).
thf(3315,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( C
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( ( c_2Einteger_2Eint__mul @ A @ C )
= ( c_2Einteger_2Eint__mul @ B @ C ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(142,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ A @ B )
= ( ( c_2Eprim__rec_2E_3C @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__OR__EQ) ).
thf(1230,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ A @ B )
= ( ( c_2Eprim__rec_2E_3C @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(183,axiom,
! [A: $o] :
( ( A
=> c_2Ebool_2EF )
= ( A = c_2Ebool_2EF ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__F__EQ__F) ).
thf(1484,plain,
! [A: $o] :
( ( A
=> c_2Ebool_2EF )
= ( A = c_2Ebool_2EF ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(288,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ A @ B )
= ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__CALCULATE) ).
thf(2224,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ A @ B )
= ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(602,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__QUOT__0) ).
thf(3305,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(177,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
~ ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
& ( c_2Ewords_2Eword__lt @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__ANTISYM) ).
thf(1452,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
~ ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
& ( c_2Ewords_2Eword__lt @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(716,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ B ) )
= ( ( B = c_2Enum_2E0 )
| ( c_2Earithmetic_2E_3C_3D @ A @ C ) ) ),
inference(cnf,[status(esa)],[715]) ).
thf(717,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ B ) )
= ( ( B = c_2Enum_2E0 )
| ( c_2Earithmetic_2E_3C_3D @ A @ C ) ) ),
inference(lifteq,[status(thm)],[716]) ).
thf(246,axiom,
! [A: $o] :
( ( A = c_2Ebool_2ET )
| ( A = c_2Ebool_2EF ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EBOOL__CASES__AX) ).
thf(1869,plain,
! [A: $o] :
( ( A = c_2Ebool_2ET )
| ( A = c_2Ebool_2EF ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(243,axiom,
! [A: $o,B: $o,C: $o,D: $o,E: $o] :
( ( ( A
=> ( C
=> B ) )
& ( ~ A
=> ( E
=> D ) ) )
=> ( ( c_2Ebool_2ECOND @ $o @ A @ C @ E )
=> ( c_2Ebool_2ECOND @ $o @ A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__cond) ).
thf(1785,plain,
! [A: $o,B: $o,C: $o,D: $o,E: $o] :
( ( ( A
=> ( C
=> B ) )
& ( ~ A
=> ( E
=> D ) ) )
=> ( ( c_2Ebool_2ECOND @ $o @ A @ C @ E )
=> ( c_2Ebool_2ECOND @ $o @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(529,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ~ ( c_2Einteger_2Eint__le @ A @ B ) )
= ( c_2Einteger_2Eint__lt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NOT__LE) ).
thf(3026,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ~ ( c_2Einteger_2Eint__le @ A @ B ) )
= ( c_2Einteger_2Eint__lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(315,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Epositive__product__implication) ).
thf(2337,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(286,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ A @ B )
= ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__div @ A @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2Eint__mod) ).
thf(2219,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__mod @ A @ B )
= ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__div @ A @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(239,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
& ( c_2Ewords_2Eword__le @ TA @ B @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__EQUAL__ANTISYM) ).
thf(1763,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
& ( c_2Ewords_2Eword__le @ TA @ B @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(670,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( A
= ( c_2Einteger_2Eint__neg @ A ) )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__SAME__EQ) ).
thf(3544,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A
= ( c_2Einteger_2Eint__neg @ A ) )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(632,axiom,
! [TA: $tType] :
( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__0) ).
thf(3412,plain,
! [TA: $tType] :
( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(117,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ~ ( c_2Eprim__rec_2E_3C @ A @ B )
& ( A != B ) )
=> ( c_2Eprim__rec_2E_3C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__CASES__IMP) ).
thf(1130,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ~ ( c_2Eprim__rec_2E_3C @ A @ B )
& ( A != B ) )
=> ( c_2Eprim__rec_2E_3C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(2467,plain,
! [TA: $tType] :
( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__L @ TA ) )
= ( c_2Ewords_2Eword__L @ TA ) ),
inference(cnf,[status(esa)],[2466]) ).
thf(2468,plain,
! [TA: $tType] :
( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__L @ TA ) )
= ( c_2Ewords_2Eword__L @ TA ) ),
inference(lifteq,[status(thm)],[2467]) ).
thf(415,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__ADD) ).
thf(2656,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(545,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
& ( c_2Ewords_2Eword__ls @ TA @ B @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__EQUAL__ANTISYM) ).
thf(3080,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
& ( c_2Ewords_2Eword__ls @ TA @ B @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(96,axiom,
! [A: tyop_2Enum_2Enum] :
~ ( c_2Eprim__rec_2E_3C @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ELESS__REFL) ).
thf(1053,plain,
! [A: tyop_2Enum_2Enum] :
~ ( c_2Eprim__rec_2E_3C @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(105,axiom,
! [A: tyop_2Enum_2Enum] :
~ ( c_2Eprim__rec_2E_3C @ A @ c_2Enum_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ENOT__LESS__0) ).
thf(1085,plain,
! [A: tyop_2Enum_2Enum] :
~ ( c_2Eprim__rec_2E_3C @ A @ c_2Enum_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(310,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__sub @ A @ B )
= C )
= ( A
= ( c_2Einteger_2Eint__add @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__SUB__RADD) ).
thf(2322,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__sub @ A @ B )
= C )
= ( A
= ( c_2Einteger_2Eint__add @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(362,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__neg @ A ) @ B )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__rem @ A @ B ) ) )
& ( ( c_2Einteger_2Eint__rem @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__rem @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM__NEG) ).
thf(2486,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( B
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__neg @ A ) @ B )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__rem @ A @ B ) ) )
& ( ( c_2Einteger_2Eint__rem @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__rem @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(37,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C )
=> ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2EDIV @ B @ C ) @ A )
= ( c_2Eprim__rec_2E_3C @ B @ ( c_2Earithmetic_2E_2A @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EDIV__LT__X) ).
thf(808,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C )
=> ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2EDIV @ B @ C ) @ A )
= ( c_2Eprim__rec_2E_3C @ B @ ( c_2Earithmetic_2E_2A @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(575,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
=> ( ( c_2Einteger_2Eint__divides @ B @ C )
= ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ejustify__divides) ).
thf(3174,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
=> ( ( c_2Einteger_2Eint__divides @ B @ C )
= ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(251,axiom,
! [TA: $tType,A: $o,B: $o,C: TA,D: TA,E: TA,F: TA] :
( ( ( A = B )
& ( B
=> ( C = D ) )
& ( ~ B
=> ( E = F ) ) )
=> ( ( c_2Ebool_2ECOND @ TA @ A @ C @ E )
= ( c_2Ebool_2ECOND @ TA @ B @ D @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CONG) ).
thf(2044,plain,
! [TA: $tType,A: $o,B: $o,C: TA,D: TA,E: TA,F: TA] :
( ( ( A = B )
& ( B
=> ( C = D ) )
& ( ~ B
=> ( E = F ) ) )
=> ( ( c_2Ebool_2ECOND @ TA @ A @ C @ E )
= ( c_2Ebool_2ECOND @ TA @ B @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(336,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ A ) @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__LINV) ).
thf(2411,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ A ) @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(240,axiom,
! [TA: $tType,A: $o,B: $o,C: TA,D: TA,E: TA,F: TA] :
( ( ( A = B )
& ( B
=> ( C = D ) )
& ( ~ B
=> ( E = F ) ) )
=> ( ( c_2Ebool_2ECOND @ TA @ A @ C @ E )
= ( c_2Ebool_2ECOND @ TA @ B @ D @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__CONG) ).
thf(1766,plain,
! [TA: $tType,A: $o,B: $o,C: TA,D: TA,E: TA,F: TA] :
( ( ( A = B )
& ( B
=> ( C = D ) )
& ( ~ B
=> ( E = F ) ) )
=> ( ( c_2Ebool_2ECOND @ TA @ A @ C @ E )
= ( c_2Ebool_2ECOND @ TA @ B @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(633,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__sub @ A @ B )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__0) ).
thf(3415,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__sub @ A @ B )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(513,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( A = B )
= ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
= ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__move__all__right) ).
thf(2975,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( A = B )
= ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
= ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(469,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__lt @ A @ B ) )
=> ( ( c_2Einteger_2Eint__mod @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LESS__MOD) ).
thf(2843,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__lt @ A @ B ) )
=> ( ( c_2Einteger_2Eint__mod @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(14,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ A @ C ) )
= ( ( A = c_2Enum_2E0 )
| ( c_2Earithmetic_2E_3C_3D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELE__MULT__LCANCEL) ).
thf(727,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ A @ C ) )
= ( ( A = c_2Enum_2E0 )
| ( c_2Earithmetic_2E_3C_3D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(542,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__add @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__RNEG) ).
thf(3071,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__add @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(393,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__mul @ A @ B ) )
& ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__mul @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__MUL) ).
thf(2584,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__mul @ A @ B ) )
& ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__mul @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(145,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TB] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
=> ( ( c_2Ewords_2Eword__extract @ TB @ TA @ A @ B @ C )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EXTRACT__ZERO) ).
thf(1240,plain,
! [TA: $tType,TB: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TB] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
=> ( ( c_2Ewords_2Eword__extract @ TB @ TA @ A @ B @ C )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(120,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
~ ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
& ( c_2Ewords_2Eword__le @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__EQ__ANTISYM) ).
thf(1141,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
~ ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
& ( c_2Ewords_2Eword__le @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(559,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ B )
| ( c_2Einteger_2Eint__lt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LET__TOTAL) ).
thf(3124,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ B )
| ( c_2Einteger_2Eint__lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(518,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEGNEG) ).
thf(2992,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(585,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__NEG) ).
thf(3224,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(174,axiom,
! [TA: $tType,A: ( tyop_2Enum_2Enum > TA ) > tyop_2Enum_2Enum > TA] :
( ! [B: tyop_2Enum_2Enum > TA,C: tyop_2Enum_2Enum > TA,D: tyop_2Enum_2Enum] :
( ! [E: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ E @ D )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( A @ B @ D )
= ( A @ C @ D ) ) )
=> ? [B: tyop_2Enum_2Enum > TA] :
! [C: tyop_2Enum_2Enum] :
( ( B @ C )
= ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewellorder_2EWF__REC__num) ).
thf(1427,plain,
! [TA: $tType,A: ( tyop_2Enum_2Enum > TA ) > tyop_2Enum_2Enum > TA] :
( ! [B: tyop_2Enum_2Enum > TA,C: tyop_2Enum_2Enum > TA,D: tyop_2Enum_2Enum] :
( ! [E: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ E @ D )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( A @ B @ D )
= ( A @ C @ D ) ) )
=> ? [B: tyop_2Enum_2Enum > TA] :
! [C: tyop_2Enum_2Enum] :
( ( B @ C )
= ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(108,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
=> ( c_2Earithmetic_2EMODEQ @ B @ ( c_2Earithmetic_2EMOD @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__MOD) ).
thf(1094,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
=> ( c_2Earithmetic_2EMODEQ @ B @ ( c_2Earithmetic_2EMOD @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(370,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( A
!= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
& ( A
!= ( c_2Ewords_2Eword__L @ TA ) ) )
=> ( ( ~ ( c_2Ewords_2Eword__msb @ TA @ A ) )
= ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2ETWO__COMP__POS__NEG) ).
thf(2511,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( A
!= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
& ( A
!= ( c_2Ewords_2Eword__L @ TA ) ) )
=> ( ( ~ ( c_2Ewords_2Eword__msb @ TA @ A ) )
= ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(663,axiom,
! [TA: $tType,TB: $tType] :
( ! [A: tyop_2Enum_2Enum] : ( c_2Ealignment_2Ealigned @ TB @ A @ ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) )
& ! [A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ealignment_2Ealigned @ TA @ c_2Enum_2E0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealigned__0) ).
thf(3520,plain,
! [TA: $tType,TB: $tType] :
( ! [A: tyop_2Enum_2Enum] : ( c_2Ealignment_2Ealigned @ TB @ A @ ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) )
& ! [A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ealignment_2Ealigned @ TA @ c_2Enum_2E0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(618,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
= B )
= ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__LID__UNIQ) ).
thf(3366,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
= B )
= ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(523,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ C ) @ ( c_2Einteger_2EABS @ B ) )
& ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C ) @ ( c_2Einteger_2Eint__le @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
& ? [D: tyop_2Einteger_2Eint] :
( A
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ B ) @ C ) ) )
=> ( ( c_2Einteger_2Eint__rem @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM__UNIQUE) ).
thf(3007,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ C ) @ ( c_2Einteger_2EABS @ B ) )
& ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C ) @ ( c_2Einteger_2Eint__le @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
& ? [D: tyop_2Einteger_2Eint] :
( A
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ B ) @ C ) ) )
=> ( ( c_2Einteger_2Eint__rem @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(50,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ A @ B )
= ( c_2Earithmetic_2E_2A @ A @ C ) )
= ( ( A = c_2Enum_2E0 )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEQ__MULT__LCANCEL) ).
thf(876,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ A @ B )
= ( c_2Earithmetic_2E_2A @ A @ C ) )
= ( ( A = c_2Enum_2E0 )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(172,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Egcd_2Egcd @ A @ c_2Enum_2E0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__0R) ).
thf(1421,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Egcd_2Egcd @ A @ c_2Enum_2E0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(564,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ B )
= ( ~ ( c_2Einteger_2Eint__lt @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2Eint__le) ).
thf(3139,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ B )
= ( ~ ( c_2Einteger_2Eint__lt @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(406,axiom,
! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( A @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2D @ B @ C ) ) )
= ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ C ) @ ( c_2Einteger_2Eint__of__num @ B ) )
& ( A @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ B ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ C ) ) ) ) )
| ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ B ) @ ( c_2Einteger_2Eint__of__num @ C ) )
& ( A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2EHO__SUB__ELIM) ).
thf(2626,plain,
! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( A @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2D @ B @ C ) ) )
= ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ C ) @ ( c_2Einteger_2Eint__of__num @ B ) )
& ( A @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ B ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ C ) ) ) ) )
| ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ B ) @ ( c_2Einteger_2Eint__of__num @ C ) )
& ( A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(908,plain,
( ( c_2Ebool_2ECOND @ $o @ $false @ c_2Ebool_2ET @ $false )
= ( ~ $false
=> $false ) ),
inference(instance,[status(thm)],[901]) ).
thf(909,plain,
~ ( c_2Ebool_2ECOND @ $o @ $false @ c_2Ebool_2ET @ $false ),
inference(simp,[status(thm)],[908]) ).
thf(3874,plain,
~ ( c_2Ebool_2ECOND @ $o @ $false @ $true @ $false ),
inference(rewrite,[status(thm)],[909,883]) ).
thf(319,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
= ( c_2Ewords_2Eword__add @ TA @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EQ__ADD__LCANCEL) ).
thf(2347,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
= ( c_2Ewords_2Eword__add @ TA @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(275,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ B )
=> ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RMUL) ).
thf(2187,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ B )
=> ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(537,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ A @ B )
= C )
= ( B
= ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__move__left__right) ).
thf(3056,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ A @ B )
= C )
= ( B
= ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(244,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
| ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__CASES) ).
thf(1866,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
| ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(111,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
& ( c_2Ewords_2Eword__lt @ TA @ B @ C ) )
=> ( c_2Ewords_2Eword__lt @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__TRANS) ).
thf(1108,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
& ( c_2Ewords_2Eword__lt @ TA @ B @ C ) )
=> ( c_2Ewords_2Eword__lt @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(480,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ A @ B )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( B
= ( c_2Einteger_2Eint__neg @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__RNEG__UNIQ) ).
thf(2875,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ A @ B )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( B
= ( c_2Einteger_2Eint__neg @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(573,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
= ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__SUB) ).
thf(3168,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
= ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(643,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__RID) ).
thf(3452,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(352,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ B )
= ( ? [C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ C @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES) ).
thf(2458,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ B )
= ( ? [C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__mul @ C @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(478,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
| ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__neg @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__NEGTOTAL) ).
thf(2870,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
| ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__neg @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(574,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ A @ B )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Einteger_2Eint__neg @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LNEG__UNIQ) ).
thf(3171,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ A @ B )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Einteger_2Eint__neg @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(508,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ B )
= ( ( c_2Einteger_2Eint__lt @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__CALCULATE) ).
thf(2960,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ B )
= ( ( c_2Einteger_2Eint__lt @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(401,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
= ( c_2Einteger_2Eint__add @ C @ B ) )
=> ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ C ) @ A ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__context__rwt2) ).
thf(2611,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
= ( c_2Einteger_2Eint__add @ C @ B ) )
=> ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ C ) @ A ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(311,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LTE__ADD) ).
thf(2325,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(494,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__add @ A @ B ) )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADDL) ).
thf(2919,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__add @ A @ B ) )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(317,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ B )
=> ~ ( c_2Einteger_2Eint__lt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__GT) ).
thf(2342,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ B )
=> ~ ( c_2Einteger_2Eint__lt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(25,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Egcd_2Egcd @ ( c_2Earithmetic_2E_2A @ C @ A ) @ ( c_2Earithmetic_2E_2A @ C @ B ) )
= ( c_2Earithmetic_2E_2A @ C @ ( c_2Egcd_2Egcd @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__COMMON__FACTOR) ).
thf(771,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( c_2Egcd_2Egcd @ ( c_2Earithmetic_2E_2A @ C @ A ) @ ( c_2Earithmetic_2E_2A @ C @ B ) )
= ( c_2Earithmetic_2E_2A @ C @ ( c_2Egcd_2Egcd @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(490,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__sub @ TA @ B @ A ) )
= ( c_2Ewords_2Eword__sub @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__SUB) ).
thf(2907,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__sub @ TA @ B @ A ) )
= ( c_2Ewords_2Eword__sub @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(646,axiom,
! [A: tyop_2Enum_2Enum] :
( ( A != c_2Enum_2E0 )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__of__num @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NZ__IMP__LT) ).
thf(3465,plain,
! [A: tyop_2Enum_2Enum] :
( ( A != c_2Enum_2E0 )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__of__num @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(347,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) )
=> ( ( c_2Eprim__rec_2E_3C @ ( c_2Einteger_2ENum @ B ) @ ( c_2Einteger_2ENum @ A ) )
= ( c_2Einteger_2Eint__lt @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__LT) ).
thf(2443,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) )
=> ( ( c_2Eprim__rec_2E_3C @ ( c_2Einteger_2ENum @ B ) @ ( c_2Einteger_2ENum @ A ) )
= ( c_2Einteger_2Eint__lt @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(150,axiom,
! [TA: $tType] :
( ! [A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A )
& ! [A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm) ).
thf(1326,plain,
! [TA: $tType] :
( ! [A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A )
& ! [A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(73,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ~ ( c_2Eprim__rec_2E_3C @ A @ B ) )
= ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ENOT__LESS) ).
thf(963,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ~ ( c_2Eprim__rec_2E_3C @ A @ B ) )
= ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(298,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ B ) @ C ) )
= ( c_2Einteger_2Eint__divides @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ejustify__divides3) ).
thf(2283,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ B ) @ C ) )
= ( c_2Einteger_2Eint__divides @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(473,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__LE0) ).
thf(2855,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(300,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ B @ A )
= ( c_2Einteger_2Eint__add @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__COMM) ).
thf(2290,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ B @ A )
= ( c_2Einteger_2Eint__add @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(263,axiom,
! [A: $o] :
( A
=> ( ~ A
=> c_2Ebool_2EF ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EAND__INV__IMP) ).
thf(2135,plain,
! [A: $o] :
( A
=> ( ~ A
=> c_2Ebool_2EF ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(384,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__ADD2) ).
thf(2554,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(624,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EABS__DIFF @ A @ B )
= c_2Enum_2E0 )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EABS__DIFF__EQ__0) ).
thf(3383,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EABS__DIFF @ A @ B )
= c_2Enum_2E0 )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(66,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
| ( c_2Eprim__rec_2E_3C @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecardinal_2ELT__CASES) ).
thf(946,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ A @ B )
| ( c_2Eprim__rec_2E_3C @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(619,axiom,
! [TA: $tType,TB: $tType] :
( ( c_2Ewords_2Esw2sw @ TB @ TA @ ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Esw2sw__0) ).
thf(3369,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Ewords_2Esw2sw @ TB @ TA @ ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(203,axiom,
! [TA: $tType,A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Einteger__word_2Ei2w @ TA @ A ) @ ( c_2Einteger__word_2Ei2w @ TA @ B ) )
= ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__i2w__mul) ).
thf(1629,plain,
! [TA: $tType,A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Einteger__word_2Ei2w @ TA @ A ) @ ( c_2Einteger__word_2Ei2w @ TA @ B ) )
= ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(657,axiom,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__of__num @ A )
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__of__num @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__NZ) ).
thf(3501,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__of__num @ A )
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__of__num @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(331,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
=> ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ C ) @ B ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__div @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eelim__le__coeffs) ).
thf(2394,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
=> ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ C ) @ B ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__div @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(72,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__le @ TA @ A @ B )
| ( c_2Ewords_2Eword__le @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__EQ__CASES) ).
thf(961,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__le @ TA @ A @ B )
| ( c_2Ewords_2Eword__le @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(226,axiom,
! [TA: $tType,A: $o,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ A @ B @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__ID) ).
thf(1721,plain,
! [TA: $tType,A: $o,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ A @ B @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(563,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( A
= ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUM__ZERO) ).
thf(3136,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( A
= ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(30,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL) ).
thf(786,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1736,plain,
( c_2Ebool_2EF
= ( ! [A: $o] : A ) ),
inference(lifteq,[status(thm)],[1735]) ).
thf(3661,plain,
~ ! [A: $o] : A,
inference(rewrite,[status(thm)],[1736,985]) ).
thf(3662,plain,
~ sk32,
inference(cnf,[status(esa)],[3661]) ).
thf(375,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ A @ B )
& ( c_2Einteger_2Eint__le @ B @ C ) )
=> ( c_2Einteger_2Eint__lt @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LTE__TRANS) ).
thf(2526,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ A @ B )
& ( c_2Einteger_2Eint__le @ B @ C ) )
=> ( c_2Einteger_2Eint__lt @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(503,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ B ) )
=> ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__neg @ B ) )
=> ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ C ) @ A ) )
= c_2Ebool_2EF ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ele__context__rwt2) ).
thf(2944,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ B ) )
=> ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__neg @ B ) )
=> ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ C ) @ A ) )
= c_2Ebool_2EF ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(89,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ C )
= ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ C ) @ ( c_2Ewords_2Eword__mul @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__RIGHT__ADD__DISTRIB) ).
thf(1030,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ C )
= ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ C ) @ ( c_2Ewords_2Eword__mul @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(221,axiom,
! [A: $o] :
( ( A
| c_2Ebool_2ET )
= c_2Ebool_2ET ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EOR__CLAUSES__XT) ).
thf(1689,plain,
! [A: $o] :
( ( A
| c_2Ebool_2ET )
= c_2Ebool_2ET ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(358,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__sub @ A @ B ) @ C )
& ( c_2Einteger_2Eint__lt @ C @ A ) )
= ( ? [D: tyop_2Einteger_2Eint] :
( ( C
= ( c_2Einteger_2Eint__sub @ A @ D ) )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
& ( c_2Einteger_2Eint__le @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ein__subtractive__range) ).
thf(2475,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__sub @ A @ B ) @ C )
& ( c_2Einteger_2Eint__lt @ C @ A ) )
= ( ? [D: tyop_2Einteger_2Eint] :
( ( C
= ( c_2Einteger_2Eint__sub @ A @ D ) )
& ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
& ( c_2Einteger_2Eint__le @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(250,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( A = B )
= ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
& ( c_2Earithmetic_2E_3C_3D @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEQ__LESS__EQ) ).
thf(2041,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( A = B )
= ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
& ( c_2Earithmetic_2E_3C_3D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(279,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ B @ A ) )
=> ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ B ) @ ( c_2Einteger_2Eint__neg @ A ) ) )
= ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
= ( c_2Einteger_2Eint__add @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ele__context__rwt5) ).
thf(2198,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ B @ A ) )
=> ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ B ) @ ( c_2Einteger_2Eint__neg @ A ) ) )
= ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
= ( c_2Einteger_2Eint__add @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(135,axiom,
! [A: $o] :
( c_2Ebool_2EF
=> A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EFALSITY) ).
thf(1193,plain,
! [A: $o] :
( c_2Ebool_2EF
=> A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(290,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
~ ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
& ( c_2Ewords_2Eword__ls @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__EQ__ANTISYM) ).
thf(2230,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
~ ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
& ( c_2Ewords_2Eword__ls @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(436,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__abs @ TA @ A )
= ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ ( c_2Einteger_2EABS @ ( c_2Einteger__word_2Ew2i @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__abs__w2i) ).
thf(2739,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__abs @ TA @ A )
= ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ ( c_2Einteger_2EABS @ ( c_2Einteger__word_2Ew2i @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(405,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ A @ B ) )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADDR) ).
thf(2623,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ A @ B ) )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(450,axiom,
! [A: tyop_2Enum_2Enum] : ( c_2Egcd_2Eis__gcd @ A @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__REF) ).
thf(2779,plain,
! [A: tyop_2Enum_2Enum] : ( c_2Egcd_2Eis__gcd @ A @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(126,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
& ( c_2Eprim__rec_2E_3C @ B @ C ) )
=> ( c_2Eprim__rec_2E_3C @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__EQ__LESS__TRANS) ).
thf(1161,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
& ( c_2Eprim__rec_2E_3C @ B @ C ) )
=> ( c_2Eprim__rec_2E_3C @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(423,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__sub @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__NEG2) ).
thf(2680,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) )
= ( c_2Einteger_2Eint__sub @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(274,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__mul @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__RMUL) ).
thf(2183,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__mul @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(217,axiom,
( ( ~ c_2Ebool_2ET ) = c_2Ebool_2EF ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ENOT__CLAUSES__T) ).
thf(1678,plain,
( ( ~ c_2Ebool_2ET ) = c_2Ebool_2EF ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Efcp_2Ecart @ $o @ TB] : ( c_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2Ew2n @ TA @ ( c_2Ewords_2Ew2w @ TB @ TA @ A ) ) @ ( c_2Ewords_2Ew2n @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Ew2n__w2w__le) ).
thf(967,plain,
! [TA: $tType,TB: $tType,A: tyop_2Efcp_2Ecart @ $o @ TB] : ( c_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2Ew2n @ TA @ ( c_2Ewords_2Ew2w @ TB @ TA @ A ) ) @ ( c_2Ewords_2Ew2n @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(200,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
= ( A != c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecardinal_2ELT__NZ) ).
thf(1546,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
= ( A != c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(165,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__abs @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
= ( c_2Ewords_2Eword__abs @ TA @ ( c_2Ewords_2Eword__sub @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__abs__diff) ).
thf(1395,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__abs @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
= ( c_2Ewords_2Eword__abs @ TA @ ( c_2Ewords_2Eword__sub @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(552,axiom,
! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( C
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( A @ ( c_2Einteger_2Eint__mod @ B @ C ) )
= ( ? [D: tyop_2Einteger_2Eint,E: tyop_2Einteger_2Eint] :
( ( B
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ C ) @ E ) )
& ( ( ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__lt @ C @ E )
& ( c_2Einteger_2Eint__le @ E @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ( ~ ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ E )
& ( c_2Einteger_2Eint__lt @ E @ C ) ) )
& ( A @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__P) ).
thf(3100,plain,
! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( C
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( A @ ( c_2Einteger_2Eint__mod @ B @ C ) )
= ( ? [D: tyop_2Einteger_2Eint,E: tyop_2Einteger_2Eint] :
( ( B
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ C ) @ E ) )
& ( ( ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__lt @ C @ E )
& ( c_2Einteger_2Eint__le @ E @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
| ( ~ ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ E )
& ( c_2Einteger_2Eint__lt @ E @ C ) ) )
& ( A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(247,axiom,
! [TA: $tType,A: $o,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ A @ B @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ECOND__CLAUSES__ID) ).
thf(1876,plain,
! [TA: $tType,A: $o,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ A @ B @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(539,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ B @ C ) )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Elt__move__left__left) ).
thf(3062,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ B @ C ) )
= ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(498,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
& ( c_2Ewords_2Eword__lo @ TA @ B @ C ) )
=> ( c_2Ewords_2Eword__lo @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__EQ__LOWER__TRANS) ).
thf(2930,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
& ( c_2Ewords_2Eword__lo @ TA @ B @ C ) )
=> ( c_2Ewords_2Eword__lo @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(295,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Ew2w @ TA @ TA @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Ew2w__id) ).
thf(2258,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Ew2w @ TA @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(118,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Ew2i @ TA @ A )
= ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Ewords_2Eword__msb @ TA @ A ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ew2i__def) ).
thf(1133,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Einteger__word_2Ew2i @ TA @ A )
= ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Ewords_2Eword__msb @ TA @ A ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(262,axiom,
! [A: $o,B: $o,C: $o,D: $o] :
( ( D
= ( c_2Ebool_2ECOND @ $o @ C @ B @ A ) )
= ( ( D
| C
| ~ A )
& ( D
| ~ B
| ~ C )
& ( D
| ~ B
| ~ A )
& ( ~ C
| B
| ~ D )
& ( C
| A
| ~ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__cond) ).
thf(2102,plain,
! [A: $o,B: $o,C: $o,D: $o] :
( ( D
= ( c_2Ebool_2ECOND @ $o @ C @ B @ A ) )
= ( ( D
| C
| ~ A )
& ( D
| ~ B
| ~ C )
& ( D
| ~ B
| ~ A )
& ( ~ C
| B
| ~ D )
& ( C
| A
| ~ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(19,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ A )
= ( c_2Earithmetic_2E_2A @ C @ A ) )
= ( ( A = c_2Enum_2E0 )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEQ__MULT__RCANCEL) ).
thf(752,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ A )
= ( c_2Earithmetic_2E_2A @ C @ A ) )
= ( ( A = c_2Enum_2E0 )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(304,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
=> ( ( B = C )
= ( ( c_2Einteger_2Eint__mul @ A @ B )
= ( c_2Einteger_2Eint__mul @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__justify__multiplication) ).
thf(2302,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
=> ( ( B = C )
= ( ( c_2Einteger_2Eint__mul @ A @ B )
= ( c_2Einteger_2Eint__mul @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(372,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__SUB__LADD) ).
thf(2517,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
= ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(424,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( A
= ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
= ( ( c_2Ewords_2Eword__add @ TA @ A @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EQ__SUB__LADD) ).
thf(2683,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( A
= ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
= ( ( c_2Ewords_2Eword__add @ TA @ A @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(459,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ A @ B )
& ( c_2Einteger_2Eint__lt @ C @ D ) )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADD2) ).
thf(2815,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ A @ B )
& ( c_2Einteger_2Eint__lt @ C @ D ) )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(435,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EABS__DIFF @ A @ B )
= ( c_2Earithmetic_2EABS__DIFF @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EABS__DIFF__COMM) ).
thf(2736,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EABS__DIFF @ A @ B )
= ( c_2Earithmetic_2EABS__DIFF @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(566,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ealignment_2Ealigned @ TA @ A @ C )
=> ( ( ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
= ( c_2Ealignment_2Ealigned @ TA @ A @ B ) )
& ( ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
= ( c_2Ealignment_2Ealigned @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealigned__add__sub) ).
thf(3145,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ealignment_2Ealigned @ TA @ A @ C )
=> ( ( ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
= ( c_2Ealignment_2Ealigned @ TA @ A @ B ) )
& ( ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
= ( c_2Ealignment_2Ealigned @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(525,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMODEQ @ A @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__REFL) ).
thf(3015,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMODEQ @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(609,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum] :
~ ( c_2Ewords_2Eword__bit @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__bit__0) ).
thf(3328,plain,
! [TA: $tType,A: tyop_2Enum_2Enum] :
~ ( c_2Ewords_2Eword__bit @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(280,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__msb @ TA @ A )
= ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2Eword__L @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__MSB__INT__MIN__LS) ).
thf(2201,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__msb @ TA @ A )
= ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2Eword__L @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(314,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__neg @ A ) )
= ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__GT0) ).
thf(2334,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__neg @ A ) )
= ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(595,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ A @ B )
& ( c_2Einteger_2Eint__le @ B @ C ) )
=> ( c_2Einteger_2Eint__le @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__TRANS) ).
thf(3277,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ A @ B )
& ( c_2Einteger_2Eint__le @ B @ C ) )
=> ( c_2Einteger_2Eint__le @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(430,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__sub @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= C )
& ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
= ( c_2Einteger_2Eint__neg @ C ) )
& ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) ) )
& ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) ) )
& ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
& ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__REDUCE) ).
thf(2704,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__sub @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= C )
& ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
= ( c_2Einteger_2Eint__neg @ C ) )
& ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) ) )
& ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) ) )
& ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
& ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
= ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(338,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__sub @ TA @ B @ A ) @ B )
= ( c_2Ewords_2Eword__2comp @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__SUB3) ).
thf(2417,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__sub @ TA @ B @ A ) @ B )
= ( c_2Ewords_2Eword__2comp @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(97,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Earithmetic_2E_3C_3D @ B @ A ) )
=> ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2D @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__LESS) ).
thf(1056,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Earithmetic_2E_3C_3D @ B @ A ) )
=> ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2D @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(326,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ B )
= ( ( c_2Einteger_2Eint__lt @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__LT) ).
thf(2366,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ A @ B )
= ( ( c_2Einteger_2Eint__lt @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(90,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ( ( c_2Earithmetic_2EMOD @ c_2Enum_2E0 @ A )
= c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EZERO__MOD) ).
thf(1033,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
=> ( ( c_2Earithmetic_2EMOD @ c_2Enum_2E0 @ A )
= c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(492,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
= ( c_2Ewords_2Eword__sub @ TA @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__RCANCEL__SUB) ).
thf(2913,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
= ( c_2Ewords_2Eword__sub @ TA @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(42,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) )
=> ! [C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2EMOD @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) @ B )
= ( c_2Earithmetic_2EMOD @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__MULT__MOD) ).
thf(828,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) )
=> ! [C: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2EMOD @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) @ B )
= ( c_2Earithmetic_2EMOD @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(154,axiom,
! [A: $o] :
( A
=> c_2Ebool_2ET ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2Etrue__imp) ).
thf(1346,plain,
! [A: $o] :
( A
=> c_2Ebool_2ET ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(53,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__mul @ TA @ A @ B )
= ( c_2Ewords_2Eword__mul @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__MULT__COMM) ).
thf(886,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__mul @ TA @ A @ B )
= ( c_2Ewords_2Eword__mul @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(636,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
=> ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Einteger_2Eint__of__num @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__POSINT__EXISTS) ).
thf(3424,plain,
! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
=> ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Einteger_2Eint__of__num @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(100,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
? [C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__mul @ D @ ( c_2Einteger_2Eint__of__num @ B ) ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Egcd_2Egcd @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2EINT__LINEAR__GCD) ).
thf(1065,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
? [C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__mul @ D @ ( c_2Einteger_2Eint__of__num @ B ) ) )
= ( c_2Einteger_2Eint__of__num @ ( c_2Egcd_2Egcd @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(719,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ c_2Enum_2E0 )
= c_2Enum_2E0 ),
inference(cnf,[status(esa)],[718]) ).
thf(720,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ c_2Enum_2E0 )
= c_2Enum_2E0 ),
inference(lifteq,[status(thm)],[719]) ).
thf(419,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
=> ( c_2Ewords_2Eword__ls @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__IMP__LOWER__OR__EQ) ).
thf(2668,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
=> ( c_2Ewords_2Eword__ls @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(589,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B )
= ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__LNEG) ).
thf(3244,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B )
= ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(654,axiom,
( ! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__0) ).
thf(3489,plain,
( ! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ! [A: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(627,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__exp @ A @ B )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( B != c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EXP__EQ0) ).
thf(3392,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__exp @ A @ B )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
& ( B != c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(668,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM0) ).
thf(3538,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(380,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ A @ B )
& ( c_2Einteger_2Eint__lt @ C @ D ) )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LET__ADD2) ).
thf(2539,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__le @ A @ B )
& ( c_2Einteger_2Eint__lt @ C @ D ) )
=> ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(476,axiom,
! [TA: $tType,TB: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__extract @ TB @ TA @ A @ B @ ( c_2Ebitstring_2Ev2w @ TB @ C ) )
= ( c_2Ewords_2Ew2w @ TB @ TA @ ( c_2Ewords_2Eword__bits @ TB @ A @ B @ ( c_2Ebitstring_2Ev2w @ TB @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebitstring_2Eword__extract__v2w) ).
thf(2864,plain,
! [TA: $tType,TB: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Elist_2Elist @ $o] :
( ( c_2Ewords_2Eword__extract @ TB @ TA @ A @ B @ ( c_2Ebitstring_2Ev2w @ TB @ C ) )
= ( c_2Ewords_2Ew2w @ TB @ TA @ ( c_2Ewords_2Eword__bits @ TB @ A @ B @ ( c_2Ebitstring_2Ev2w @ TB @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(691,plain,
! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Earithmetic_2E_3C_3D @ A @ C )
| ~ ( c_2Earithmetic_2E_3C_3D @ B @ D )
| ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ D ) ) ),
inference(cnf,[status(esa)],[690]) ).
thf(361,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ B )
=> ( c_2Einteger_2Eint__le @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__IMP__LE) ).
thf(2484,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ B )
=> ( c_2Einteger_2Eint__le @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(614,axiom,
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__of__num @ A )
= ( c_2Einteger_2Eint__of__num @ B ) )
= ( A = B ) )
& ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__neg @ A )
= ( c_2Einteger_2Eint__neg @ B ) )
= ( A = B ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( ( c_2Einteger_2Eint__of__num @ A )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
= ( ( A = c_2Enum_2E0 )
& ( B = c_2Enum_2E0 ) ) )
& ( ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ A ) )
= ( c_2Einteger_2Eint__of__num @ B ) )
= ( ( A = c_2Enum_2E0 )
& ( B = c_2Enum_2E0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__CALCULATE) ).
thf(3341,plain,
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__of__num @ A )
= ( c_2Einteger_2Eint__of__num @ B ) )
= ( A = B ) )
& ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__neg @ A )
= ( c_2Einteger_2Eint__neg @ B ) )
= ( A = B ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( ( c_2Einteger_2Eint__of__num @ A )
= ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
= ( ( A = c_2Enum_2E0 )
& ( B = c_2Enum_2E0 ) ) )
& ( ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ A ) )
= ( c_2Einteger_2Eint__of__num @ B ) )
= ( ( A = c_2Enum_2E0 )
& ( B = c_2Enum_2E0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(321,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ A @ B )
& ( c_2Einteger_2Eint__lt @ B @ C ) )
=> ( c_2Einteger_2Eint__lt @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__TRANS) ).
thf(2353,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__lt @ A @ B )
& ( c_2Einteger_2Eint__lt @ B @ C ) )
=> ( c_2Einteger_2Eint__lt @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(46,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum,E: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMODEQ @ E @ D @ C )
=> ( ( c_2Earithmetic_2EMODEQ @ E @ B @ A )
=> ( c_2Earithmetic_2EMODEQ @ E @ ( c_2Earithmetic_2E_2A @ D @ B ) @ ( c_2Earithmetic_2E_2A @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__MULT__CONG) ).
thf(839,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum,E: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMODEQ @ E @ D @ C )
=> ( ( c_2Earithmetic_2EMODEQ @ E @ B @ A )
=> ( c_2Earithmetic_2EMODEQ @ E @ ( c_2Earithmetic_2E_2A @ D @ B ) @ ( c_2Earithmetic_2E_2A @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(510,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
( ( ( c_2Enumpair_2Encons @ B @ A )
= ( c_2Enumpair_2Encons @ D @ C ) )
= ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Encons__11) ).
thf(2966,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
( ( ( c_2Enumpair_2Encons @ B @ A )
= ( c_2Enumpair_2Encons @ D @ C ) )
= ( ( B = D )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(343,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ~ ( c_2Ewords_2Eword__ls @ TA @ A @ B ) )
= ( c_2Ewords_2Eword__lo @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NOT__LOWER__EQUAL) ).
thf(2430,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ~ ( c_2Ewords_2Eword__ls @ TA @ A @ B ) )
= ( c_2Ewords_2Eword__lo @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(397,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ D ) @ B ) )
= ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ D ) @ B ) )
& ( c_2Einteger_2Eint__divides @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ejustify__divides2) ).
thf(2600,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ D ) @ B ) )
= ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ D ) @ B ) )
& ( c_2Einteger_2Eint__divides @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(679,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ A @ B )
= A )
= ( B
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__RID__UNIQ) ).
thf(3570,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ A @ B )
= A )
= ( B
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(722,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
| ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C )
| ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2EMOD @ B @ C ) )
= ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ A @ C ) ) ) ),
inference(cnf,[status(esa)],[721]) ).
thf(723,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ A @ C ) )
= ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2EMOD @ B @ C ) ) )
| ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
| ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C ) ),
inference(lifteq,[status(thm)],[722]) ).
thf(527,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
~ ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
& ( c_2Ewords_2Eword__lo @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__ANTISYM) ).
thf(3020,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
~ ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
& ( c_2Ewords_2Eword__lo @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(649,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__slice @ TA @ B @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SLICE__ZERO2) ).
thf(3474,plain,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__slice @ TA @ B @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(665,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__of__num @ A )
= ( c_2Einteger_2Eint__of__num @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__INJ) ).
thf(3528,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Einteger_2Eint__of__num @ A )
= ( c_2Einteger_2Eint__of__num @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(638,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__2comp @ TA @ A )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__EQ__0) ).
thf(3437,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Ewords_2Eword__2comp @ TA @ A )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(482,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ~ ( c_2Einteger_2Eint__lt @ A @ B ) )
= ( c_2Einteger_2Eint__le @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NOT__LT) ).
thf(2881,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ~ ( c_2Einteger_2Eint__lt @ A @ B ) )
= ( c_2Einteger_2Eint__le @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(233,axiom,
! [A: $o] :
( ( ( c_2Ebool_2ET = A )
= A )
& ( ( A = c_2Ebool_2ET )
= A )
& ( ( c_2Ebool_2EF = A )
= ( ~ A ) )
& ( ( A = c_2Ebool_2EF )
= ( ~ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
thf(1737,plain,
! [A: $o] :
( ( ( c_2Ebool_2ET = A )
= A )
& ( ( A = c_2Ebool_2ET )
= A )
& ( ( c_2Ebool_2EF = A )
= ( ~ A ) )
& ( ( A = c_2Ebool_2EF )
= ( ~ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(484,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ C )
= ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__SUB__SYM) ).
thf(2887,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ C )
= ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(520,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__add @ A @ C ) )
= ( c_2Einteger_2Eint__le @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__LADD) ).
thf(2998,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__add @ A @ C ) )
= ( c_2Einteger_2Eint__le @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(345,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ B )
=> ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__add @ C @ B ) )
= ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RADD) ).
thf(2436,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__divides @ A @ B )
=> ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__add @ C @ B ) )
= ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(640,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( c_2Ewords_2Eword__concat @ TC @ TB @ TA @ ( c_2Ewords_2En2w @ TC @ c_2Enum_2E0 ) @ ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__concat__0__0) ).
thf(3443,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( c_2Ewords_2Eword__concat @ TC @ TB @ TA @ ( c_2Ewords_2En2w @ TC @ c_2Enum_2E0 ) @ ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) )
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(20,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) )
=> ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) @ B )
= ( c_2Earithmetic_2EMOD @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__SUB) ).
thf(755,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
& ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) )
=> ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) @ B )
= ( c_2Earithmetic_2EMOD @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(536,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
=> ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) )
= ( c_2Einteger_2Eint__le @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__MONO) ).
thf(3052,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
=> ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) )
= ( c_2Einteger_2Eint__le @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(106,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT) ).
thf(1088,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(579,axiom,
! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ! [D: tyop_2Einteger_2Eint] :
( ( A @ D )
=> ( A @ ( c_2Einteger_2Eint__add @ D @ B ) ) )
& ( A @ C ) )
=> ! [D: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
=> ( A @ ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__mul @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ebot__and__greaters) ).
thf(3200,plain,
! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( ! [D: tyop_2Einteger_2Eint] :
( ( A @ D )
=> ( A @ ( c_2Einteger_2Eint__add @ D @ B ) ) )
& ( A @ C ) )
=> ! [D: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
=> ( A @ ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__mul @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(534,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ B ) @ A )
= ( c_2Ewords_2Eword__sub @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB) ).
thf(3047,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ B ) @ A )
= ( c_2Ewords_2Eword__sub @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(599,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ A @ B )
= B )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__LID__UNIQ) ).
thf(3296,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( ( c_2Einteger_2Eint__add @ A @ B )
= B )
= ( A
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(681,axiom,
! [A: tyop_2Estring_2Echar] :
( ( c_2Estring_2Echar__size @ A )
= c_2Enum_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Estring_2Echar__size__def) ).
thf(3575,plain,
! [A: tyop_2Estring_2Echar] :
( ( c_2Estring_2Echar__size @ A )
= c_2Enum_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(77,axiom,
! [A: $o,B: $o] :
( ( ~ ( ~ B
| A )
=> c_2Ebool_2EF )
= ( B
=> ( ~ A
=> c_2Ebool_2EF ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL3) ).
thf(972,plain,
! [A: $o,B: $o] :
( ( ~ ( ~ B
| A )
=> c_2Ebool_2EF )
= ( B
=> ( ~ A
=> c_2Ebool_2EF ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(683,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__of__num @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__OF__INT) ).
thf(3580,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__of__num @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(645,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( B = C )
= ( ( c_2Einteger_2Eint__mul @ A @ B )
= ( c_2Einteger_2Eint__mul @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__LMUL2) ).
thf(3461,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ( ( B = C )
= ( ( c_2Einteger_2Eint__mul @ A @ B )
= ( c_2Einteger_2Eint__mul @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(148,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2D @ A @ A )
= c_2Enum_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__EQUAL__0) ).
thf(1320,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2D @ A @ A )
= c_2Enum_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(210,axiom,
! [A: tyop_2Enum_2Enum > $o] :
( ( ? [B: tyop_2Enum_2Enum] : ( A @ B ) )
= ( ? [B: tyop_2Enum_2Enum] :
( ( A @ B )
& ! [C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ C @ B )
=> ~ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2ETemporal__Logic_2EWELL__ORDER) ).
thf(1653,plain,
! [A: tyop_2Enum_2Enum > $o] :
( ( ? [B: tyop_2Enum_2Enum] : ( A @ B ) )
= ( ? [B: tyop_2Enum_2Enum] :
( ( A @ B )
& ! [C: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ C @ B )
=> ~ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(586,axiom,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ B )
= ( ( c_2Einteger_2Eint__le @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__LE) ).
thf(3227,plain,
! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__lt @ A @ B )
= ( ( c_2Einteger_2Eint__le @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(581,axiom,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ! [B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__mul @ B @ A ) @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM__COMMON__FACTOR) ).
thf(3212,plain,
! [A: tyop_2Einteger_2Eint] :
( ( A
!= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
=> ! [B: tyop_2Einteger_2Eint] :
( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__mul @ B @ A ) @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(600,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Einteger__word_2Ew2i @ TA @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ew2i__eq__0) ).
thf(3299,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( ( c_2Einteger__word_2Ew2i @ TA @ A )
= ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,A: $o,B: TB > TA,C: TB > TA,D: TB] :
( ( c_2Ebool_2ECOND @ ( TB > TA ) @ A @ B @ C @ D )
= ( c_2Ebool_2ECOND @ TA @ A @ ( B @ D ) @ ( C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__RATOR) ).
thf(1009,plain,
! [TA: $tType,TB: $tType,A: $o,B: TB > TA,C: TB > TA,D: TB] :
( ( c_2Ebool_2ECOND @ ( TB > TA ) @ A @ B @ C @ D )
= ( c_2Ebool_2ECOND @ TA @ A @ ( B @ D ) @ ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(258,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ B @ A )
=> ( ( c_2Earithmetic_2EMOD @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__MOD) ).
thf(2087,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ B @ A )
=> ( ( c_2Earithmetic_2EMOD @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(673,axiom,
! [TA: $tType] :
( ( c_2Ewords_2Ew2n @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= c_2Enum_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__0__n2w) ).
thf(3553,plain,
! [TA: $tType] :
( ( c_2Ewords_2Ew2n @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
= c_2Enum_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(4436,plain,
$false,
inference(e,[status(thm)],[2452,1879,1190,1454,3399,1729,3477,1083,3449,2544,1549,1110,1686,2163,892,1036,2822,3873,2094,1411,1168,2306,2463,3397,1179,2331,777,3566,1750,2309,2210,730,1068,2062,2947,3108,2099,3498,3402,1437,1041,1200,3534,1522,2644,2495,3230,2776,2659,3377,994,2953,2590,1401,2686,1756,3365,1735,1233,814,1497,2195,3017,3004,3332,2316,3446,715,3338,2168,698,1761,913,3562,1640,1354,2146,1507,1222,3335,2972,709,1046,3308,1359,1386,2082,1724,2819,1518,2405,2957,3103,898,1243,1127,2985,2227,841,3513,2067,2825,724,3221,3029,3116,2339,3495,3574,2501,2217,1323,702,802,3089,2897,2466,2603,2916,2698,1660,949,2745,2571,817,3517,3374,1704,2767,969,3951,2852,3258,2829,1545,2420,1398,881,1115,2635,2520,2730,2989,1362,2388,2533,2222,3322,3966,789,2090,3295,1418,3525,2925,966,1489,2950,2237,1415,2893,1632,2469,1136,834,2058,687,3068,2861,956,774,3157,1351,2286,2804,2884,3510,2762,3389,981,2618,2833,692,2190,3421,3808,2523,2530,3361,2809,2750,1405,1697,3559,1651,2922,3011,2204,3567,2574,761,1338,1783,2641,2621,3418,3151,3097,942,3591,2910,3531,2364,2232,2296,714,1868,3550,2773,3037,1163,2673,2264,910,1091,2428,3022,1666,2969,3233,2606,3154,2528,1238,3471,2733,825,1343,2560,952,2541,2890,2414,916,2433,879,2663,3578,2872,1457,1624,2609,889,1159,1656,3050,1392,710,1012,2653,1365,2670,3065,3556,1027,2327,2213,2344,2492,3105,3122,2801,1017,1227,3218,2692,1006,3386,3119,3440,697,2498,2157,2840,1143,1096,2509,2724,2858,783,2638,1118,3001,989,3311,1028,3210,3094,901,3194,2666,2781,2798,1683,2830,1182,1424,2312,2455,2978,2472,3294,1155,3573,706,3059,2900,2355,721,3937,3247,3074,3364,2932,3486,1099,985,1150,1478,2536,3126,3541,1530,1539,2836,1382,2581,1060,1050,2140,2756,3083,3162,3215,1525,1333,1434,1318,2546,805,3279,765,2963,1071,2440,1515,1026,2995,718,1732,1202,792,2076,2748,1170,2408,1663,953,1185,2235,1648,2677,1146,1219,2941,3375,3274,733,1727,1510,2391,2904,1680,3358,3871,2149,3372,3547,2727,2938,2849,2981,3086,2806,2695,694,3319,3504,1884,1389,3255,2514,2568,1701,2398,1520,2817,1503,1669,936,2293,3077,3330,713,1058,3594,2166,2557,2425,704,3091,3302,1675,1635,2935,2759,2753,1638,3355,2358,2319,1356,831,2383,2422,3287,736,3197,3160,2079,2361,2478,3251,1492,2299,3468,1542,811,1471,2742,758,3133,2261,799,2446,3165,3034,2647,2928,2461,2812,1080,2632,848,700,2593,895,3483,3583,1112,2578,3480,2770,1198,2401,768,868,780,883,986,1726,3178,2207,1694,2867,1474,2350,959,2171,2765,1044,695,2481,2369,1015,3325,3142,2506,3380,3031,2614,3427,1166,944,2449,2629,939,3455,2597,836,795,3395,2784,2878,2503,2846,2256,2564,1748,712,3507,707,2192,2143,954,3129,739,2175,1780,1753,3872,1531,2689,690,3315,1230,1484,2224,3305,1452,717,1869,1785,3026,2337,2219,1763,3544,3412,1130,2468,2656,3080,1053,1085,2322,2486,808,3174,2044,2411,1766,3415,2975,2843,727,3071,2584,1240,1141,3124,2992,3224,1427,1094,2511,3520,3366,3007,876,1421,3139,2626,3565,3874,2347,2187,3056,1866,1108,2875,3168,3452,2458,2870,2828,3171,2960,2611,2325,2919,2342,771,2907,3465,2443,1326,963,2283,2855,2290,2135,2554,3383,946,3369,1629,3501,2394,961,1721,3136,786,3662,2526,2944,1030,1689,2475,2041,2198,1193,2230,2739,2623,2779,1161,2680,2183,1678,967,1546,1395,3100,1876,3062,2930,2258,1133,2102,752,2302,2517,2683,2815,2736,3145,3015,3328,2201,2334,3277,2704,2417,1056,2366,1033,2913,828,1346,886,3424,1065,720,2668,3244,3489,3392,3538,2539,2864,691,2484,3341,2353,839,2966,2430,2600,3570,723,3020,3474,3528,3437,2881,1737,2887,2998,2436,3443,755,3052,1088,3200,3047,3296,3575,972,3580,3461,1320,1653,3227,3212,3299,1009,2087,3553]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP015^7 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.18 % Computer : n017.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 19:25:22 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.65/0.48 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 7.32/2.32 % [INFO] Parsing done (1836ms).
% 7.32/2.34 % [INFO] Running in sequential loop mode.
% 7.76/2.52 % [INFO] eprover registered as external prover.
% 7.76/2.52 % [INFO] Scanning for conjecture ...
% 10.57/3.27 % [INFO] Found a conjecture (or negated_conjecture) and 10012 axioms. Running axiom selection ...
% 12.95/4.14 % [INFO] Axiom selection finished. Selected 684 axioms (removed 9328 axioms).
% 14.16/4.51 % [INFO] Problem is higher-order (TPTP THF).
% 14.16/4.54 % [INFO] Type checking passed.
% 14.16/4.55 % [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 ...
% 42.63/12.24 % External prover 'e' found a proof!
% 42.63/12.24 % [INFO] Killing All external provers ...
% 42.63/12.24 % Time passed: 11960ms (effective reasoning time: 9897ms)
% 42.63/12.24 % 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)>
% 42.63/12.25 % Axioms used in derivation (684): thm_2Ewords_2Eword__sub__w2n, thm_2Einteger_2EINT__NEG__RMUL, thm_2Ewords_2EWORD__NEG__EQ, thm_2Eint__arith_2Elt__justify__multiplication, thm_2Ebool_2EBOOL__CASES__AX, thm_2Einteger_2EINT__LT__SUB__LADD, thm_2Ewords_2EWORD__LESS__REFL, thm_2Ewords_2Ew2w__0, thm_2Ewords_2EWORD__SLICE__ZERO2, thm_2Ewords_2EWORD__ADD__RIGHT__LO2, thm_2Ewords_2EWORD__ADD__RIGHT__LS2, thm_2Egcd_2EIS__GCD__MINUS__L, thm_2Einteger_2EINT__LT__LE, thm_2Ewords_2EWORD__ADD__ASSOC, thm_2Einteger_2EINT__SUB__LT, thm_2Ewellorder_2EWF__REC__num, thm_2EConseqConv_2EOR__CLAUSES__FX, thm_2Einteger_2EINT__LE__LADD, thm_2Earithmetic_2EABS__DIFF__EQS, thm_2Einteger_2EINT__LT__MONO, thm_2Einteger_2EINT__RNEG__UNIQ, thm_2Ewords_2EWORD__MULT__ASSOC, thm_2Einteger_2EINT__LT__MUL2, thm_2Einteger_2EINT__ABS__ABS, thm_2Einteger_2EINT__ADD__DIV, thm_2Ewords_2EWORD__LOWER__CASES__IMP, thm_2Eint__arith_2Ejustify__divides2, thm_2Einteger_2EINT__MOD0, thm_2Eint__arith_2Epositive__product__implication, thm_2Eint__arith_2Ele__move__right__left, thm_2Einteger_2EINT__LE__ADD2, thm_2Einteger_2EINT__DIVIDES__MUL, thm_2Eint__arith_2EINT__LINEAR__GCD, thm_2Earithmetic_2ESUB__CANCEL, thm_2Ewords_2EWORD__NOT__LESS, thm_2Einteger_2Eint__sub, thm_2Earithmetic_2EABS__DIFF__EQ__0, thm_2Einteger_2EINT__ADD__LID__UNIQ, thm_2Ewords_2EWORD__LESS__EQ__LESS__TRANS, thm_2Ebool_2ECOND__ABS, thm_2Ebool_2ENOT__CLAUSES, thm_2Ewords_2EWORD__LOWER__OR__EQ, thm_2Ecardinal_2ELT__NZ, thm_2Earithmetic_2ELESS__LESS__EQ__TRANS, thm_2Einteger_2EINT__DIVIDES__MOD0, thm_2EternaryComparisons_2Ebool__compare__ind, thm_2Einteger_2EINT__MUL__REDUCE, thm_2Ewords_2EWORD__LESS__EQ__TRANS, thm_2Eint__arith_2Ele__context__rwt3, thm_2Einteger_2EINT__LT__NEG, thm_2Einteger_2EINT__NEG__GE0, thm_2Einteger_2EINT__LE__RADD, thm_2Einteger_2EINT__ADD__ASSOC, thm_2Ebool_2Ebool__INDUCT, thm_2Earithmetic_2ENOT__ZERO__LT__ZERO, thm_2Einteger_2EINT__DIV__RMUL, thm_2Earithmetic_2EDIV__MOD__MOD__DIV, thm_2Einteger_2EINT__LESS__MOD, thm_2Eint__arith_2Ebot__and__greaters, thm_2Einteger_2EINT__NZ__IMP__LT, thm_2Ebool_2EIMP__F__EQ__F, thm_2Einteger_2EINT__NEG__SUB, thm_2Earithmetic_2ECOMPLETE__INDUCTION, thm_2Earithmetic_2ESUB__EQ__EQ__0, thm_2Einteger_2EINT__LE__ADDR, thm_2Einteger_2EINT__SUB__REDUCE, thm_2EConseqConv_2EIMP__CLAUSES__XF, thm_2Ewords_2Ebit__count__upto__0, thm_2Einteger_2EINT__MOD__UNIQUE, thm_2Esat_2ENOT__ELIM2, thm_2Eint__arith_2EINT__NUM__EXISTS, thm_2Einteger_2EINT__SUB__LE, thm_2Esat_2EAND__INV__IMP, thm_2Ewords_2EWORD__LOWER__NOT__EQ, thm_2Ewords_2EWORD__ADD__COMM, thm_2Ewords_2Eword__sub__def, thm_2Esat_2EOR__DUAL3, thm_2Ewords_2EWORD__LEFT__ADD__DISTRIB, thm_2Einteger_2ENUM__NEGINT__EXISTS, thm_2Einteger_2EINT__SUB__CALCULATE, thm_2Egcd_2EIS__GCD__UNIQUE, thm_2Ewords_2EWORD__0__LS, thm_2Einteger_2EINT__MOD__SUB, thm_2Ebool_2EREFL__CLAUSE, thm_2Einteger_2EINT__QUOT__NEG, thm_2Einteger__word_2Eint__word__nchotomy, thm_2Einteger_2EINT__OF__NUM, thm_2Ealignment_2Ealigned__def, thm_2Einteger_2EINT__LTE__ADD2, thm_2Ewords_2EWORD__ADD__LEFT__LO2, thm_2Ewords_2EWORD__LESS__NEG__LEFT, thm_2Enumpair_2Enlist__cases, thm_2Ealignment_2Ealigned__add__sub, thm_2Ewords_2EWORD__LOWER__CASES, thm_2Earithmetic_2ELESS__CASES, thm_2Ebool_2ECOND__RAND, thm_2Einteger_2EINT__ABS__LT, thm_2Eint__arith_2Eadd__to__great, thm_2Ewords_2ETWO__COMP__POS, thm_2Einteger_2EINT__LE__REFL, thm_2Earithmetic_2EMOD__MULT__MOD, thm_2Ewords_2EWORD__LOWER__EQ__LOWER__TRANS, thm_2Ewords_2EWORD__LO__word__0, thm_2Einteger_2EINT__REM__UNIQUE, thm_2Einteger_2EINT__DIV, thm_2Earithmetic_2ELESS__TRANS, thm_2Einteger_2EINT__EQ__NEG, thm_2Ewords_2EWORD__NEG__LMUL, thm_2Ewords_2EWORD__ADD__SUB__SYM, thm_2Eint__arith_2Ein__subtractive__range, thm_2Ebool_2EEQ__CLAUSES, thm_2Earithmetic_2EMODEQ__REFL, thm_2Einteger_2EINT__ABS__MUL, thm_2Ewords_2EWORD__LE, thm_2Ewords_2EWORD__LOWER__TRANS, thm_2Einteger_2EINT__ABS__POS, thm_2Einteger__word_2Eword__sdiv__def, thm_2Earithmetic_2EMULT__ASSOC, thm_2Ewords_2EWORD__EXTRACT__ZERO2, thm_2Einteger_2EINT__NOT__LT, thm_2Einteger_2EINT__LE__SQUARE, thm_2Earithmetic_2ELE__MULT__LCANCEL, thm_2Earithmetic_2ESUB__EQUAL__0, thm_2Ewords_2EWORD__NEG__L, thm_2Einteger_2EINT__LT__ADD, thm_2Egcd_2EGCD__0R, thm_2Eint__arith_2Ele__move__all__right, thm_2Einteger_2EINT__SUMSQ, thm_2Einteger_2EINT__LE__ADDL, thm_2Einteger_2EINT__REM__CALCULATE, thm_2Eint__arith_2Elcm__eliminate, thm_2Einteger_2EINT__ABS__NUM, thm_2Egcd_2EGCD__SYM, thm_2Ewords_2EWORD__LOWER__LOWER__CASES, thm_2Einteger_2EINT__LE__SUB__LADD, thm_2Einteger_2EINT__SUB__NEG2, thm_2Einteger_2EINT__MOD__PLUS, thm_2Enum_2EZERO__DEF, thm_2Eint__arith_2Ecooper__lemma__1, thm_2Earithmetic_2EMULT__SYM, thm_2Einteger_2EINT__DIVIDES__MUL__BOTH, thm_2Einteger_2EINT__DIVIDES__LSUB, thm_2Ecardinal_2ELE__CASES, thm_2Earithmetic_2ELE__MULT__RCANCEL, thm_2Einteger_2EINT__EQ__LMUL__IMP, thm_2Einteger_2EINT__MUL__DIV, thm_2Ewords_2EWORD__ADD__INV__0__EQ, thm_2EConseqConv_2ENOT__CLAUSES__T, thm_2Einteger_2EINT__DIVIDES__REFL, thm_2EConseqConv_2EIMP__CONG__cond__simple, thm_2Einteger_2EINT__DIV__LMUL, thm_2EConseqConv_2EAND__CLAUSES__TX, thm_2Ewords_2Eword__mul__n2w, thm_2Einteger_2EINT__DIVIDES__0, thm_2Einteger__word_2Eword__smod__def, thm_2Einteger_2EINT__SUB__REFL, thm_2Ewords_2Eword__0__n2w, thm_2Einteger_2EINT__QUOT, thm_2Einteger_2EINT__NOT__LE, thm_2Earithmetic_2EDIV__LE__MONOTONE, thm_2Earithmetic_2ELT__SUB__RCANCEL, thm_2Ewords_2Esw2sw__0, thm_2EConseqConv_2EIMP__CLAUSES__XX, thm_2Ebool_2EIMP__F, thm_2Ewords_2EWORD__SUB__REFL, thm_2Egcd_2ELCM__COMM, thm_2Ewords_2EWORD__EQ__ADD__RCANCEL, thm_2Einteger_2EINT__DIVIDES__RADD, thm_2Earithmetic_2ERIGHT__SUB__DISTRIB, thm_2Earithmetic_2ESUB__EQ__0, thm_2Einteger_2EINT__MOD__MOD, thm_2Einteger_2EINT__LE__SUB__RADD, thm_2Einteger_2EINT__EXP__SUBTRACT__EXPONENTS, thm_2Ewords_2EWORD__LOWER__EQ__TRANS, thm_2Ewords_2EWORD__LS__word__0, thm_2Einteger_2EINT__SUB__TRIANGLE, thm_2Einteger_2EINT__MUL__SYM, thm_2Ewords_2En2w__w2n, thm_2Eint__arith_2EHO__SUB__ELIM, thm_2Einteger__word_2Eword__0__w2i, thm_2Einteger_2EINT__ADD__LINV, thm_2Ewords_2EWORD__LITERAL__MULT, thm_2Einteger_2EINT__DIVIDES__RSUB, thm_2Einteger_2EINT__LT__LADD, thm_2Einteger_2EINT__POS, thm_2Einteger_2EINT__SUB__SUB2, thm_2Einteger_2EINT__DIVIDES, thm_2Einteger_2EINT__MUL__COMM, thm_2Ewords_2ETWO__COMP__POS__NEG, thm_2Ewords_2EWORD__LOWER__EQUAL__ANTISYM, thm_2Eint__arith_2Eeq__justify__multiplication, thm_2Einteger_2EINT__ABS__EQ__ABS, thm_2EConseqConv_2Efalse__imp, thm_2Ewords_2EWORD__L__LESS__EQ, thm_2Einteger_2EINT__LE__MUL, thm_2Earithmetic_2EMULT__0, thm_2Einteger_2EINT__LE__TOTAL, thm_2Einteger_2EINT__MUL, thm_2Einteger_2EINT__ADD__SUB2, thm_2Einteger_2EINT__ABS__NEG, thm_2Earithmetic_2EMOD__MOD, thm_2Einteger__word_2Eword__mul__i2w, thm_2Einteger_2EINT__SUB__0, thm_2Earithmetic_2EMODEQ__MOD, thm_2Einteger_2EINT__LT__GT, thm_2Ewords_2EWORD__LESS__LESS__EQ__TRANS, thm_2Einteger_2EINT__NEG__LT0, thm_2Ewords_2Eword__abs__def, thm_2Ewords_2EWORD__ADD__SUB__ASSOC, thm_2Ewords_2EWORD__ADD__LINV, thm_2Ewords_2EWORD__LT__EQ__LO, thm_2Einteger_2EINT__LT__RADD, thm_2Einteger_2EINT__DIVIDES__RMUL, thm_2Einteger_2EINT__EXP__EQ0, thm_2Eint__arith_2Eelim__le__coeffs, thm_2Einteger_2EINT__DIV__UNIQUE, thm_2Ewords_2EWORD__LESS__TRANS, thm_2Eint__arith_2Ele__context__rwt4, thm_2Eint__arith_2Elt__move__all__right, thm_2Einteger__word_2Ew2i__eq__0, thm_2Earithmetic_2ENOT__LT__ZERO__EQ__ZERO, thm_2Earithmetic_2ELESS__ANTISYM, thm_2Egcd_2EGCD__COMMON__FACTOR, thm_2Ewords_2EWORD__SUB__PLUS, thm_2Einteger_2EINT__LE__DOUBLE, thm_2Einteger_2EINT__LE__TRANS, thm_2Ewords_2EWORD__NEG__ADD, thm_2Einteger__word_2Ei2w__w2i, thm_2Ebool_2EFALSITY, thm_2Einteger_2EINT__LE, thm_2Einteger_2EINT__ABS__EQ__ID, thm_2Einteger_2EINT__REMQUOT, thm_2Einteger_2EINT__NEG__LE0, thm_2Einteger__word_2Eword__sub__i2w, thm_2Earithmetic_2ELESS__EQ__REFL, thm_2Einteger_2EINT__LT__LADD__IMP, thm_2Ewords_2EWORD__ADD__SUB2, thm_2EConseqConv_2ECOND__CLAUSES__FT, thm_2Ewords_2EWORD__LESS__IMP__LESS__OR__EQ, thm_2Ebitstring_2Eword__extract__v2w, thm_2Einteger__word_2Ew2i__neg, thm_2Earithmetic_2EABS__DIFF__SYM, thm_2Einteger_2EINT__SUB__RNEG, thm_2Ewords_2EWORD__NEG__SUB, thm_2Ewords_2Ew2n__11, thm_2Einteger_2EINT__LE__NEGL, thm_2Ewords_2EWORD__LESS__LESS__CASES, thm_2Earithmetic_2EMODEQ__TRANS, thm_2Ecardinal_2ELT__LE, thm_2Eint__arith_2EINT__SUB__SUB3, thm_2Ewords_2EWORD__ADD__RINV, thm_2Earithmetic_2ELESS__MONO__MULT2, thm_2Einteger_2EINT__ENTIRE, thm_2EternaryComparisons_2Eordering__size__def, thm_2Einteger_2EINT__LTE__TRANS, thm_2Eint__arith_2Elt__move__left__left, thm_2EbasicSize_2Eone__size__def, thm_2Earithmetic_2EX__LE__DIV, thm_2Ewords_2EWORD__LT__LO, thm_2Earithmetic_2ESUB__0, thm_2Einteger_2EINT__LET__ADD2, thm_2Einteger_2EINT__LT__ADDR, thm_2Ewords_2Eword__msb__add__word__L, thm_2Ewords_2Eword__nchotomy, thm_2Einteger__word_2Eword__add__i2w, thm_2Einteger_2EINT__DIVIDES__LMUL, thm_2Einteger_2EINT__LT__ADD2, thm_2Ealignment_2Ealign__0, thm_2Ewords_2EWORD__EQ__NEG, thm_2Ebag_2Emlt__UNION__EMPTY__EQN, thm_2Einteger_2EINT__LT__ANTISYM, thm_2Ewords_2EWORD__EQ__SUB__LADD, thm_2Einteger_2EINT__LE__CALCULATE, thm_2EConseqConv_2ECOND__CLAUSES__FF, thm_2Einteger_2EINT__INJ, thm_2Ebool_2Ebool__case__CONG, thm_2Ewords_2EWORD__EQ__SUB__ZERO, thm_2Ebool_2ECOND__CLAUSES, thm_2Einteger_2EINT__EQ__RMUL__IMP, thm_2Ewords_2En2w__sub, thm_2Egcd_2ELCM__0, thm_2Einteger_2EINT__LT__TOTAL, thm_2Ewords_2EWORD__LOWER__EQ__CASES, thm_2Ewords_2EWORD__EQ__ADD__LCANCEL, thm_2Ewords_2EWORD__SUB, thm_2Ewords_2EWORD__SLICE__BITS__THM, thm_2Earithmetic_2EX__MOD__Y__EQ__X, thm_2Einteger_2EINT__QUOT__0, thm_2Earithmetic_2EZERO__LESS__MULT, thm_2Earithmetic_2EMODEQ__0, thm_2Ewords_2Eword__abs__diff, thm_2Einteger_2EINT__NEG__SAME__EQ, thm_2Earithmetic_2ENRC__0, thm_2Earithmetic_2ELESS__EQ__0, thm_2Ewords_2EWORD__SUB__TRIANGLE, thm_2Earithmetic_2ENOT__LESS__EQUAL, thm_2Einteger_2EINT__ADD__LID, thm_2Ewords_2EWORD__LCANCEL__SUB, thm_2Ewords_2EWORD__LOWER__REFL, thm_2Einteger__word_2Eword__sub__i2w__w2n, thm_2Earithmetic_2ELESS__OR__EQ, thm_2Enumpair_2Encons__not__nnil, thm_2Einteger__word_2Eword__i2w__mul, thm_2Earithmetic_2EDIV__LESS__EQ, thm_2Ewords_2Ew2w__def, thm_2Einteger_2EINT__ADD__RID__UNIQ, thm_2Einteger_2EINT__SUB, thm_2Egcd_2EIS__GCD__REF, thm_2Ewords_2EWORD__BITS__ZERO2, thm_2Einteger_2EINT__LT__NEGTOTAL, thm_2Ewords_2EMOD__COMPLEMENT, thm_2Ebool_2ECOND__EXPAND, thm_2Einteger_2EINT__DIVIDES__NEG, thm_2Einteger_2ENUM__LT, thm_2Einteger_2EINT__NEGNEG, thm_2Ebool_2ECOND__CONG, thm_2Ebitstring_2Eshiftr__0, thm_2Ebit_2EDIV__GT0, thm_2Eint__arith_2Eeq__move__right__left, thm_2Eint__arith_2Emove__sub, thm_2Ewords_2EWORD__LESS__EQ__REFL, thm_2Earithmetic_2ELT__MULT__CANCEL__RBARE, thm_2Estring_2Echar__size__def, thm_2Eprim__rec_2ELESS__NOT__EQ, thm_2Earithmetic_2ELESS__EQ__CASES, thm_2Ewords_2Eword__abs__neg, thm_2Ewords_2Eword__mul__def, thm_2Einteger_2EINT__EQ__IMP__LE, thm_2EConseqConv_2ECOND__CLAUSES__ID, thm_2Ewords_2EWORD__NOT__LESS__EQ, thm_2Einteger__word_2Eword__mul__i2w__w2n, thm_2Earithmetic_2ELE__MULT__CANCEL__LBARE, thm_2Einteger_2EINT__MOD__P, thm_2Ewords_2EWORD__NOT__LESS__EQUAL, thm_2Earithmetic_2EABS__DIFF__COMM, thm_2Ewords_2EWORD__LESS__CASES__IMP, thm_2ETemporal__Logic_2EWELL__ORDER, thm_2Einteger_2Eint__mod, thm_2Ebool_2ECOND__ID, thm_2Einteger_2EINT__EQ__CALCULATE, thm_2Einteger_2EINT__NEG__0, thm_2Einteger_2EINT__NEG__EQ, thm_2Eint__arith_2Eeq__context__rwt1, thm_2Earithmetic_2EMODEQ__THM, thm_2Einteger_2EINT__MOD__NEG__NUMERATOR, thm_2Ewords_2EWORD__RIGHT__SUB__DISTRIB, thm_2Einteger_2EINT__DIVIDES__TRANS, thm_2Einteger_2EINT__LT__IMP__LE, thm_2Ewords_2EWORD__EXTRACT__ZERO, thm_2Einteger_2EINT__ADD2__SUB2, thm_2Ebool_2ETRUTH, thm_2Einteger_2EINT__NEG__MUL2, thm_2Ebool_2ENOT__F, thm_2Earithmetic_2EMODEQ__SYM, thm_2Einteger_2EINT__DIVIDES__LADD, thm_2Ewords_2EWORD__LESS__CASES, thm_2Einteger_2EINT__ADD__COMM, thm_2Einteger_2EINT__LT__IMP__NE, thm_2Ebool_2EFORALL__BOOL, thm_2Ewords_2EWORD__SUB__LT, thm_2Ebool_2EIMP__CLAUSES, thm_2Earithmetic_2EABS__DIFF__ZERO, thm_2Earithmetic_2EMODEQ__NONZERO__MODEQUALITY, thm_2Egcd_2EGCD__IS__GCD, thm_2Ewords_2EWORD__SUB__LNEG, thm_2Earithmetic_2ELESS__EQUAL__ANTISYM, thm_2Earithmetic_2ELESS__EQ__TRANS, thm_2EConseqConv_2EIMP__CLAUSES__TX, thm_2EConseqConv_2EAND__CLAUSES__XF, thm_2Ebit_2ELESS__MULT__MONO2, thm_2Ewords_2Eword__reverse__0, thm_2Einteger__word_2Eword__i2w__add, thm_2Eint__arith_2Eeq__move__left__right, thm_2Einteger_2EINT__SUB__RDISTRIB, thm_2Einteger_2EINT__ABS__LE0, thm_2Earithmetic_2ELT__MULT__LCANCEL, thm_2Ewords_2EWORD__SUB__LE, thm_2Ebool_2EF__IMP, thm_2Einteger_2EINT__LDISTRIB, thm_2Ebool_2ECOND__EXPAND__OR, thm_2Einteger_2EINT__DIV__MUL__ID, thm_2Ewords_2EWORD__LEFT__SUB__DISTRIB, thm_2Ebool_2EboolAxiom, thm_2Einteger_2EINT__MOD__NEG, thm_2Eint__arith_2EINT__NUM__SUB, thm_2Einteger_2EINT__DIV__FORALL__P, thm_2Earithmetic_2EDIV__DIV__DIV__MULT, thm_2Ewords_2EWORD__LOWER__IMP__LOWER__OR__EQ, thm_2Earithmetic_2ESUB__LESS, thm_2EConseqConv_2ECOND__CLAUSES__CT, thm_2Einteger_2EINT__SUB__LDISTRIB, thm_2Eint__arith_2Ejustify__divides, thm_2EConseqConv_2EIMP__CLAUSES__XT, thm_2Einteger_2EINT__LT__MUL, thm_2Einteger_2EINT__LE__MONO, thm_2Ebool_2EMONO__COND, thm_2Earithmetic_2ELESS__IMP__LESS__OR__EQ, thm_2Eprim__rec_2ENOT__LESS__0, thm_2Earithmetic_2ESUB__MOD, thm_2Einteger_2EINT__MUL__ASSOC, thm_2Ebit_2EMOD__LEQ, thm_2Ewords_2EWORD__LOWER__EQ__REFL, thm_2Ewords_2EWORD__LESS__EQ__CASES, thm_2Earithmetic_2EWOP, thm_2Ewords_2EWORD__ADD__SUB3, thm_2Ealignment_2Ealigned__0, thm_2Ewords_2EWORD__BITS__SLICE__THM, thm_2Earithmetic_2ESUB__LESS__0, thm_2Einteger_2ENUM__POSINT__EXISTS, thm_2Ewords_2EWORD__LE__EQ__LS, thm_2Einteger__word_2Ew2i__def, thm_2EConseqConv_2ECOND__CLAUSES__TF, thm_2Einteger__word_2Eword__abs__w2i, thm_2Einteger_2ENUM__POSINT__EX, thm_2Ealignment_2Ealigned__imp, thm_2Einteger_2EINT__ABS__0LT, thm_2Einteger_2EINT__MUL__RZERO, thm_2Einteger_2EINT__ADD__RID, thm_2Einteger_2EINT__MOD__ADD__MULTIPLES, thm_2Ewords_2EWORD__LT__SUB__UPPER, thm_2Ewords_2EWORD__LESS__ANTISYM, thm_2Ewords_2EWORD__NEG__NEG, thm_2Einteger_2EINT__REM__NEG, thm_2Ewords_2En2w__sub__eq__0, thm_2Ebool_2ET__DEF, thm_2Eint__arith_2Ele__context__rwt5, thm_2Einteger_2EINT__LE__NEGR, thm_2Ewords_2Ew2w__id, thm_2Esat_2Edc__cond, thm_2Earithmetic_2EEQ__LESS__EQ, thm_2Ewords_2Eword__abs__word__abs, thm_2Ealignment_2Ealign__align, thm_2Ewords_2EWORD__LOWER__ANTISYM, thm_2Earithmetic_2EMOD__EQ__0__DIVISOR, thm_2EbasicSize_2Ebool__size__def, thm_2EConseqConv_2EAND__CLAUSES__FX, thm_2Earithmetic_2ELESS__DIV__EQ__ZERO, thm_2Egcd_2EIS__GCD__SYM, thm_2Einteger_2EINT__LT__CALCULATE, thm_2Ewords_2ENOT__INT__MIN__ZERO, thm_2Einteger_2EINT__LE__NEGTOTAL, thm_2Ewords_2EWORD__LS, thm_2Esat_2EAND__INV2, thm_2Earithmetic_2EMULT__COMM, thm_2Einteger_2EINT__LE__NEG, thm_2Ebool_2EF__DEF, thm_2Einteger_2EINT__POS__NZ, thm_2Earithmetic_2EMOD__SUB, thm_2Esat_2EOR__DUAL, thm_2Einteger_2EINT__REM__ID, thm_2Earithmetic_2EMOD__LESS__EQ, thm_2Einteger_2Eint__le, thm_2Ewhile_2EITERATION, thm_2Ewords_2EWORD__ADD__RID__UNIQ, thm_2Ewords_2Esw2sw__id, thm_2Ewords_2EWORD__EQ__SUB__RADD, thm_2Ebitstring_2Ebitstring__nchotomy, thm_2EConseqConv_2EOR__CLAUSES__XT, thm_2Earithmetic_2EMOD__TIMES2, thm_2Earithmetic_2EZERO__LESS__EQ, thm_2Ebool_2ECOND__RATOR, thm_2Earithmetic_2ENOT__LESS, thm_2Einteger_2EINT__MOD__BOUNDS, thm_2Einteger_2ELE__NUM__OF__INT, thm_2Einteger_2EINT__RDISTRIB, thm_2Earithmetic_2EEQ__MULT__LCANCEL, thm_2Earithmetic_2EDIV__LT__X, thm_2Earithmetic_2EMODEQ__0__CONG, thm_2Ealignment_2Ealigned__add__sub__cor, thm_2Ewords_2EWORD__MULT__COMM, thm_2Einteger_2EINT__LT__ADDL, thm_2Einteger_2EINT__REM, thm_2Eint__arith_2Elt__move__all__left, thm_2Einteger_2EINT__LET__ADD, thm_2Einteger_2EINT__ADD__RINV, thm_2Eint__arith_2Ele__context__rwt1, thm_2Einteger_2EINT__MOD__CALCULATE, thm_2Einteger_2EINT__SUB__LZERO, thm_2Ewords_2EWORD__SUB__SUB3, thm_2Einteger_2EINT__EQ__LMUL2, thm_2Ewords_2EWORD__NEG__EQ__0, thm_2Eint__arith_2Eeq__move__left__left, thm_2Ewords_2EWORD__0__POS, thm_2Einteger_2EINT__NUM__CASES, thm_2Ewords_2EWORD__LOWER__LOWER__EQ__TRANS, thm_2Ewords_2EWORD__ADD__LEFT__LS2, thm_2Einteger_2EINT__MUL__LZERO, thm_2Earithmetic_2ELESS__LESS__CASES, thm_2Einteger_2EINT__0, thm_2Earithmetic_2ELESS__EQ__LESS__TRANS, thm_2Ebool_2Ebool__case__ID, thm_2Einteger_2EINT__MOD__EQ0, thm_2Einteger_2EINT__ABS, thm_2Eint__arith_2Eeq__move__all__right, thm_2Einteger_2EINT__REM__COMMON__FACTOR, thm_2EConseqConv_2EOR__CLAUSES__XF, thm_2Einteger_2EINT__MOD__ID, thm_2Ewords_2EWORD__NEG__RMUL, thm_2Einteger_2EINT__LE__LT, thm_2EConseqConv_2Etrue__imp, thm_2Ewords_2EWORD__LESS__OR__EQ, thm_2Earithmetic_2ELESS__0__CASES, thm_2EConseqConv_2ENOT__CLAUSES__F, thm_2Earithmetic_2EMODEQ__MULT__CONG, thm_2Esat_2EEQF__Imp1, thm_2Einteger_2EINT__SUB__ADD, thm_2Einteger_2EINT__EQ__RADD, thm_2Earithmetic_2EMOD__LESS, thm_2Ewords_2EWORD__ADD__SUB, thm_2Einteger_2EINT__LET__TOTAL, thm_2Enumpair_2Encons__11, thm_2Einteger_2EINT__MUL__SIGN__CASES, thm_2Earithmetic_2EEQ__MULT__RCANCEL, thm_2Ebool_2EOR__CLAUSES, thm_2Einteger_2EINT__LTE__TOTAL, thm_2Eint__arith_2EINT__DIVIDES__LRMUL, thm_2Einteger_2EINT__LTE__ADD, thm_2Ewords_2Eword__msb__neg, thm_2Eprim__rec_2ENOT__LESS__EQ, thm_2Egcd_2EGCD__EQ__0, thm_2Einteger_2EINT__LT__NZ, thm_2Einteger__word_2EWORD__LTi, thm_2Ewords_2EWORD__BITS__EXTRACT, thm_2Earithmetic_2ELE__SUB__RCANCEL, thm_2Earithmetic_2EMODEQ__INTRO__CONG, thm_2Einteger_2EINT__SUB__LNEG, thm_2Ewords_2EWORD__SUB__LZERO, thm_2Earithmetic_2EMULT__EQ__0, thm_2Ewords_2EWORD__LO, thm_2Einteger_2EINT__MUL__QUOT, thm_2Einteger_2EINT__LT__ADDNEG, thm_2Einteger_2EINT__NEG__LMUL, thm_2Earithmetic_2EMOD__EQ__0, thm_2Earithmetic_2ELESS__MOD, thm_2Ewords_2EWORD__NOT__LOWER__EQ, thm_2EConseqConv_2ECOND__CLAUSES__TT, thm_2Einteger_2EINT__LT__TRANS, thm_2Einteger_2EINT__ABS__EQ, thm_2Einteger_2EINT__NEG__ADD, thm_2Einteger_2EINT__LT__REFL, thm_2Einteger_2EINT__LE__ANTISYM, thm_2Einteger__word_2EWORD__LEi, thm_2Ewords_2EWORD__LESS__EQUAL__ANTISYM, thm_2Eint__arith_2Eelim__eq__coeffs, thm_2Einteger__word_2Eword__add__i2w__w2n, thm_2Earithmetic_2ENUMERAL__DEF, thm_2Ewords_2EWORD__LESS__NEG__RIGHT, thm_2Ewords_2EWORD__ADD__EQ__SUB, thm_2Einteger__word_2Ew2i__lt__0, thm_2Eint__arith_2Egcdthm2, thm_2Einteger_2EINT__QUOT__UNIQUE, thm_2Ewords_2EWORD__ADD__LID__UNIQ, thm_2Eint__arith_2Ecan__get__small, thm_2EConseqConv_2EAND__CLAUSES__XT, thm_2Einteger_2EINT__ABS__LT0, thm_2Ewords_2EWORD__SUB__SUB, thm_2EConseqConv_2EOR__CLAUSES__TX, thm_2Eint__arith_2Eeq__context__rwt2, thm_2Ewords_2EWORD__SUB__RNEG, thm_2Earithmetic_2ESUB__LESS__EQ, thm_2Egcd_2EIS__GCD__MINUS__R, thm_2Ebool_2ECOND__EXPAND__IMP, thm_2Eint__arith_2Esubtract__to__small, thm_2Einteger_2EINT__LNEG__UNIQ, thm_2Eprim__rec_2ELESS__REFL, thm_2Einteger_2EINT__NEG__EQ0, thm_2Earithmetic_2ELT__SUB__LCANCEL, thm_2Ewords_2EWORD__SUB__ADD, thm_2Einteger_2EINT__LET__ANTISYM, thm_2Eint__arith_2Eeq__move__all__left, thm_2Ewords_2Ew2n__w2w__le, thm_2Einteger_2EINT__EQ__LMUL, thm_2Earithmetic_2EDIV__SUB, thm_2Ewords_2EWORD__RCANCEL__SUB, thm_2Einteger_2EINT__REM__EQ0, thm_2Earithmetic_2ELESS__EQ__ANTISYM, thm_2Ealignment_2Ealign__aligned, thm_2Ewords_2EWORD__ADD__0, thm_2EConseqConv_2EIMP__CLAUSES__FX, thm_2Einteger_2EINT__ADD__SYM, thm_2Ewords_2EWORD__BITS__ZERO, thm_2Eint__arith_2Etop__and__lessers, thm_2Ewords_2EWORD__SUB__SUB2, thm_2Einteger_2EINT__MOD__COMMON__FACTOR, thm_2Earithmetic_2ELE__SUB__LCANCEL, thm_2Einteger_2EINT__EQ__SUB__RADD, thm_2Einteger_2EINT__ADD__SUB, thm_2Ewords_2Eword__concat__0__0, thm_2Ebool_2EAND__CLAUSES, thm_2Einteger_2EINT__LT__ADDNEG2, thm_2Einteger_2EINT__DIVISION, thm_2Ecardinal_2ELT__CASES, thm_2Einteger_2EINT__ABS__LE, thm_2Einteger_2EINT__POASQ, thm_2Einteger_2EINT__EQ__SUB__LADD, thm_2Earithmetic_2ELESS__EQUAL__DIFF, thm_2Einteger_2EINT__LTE__ANTSYM, thm_2Eint__arith_2Ele__context__rwt2, thm_2Einteger_2EINT__LE__ADD, thm_2Ewords_2EWORD__NOT__LOWER__EQUAL, thm_2Ewords_2Ebit__count__is__zero, thm_2Earithmetic_2EMOD__TIMES__SUB, thm_2Eint__arith_2Eelim__lt__coeffs1, thm_2Eint__arith_2Ecan__get__big, thm_2Einteger_2EINT__ABS__EQ0, thm_2Ewords_2EWORD__LE__LS, thm_2Esat_2EOR__DUAL2, thm_2Einteger__word_2Ew2i__w2n__pos, thm_2Ewords_2EWORD__LOWER__EQ__ANTISYM, logicdef_2E_2F_5C, thm_2Ewords_2EWORD__MSB__INT__MIN__LS, thm_2Einteger_2EINT__EXP__MULTIPLY__EXPONENTS, thm_2Einteger__word_2Ei2w__def, thm_2Egcd_2EIS__GCD__0R, thm_2Esat_2EEQT__Imp1, thm_2Ewords_2EWORD__SUB__ADD2, thm_2Einteger_2EINT__ABS__QUOT, thm_2Ewords_2EWORD__RIGHT__ADD__DISTRIB, thm_2Ewords_2EWORD__LESS__NOT__EQ, thm_2Ewords_2EWORD__LESS__EQ__ANTISYM, thm_2Einteger_2EINT__SUB__SUB, thm_2Einteger_2EINT__EXP__MOD, thm_2Ewords_2Ew2n__eq__0, thm_2Earithmetic_2ELESS__MONO__MULT, thm_2Earithmetic_2ECANCEL__SUB, thm_2ETemporal__Logic_2EWELL__ORDER__UNIQUE, thm_2Earithmetic_2EMULT__EQ__DIV, thm_2Earithmetic_2EZERO__MOD, thm_2Earithmetic_2EMULT__DIV, thm_2Earithmetic_2ELEFT__SUB__DISTRIB, thm_2EConseqConv_2ECOND__CLAUSES__CF, thm_2Einteger_2EINT__DIV__NEG, thm_2Einteger_2EINT__EQ__LADD, thm_2Earithmetic_2ELESS__MULT2, thm_2Earithmetic_2EMOD__COMMON__FACTOR, thm_2Eint__arith_2EINT__NUM__FORALL, thm_2Einteger_2EINT__QUOT__CALCULATE, thm_2Ewords_2Eword__bit__0, thm_2Einteger_2EINT__LT__SUB__RADD, thm_2Egcd_2ELCM__LE, thm_2Egcd_2EGCD__0L, thm_2Ewords_2EWORD__NEG__0, thm_2Einteger_2EINT__SUB__RZERO, thm_2Earithmetic_2EZERO__DIV, thm_2Einteger_2ENUM__OF__INT, thm_2Ewords_2EWORD__LT, thm_2Eint__arith_2Ejustify__divides3, thm_2Einteger_2EINT__DIV__0, thm_2Ebool_2Ebool__case__thm, thm_2Einteger_2EINT__LT, thm_2Ewords_2EWORD__SUB__RZERO, thm_2Egcd_2EGCD__REF, thm_2Enumpair_2Enlist__ind, thm_2Eint__arith_2Ein__additive__range, thm_2Einteger_2EINT__DIV__P, thm_2Einteger_2EINT__EQ__RMUL, thm_2Eint__arith_2Elt__move__left__right, thm_2Einteger_2EINT__REM0, thm_2Egcd_2EIS__GCD__0L, thm_2Esptree_2Espt__acc__0, thm_2Earithmetic_2ELESS__CASES__IMP, thm_2Ebool_2EBOOL__EQ__DISTINCT, thm_2Einteger_2EINT__NEG__GT0, thm_2Ewords_2EZERO__LO__INT__MIN, thm_2Ewords_2EWORD__SUM__ZERO, thm_2Ealignment_2Ealigned__align, thm_2Einteger_2EINT__LET__TRANS, thm_2Einteger_2EINT__MUL__CALCULATE, thm_2Einteger_2EINT__SUB__ADD2, thm_2Esat_2EAND__INV, thm_2EConseqConv_2EIMP__CONG__cond, thm_2Einteger_2EINT__MOD, thm_2Einteger_2EINT__MOD__FORALL__P, thm_2Einteger_2EINT__DIV__CALCULATE, thm_2Earithmetic_2ELT__MULT__RCANCEL, thm_2Ewords_2EWORD__SUB__NEG, thm_2Ewords_2EWORD__L__NEG, thm_2Einteger__word_2Ew2i__11, thm_2Einteger_2Eint__rem, thm_2Einteger_2EINT__DIFFSQ, thm_2Einteger_2Eint__quot, thm_2Ewords_2EWORD__SLICE__ZERO, thm_2Ewords_2EWORD__NOT__LOWER, thm_2Einteger_2EINT__LT__ADD__SUB
% 42.63/12.25 % No. of inferences in proof: 1441
% 42.63/12.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 11960 ms resp. 9897 ms w/o parsing
% 42.98/12.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 42.98/12.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------