%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV631+1 : TPTP v9.3.1. Released v9.3.0.
% 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 : n003.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 : Sun Sep 27 08:48:16 AM UTC 2026
% Result : Theorem 41.87s 12.58s
% Output : Refutation 46.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 377
% Syntax : Number of formulae : 756 ( 69 unt; 0 typ; 0 def)
% Number of atoms : 5355 ( 532 equ; 0 cnn)
% Maximal formula atoms : 26 ( 7 avg)
% Number of connectives : 21687 ( 84 ~; 126 |; 702 &;17004 @)
% ( 145 <=>;3626 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 15 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 203 ( 201 usr; 29 con; 0-23 aty)
% Number of variables : 3972 ( 0 ^;3691 !; 281 ?;3972 :)
% Comments :
%------------------------------------------------------------------------------
thf(ciT___24t_decl,type,
ciT___24t: $i > $o ).
thf(cCoq_2eInit_2eDatatypes_2elist___24t_decl,type,
cCoq_2eInit_2eDatatypes_2elist___24t: $i > $i > $o ).
thf(ciT_decl,type,
ciT: $i ).
thf(cF___24t_decl,type,
cF___24t: $i > $i > $o ).
thf(cHList_2ehlist_2ehlist___24t_decl,type,
cHList_2ehlist_2ehlist___24t: $i > $i > $o ).
thf(cHList_2ehlist_2eHcons___24a4_decl,type,
cHList_2ehlist_2eHcons___24a4: $i > $i > $i > $i > $i ).
thf(cType___24t_decl,type,
cType___24t: $i > $o ).
thf(c_24__type__646___24t_decl,type,
c_24__type__646___24t: $i > $i > $o ).
thf(t_decl,type,
t: $i > $i > $o ).
thf(cCoq_2eSorting_2eSorted_2eSorted___24a3_decl,type,
cCoq_2eSorting_2eSorted_2eSorted___24a3: $i > $i > $i > $o ).
thf(cCoq_2eSorting_2eSorted_2eHdRel___24a4_decl,type,
cCoq_2eSorting_2eSorted_2eHdRel___24a4: $i > $i > $i > $i > $o ).
thf(cCoq_2eInit_2eDatatypes_2econs___24a3_decl,type,
cCoq_2eInit_2eDatatypes_2econs___24a3: $i > $i > $i > $i ).
thf(cCoq_2eLists_2eSetoidList_2eInA___24a4_decl,type,
cCoq_2eLists_2eSetoidList_2eInA___24a4: $i > $i > $i > $i > $o ).
thf(cCoq_2eInit_2eDatatypes_2enil___24a1_decl,type,
cCoq_2eInit_2eDatatypes_2enil___24a1: $i > $i ).
thf(p_decl,type,
p: $i > $o ).
thf(c_24False_decl,type,
c_24False: $i ).
thf(c_24__type__2125___24t_decl,type,
c_24__type__2125___24t: $i > $i > $i > $o ).
thf(cCoq_2eLists_2eList_2eForall2___24a5_decl,type,
cCoq_2eLists_2eList_2eForall2___24a5: $i > $i > $i > $i > $i > $o ).
thf(c_24__type__2177___24t_decl,type,
c_24__type__2177___24t: $i > $i > $o ).
thf(cCoq_2eLists_2eList_2eForall___24a3_decl,type,
cCoq_2eLists_2eList_2eForall___24a3: $i > $i > $i > $i ).
thf(cCoq_2eLists_2eList_2eExists___24a3_decl,type,
cCoq_2eLists_2eList_2eExists___24a3: $i > $i > $i > $o ).
thf(happ_decl,type,
happ: $i > $i > $i ).
thf(cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2_decl,type,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2: $i > $i > $o ).
thf(cCoq_2eSorting_2eSorted_2eStronglySorted___24a3_decl,type,
cCoq_2eSorting_2eSorted_2eStronglySorted___24a3: $i > $i > $i > $i ).
thf(cCoq_2eSets_2eRelations__1_2eTransitive___24a2_decl,type,
cCoq_2eSets_2eRelations__1_2eTransitive___24a2: $i > $i > $o ).
thf(cCoq_2eInit_2eDatatypes_2eapp___24a3_decl,type,
cCoq_2eInit_2eDatatypes_2eapp___24a3: $i > $i > $i > $i ).
thf(cProp___24t_decl,type,
cProp___24t: $i > $o ).
thf(c_24__type__2361___24t_decl,type,
c_24__type__2361___24t: $i > $i > $i > $o ).
thf(cCoq_2eLists_2eList_2emap___24a4_decl,type,
cCoq_2eLists_2eList_2emap___24a4: $i > $i > $i > $i > $i ).
thf(cCoq_2emicromega_2eRefl_2emake__conj___24a3_decl,type,
cCoq_2emicromega_2eRefl_2emake__conj___24a3: $i > $i > $i > $o ).
thf(cCoq_2emicromega_2eRefl_2emake__impl___24a4_decl,type,
cCoq_2emicromega_2eRefl_2emake__impl___24a4: $i > $i > $i > $i > $o ).
thf(cCoq_2eLists_2eSetoidList_2eeqlistA___24a4_decl,type,
cCoq_2eLists_2eSetoidList_2eeqlistA___24a4: $i > $i > $i > $i > $o ).
thf(cCoq_2eLists_2eSetoidList_2eNoDupA___24a3_decl,type,
cCoq_2eLists_2eSetoidList_2eNoDupA___24a3: $i > $i > $i > $o ).
thf(c_24True_decl,type,
c_24True: $i ).
thf(c_24__type__2434___24t_decl,type,
c_24__type__2434___24t: $i > $i > $o ).
thf(c_24__case__Coq_2eInit_2eDatatypes_2elist_2435694___24a4_decl,type,
c_24__case__Coq_2eInit_2eDatatypes_2elist_2435694___24a4: $i > $i > $i > $i > $i ).
thf(cCoq_2eLists_2eList_2erev___24a2_decl,type,
cCoq_2eLists_2eList_2erev___24a2: $i > $i > $i ).
thf(cCoq_2eLists_2eList_2eNoDup___24a2_decl,type,
cCoq_2eLists_2eList_2eNoDup___24a2: $i > $i > $o ).
thf(c_24__type__46580___24t_decl,type,
c_24__type__46580___24t: $i > $o ).
thf(cHList_2ehlist_2ehlist__rect_decl,type,
cHList_2ehlist_2ehlist__rect: $i ).
thf(cCoq_2eLists_2eList_2eincl___24a3_decl,type,
cCoq_2eLists_2eList_2eincl___24a3: $i > $i > $i > $o ).
thf(cCoq_2eLists_2eList_2eIn___24a3_decl,type,
cCoq_2eLists_2eList_2eIn___24a3: $i > $i > $i > $i ).
thf(cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4_decl,type,
cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4: $i > $i > $i > $i > $o ).
thf(c_24__type__46531___24t_decl,type,
c_24__type__46531___24t: $i > $o ).
thf(cHList_2ehlist_2ehlist__tl_decl,type,
cHList_2ehlist_2ehlist__tl: $i ).
thf(c_24__type__3945___24t_decl,type,
c_24__type__3945___24t: $i > $i > $i > $i > $o ).
thf(c_24__type__47653___24t_decl,type,
c_24__type__47653___24t: $i > $o ).
thf(cHList_2ehlist_2ehlist__app_decl,type,
cHList_2ehlist_2ehlist__app: $i ).
thf(cCoq_2eSorting_2eSorted_2eLocallySorted___24a3_decl,type,
cCoq_2eSorting_2eSorted_2eLocallySorted___24a3: $i > $i > $i > $o ).
thf(c_24__lam__46514_decl,type,
c_24__lam__46514: $i ).
thf(c_24__lam__46514___24a3_decl,type,
c_24__lam__46514___24a3: $i > $i > $i > $i ).
thf(c_24__lam__46511___24a1_decl,type,
c_24__lam__46511___24a1: $i > $i ).
thf(cHList_2ehlist_2eHnil_decl,type,
cHList_2ehlist_2eHnil: $i ).
thf(c_24__type__72___24t_decl,type,
c_24__type__72___24t: $i > $i > $o ).
thf(cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2_decl,type,
cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2: $i > $i > $o ).
thf(c_24__type__46547___24t_decl,type,
c_24__type__46547___24t: $i > $o ).
thf(cHList_2ehlist_2ehlist__hd_decl,type,
cHList_2ehlist_2ehlist__hd: $i ).
thf(c_24__type__48333___24t_decl,type,
c_24__type__48333___24t: $i > $o ).
thf(cHList_2ehlist_2ehlist__rev_27_decl,type,
cHList_2ehlist_2ehlist__rev_27: $i ).
thf(cCoq_2eLists_2eList_2elel___24a3_decl,type,
cCoq_2eLists_2eList_2elel___24a3: $i > $i > $i > $o ).
thf(cCoq_2eLists_2eList_2eAdd___24a4_decl,type,
cCoq_2eLists_2eList_2eAdd___24a4: $i > $i > $i > $i > $o ).
thf(cCoq_2eLists_2eList_2eForallOrdPairs___24a3_decl,type,
cCoq_2eLists_2eList_2eForallOrdPairs___24a3: $i > $i > $i > $o ).
thf(c_24__type__2663___24t_decl,type,
c_24__type__2663___24t: $i > $i > $i > $i > $o ).
thf(cHList_2ehlist_2ehlist__app___24a4_decl,type,
cHList_2ehlist_2ehlist__app___24a4: $i > $i > $i > $i > $i ).
thf(c_24__type__4367___24t_decl,type,
c_24__type__4367___24t: $i > $i > $i > $i > $o ).
thf(c_24__case__Coq_2eInit_2eDatatypes_2elist_24505___24a3_decl,type,
c_24__case__Coq_2eInit_2eDatatypes_2elist_24505___24a3: $i > $i > $i > $i ).
thf(c_24__fix__550__v__CANONICAL__1___24a3_decl,type,
c_24__fix__550__v__CANONICAL__1___24a3: $i > $i > $i > $i ).
thf(c_24__type__3259___24t_decl,type,
c_24__type__3259___24t: $i > $i > $i > $i > $o ).
thf(c_24__type__2511___24t_decl,type,
c_24__type__2511___24t: $i > $i > $i > $i > $i > $o ).
thf(c_24__type__17419___24t_decl,type,
c_24__type__17419___24t: $i > $i > $i > $o ).
thf(c_24__type__19092___24t_decl,type,
c_24__type__19092___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_24__prop__126684___24a7_decl,type,
c_24__prop__126684___24a7: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(cHList_2ehlist_2eequiv__hlist___24a4_decl,type,
cHList_2ehlist_2eequiv__hlist___24a4: $i > $i > $i > $i > $i ).
thf(c_24__type__46686___24t_decl,type,
c_24__type__46686___24t: $i > $o ).
thf(c_24__type__46686_decl,type,
c_24__type__46686: $i ).
thf(c_24__type__120501___24t_decl,type,
c_24__type__120501___24t: $i > $i > $i > $o ).
thf(c_24__type__15488___24t_decl,type,
c_24__type__15488___24t: $i > $o ).
thf(c_24__type__15450___24t_decl,type,
c_24__type__15450___24t: $i > $o ).
thf(cCoq_2eLists_2eList_2eremovelast___24a2_decl,type,
cCoq_2eLists_2eList_2eremovelast___24a2: $i > $i > $i ).
thf(c_24__type__19752___24t_decl,type,
c_24__type__19752___24t: $i > $i > $i > $i > $i > $o ).
thf(c_24__lam__47646_decl,type,
c_24__lam__47646: $i ).
thf(c_24__lam__47646___24a7_decl,type,
c_24__lam__47646___24a7: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_24__type__1966___24t_decl,type,
c_24__type__1966___24t: $i > $i > $i > $o ).
thf(c_24__type__33241___24t_decl,type,
c_24__type__33241___24t: $i > $o ).
thf(c_24__type__46583___24t_decl,type,
c_24__type__46583___24t: $i > $o ).
thf(c_24__type__46600___24t_decl,type,
c_24__type__46600___24t: $i > $i > $o ).
thf(c_24__type__45164___24t_decl,type,
c_24__type__45164___24t: $i > $i > $i > $i > $o ).
thf(c_24__type__46627___24t_decl,type,
c_24__type__46627___24t: $i > $i > $i > $o ).
thf(c_24__type__46627___24a2_decl,type,
c_24__type__46627___24a2: $i > $i > $i ).
thf(cCoq_2eLists_2eList_2erev__append___24a3_decl,type,
cCoq_2eLists_2eList_2erev__append___24a3: $i > $i > $i > $i ).
thf(c_24__type__122667___24t_decl,type,
c_24__type__122667___24t: $i > $o ).
thf(c_24__type__122667_decl,type,
c_24__type__122667: $i ).
thf(c_24__type__121389___24t_decl,type,
c_24__type__121389___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_24__type__33834___24t_decl,type,
c_24__type__33834___24t: $i > $i > $i > $o ).
thf(cHList_2ehlist_2ehlist__hd___24a3_decl,type,
cHList_2ehlist_2ehlist__hd___24a3: $i > $i > $i > $i ).
thf(cHList_2ehlist_2ehlist__tl___24a3_decl,type,
cHList_2ehlist_2ehlist__tl___24a3: $i > $i > $i > $i ).
thf(cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5_decl,type,
cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5: $i > $i > $i > $i > $i > $o ).
thf(cHList_2ehlist_2ehlist__rev_27___24a3_decl,type,
cHList_2ehlist_2ehlist__rev_27___24a3: $i > $i > $i > $i ).
thf(c_24__type__1926___24t_decl,type,
c_24__type__1926___24t: $i > $i > $i > $o ).
thf(cCoq_2eInit_2eDatatypes_2elist__rect___24a5_decl,type,
cCoq_2eInit_2eDatatypes_2elist__rect___24a5: $i > $i > $i > $i > $i > $i ).
thf(c_24__prop__126659___24a7_decl,type,
c_24__prop__126659___24a7: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_24__type__45156___24t_decl,type,
c_24__type__45156___24t: $i > $i > $i > $i > $o ).
thf(c_24__type__87___24t_decl,type,
c_24__type__87___24t: $i > $o ).
thf(cExtLib_2eTactics_2eInjection_2eInjective___24t_decl,type,
cExtLib_2eTactics_2eInjection_2eInjective___24t: $i > $i > $o ).
thf(cExtLib_2eTactics_2eInjection_2eInjective___24a1_decl,type,
cExtLib_2eTactics_2eInjection_2eInjective___24a1: $i > $i ).
thf(c_24__type__3068___24t_decl,type,
c_24__type__3068___24t: $i > $i > $i > $o ).
thf(c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502_decl,type,
c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502: $i ).
thf(c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a2_decl,type,
c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a2: $i > $i > $i ).
thf(c_24__type__29599___24t_decl,type,
c_24__type__29599___24t: $i > $i > $i > $i > $i > $o ).
thf(c_24__type__114118___24t_decl,type,
c_24__type__114118___24t: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(cCoq_2eLists_2eList_2etl___24a2_decl,type,
cCoq_2eLists_2eList_2etl___24a2: $i > $i > $i ).
thf(c_24__lam__47646___24a6_decl,type,
c_24__lam__47646___24a6: $i > $i > $i > $i > $i > $i > $i ).
thf(c_24__type__2211___24t_decl,type,
c_24__type__2211___24t: $i > $i > $i > $o ).
thf(c_24__type__29901___24t_decl,type,
c_24__type__29901___24t: $i > $i > $i > $i > $i > $i > $o ).
thf(c_24__prop__126660___24a7_decl,type,
c_24__prop__126660___24a7: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(cCoq_2eLists_2eList_2elast___24a3_decl,type,
cCoq_2eLists_2eList_2elast___24a3: $i > $i > $i > $i ).
thf(cHList_2ehlist_2ehlist__rev___24a2_decl,type,
cHList_2ehlist_2ehlist__rev___24a2: $i > $i > $i ).
thf(c_24__lam__2046___24a4_decl,type,
c_24__lam__2046___24a4: $i > $i > $i > $i > $o ).
thf(c_24__type__64___24t_decl,type,
c_24__type__64___24t: $i > $o ).
thf(c_24__type__17521___24t_decl,type,
c_24__type__17521___24t: $i > $o ).
thf(c_24__type__15477___24t_decl,type,
c_24__type__15477___24t: $i > $o ).
thf(cHList_2ehlist_2ehlist__rect___24a5_decl,type,
cHList_2ehlist_2ehlist__rect___24a5: $i > $i > $i > $i > $i > $i ).
thf(c_24__type__159676___24t_decl,type,
c_24__type__159676___24t: $i > $i > $i > $o ).
thf(c_24__generic__case__48326_decl,type,
c_24__generic__case__48326: $i ).
thf(c_24__generic__case__48326___24a1_decl,type,
c_24__generic__case__48326___24a1: $i > $i ).
thf(c_24__type__35233___24t_decl,type,
c_24__type__35233___24t: $i > $i > $i > $o ).
thf(cCoq_2eLists_2eSetoidList_2etranspose___24a4_decl,type,
cCoq_2eLists_2eSetoidList_2etranspose___24a4: $i > $i > $i > $i > $o ).
thf(cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5_decl,type,
cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5: $i > $i > $i > $i > $i > $o ).
thf(c_24__type__32967___24t_decl,type,
c_24__type__32967___24t: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_24__type__120240___24t_decl,type,
c_24__type__120240___24t: $i > $i > $i > $i > $i > $i > $o ).
thf(c_24__type__3218___24t_decl,type,
c_24__type__3218___24t: $i > $i > $i > $i > $o ).
thf(c_24__type__40361___24t_decl,type,
c_24__type__40361___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_24__type__3185___24t_decl,type,
c_24__type__3185___24t: $i > $o ).
thf(c_24__type__15463___24t_decl,type,
c_24__type__15463___24t: $i > $o ).
thf(c_24__type__47653_decl,type,
c_24__type__47653: $i ).
thf(c_24__type__3988___24t_decl,type,
c_24__type__3988___24t: $i > $i > $i > $i > $i > $o ).
thf(c_24__type__19193___24t_decl,type,
c_24__type__19193___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_24__type__69___24t_decl,type,
c_24__type__69___24t: $i > $o ).
thf(c_24__type__34447___24t_decl,type,
c_24__type__34447___24t: $i > $i > $i > $o ).
thf(c_24__type__46391___24t_decl,type,
c_24__type__46391___24t: $i > $o ).
thf(c_24__type__7607___24t_decl,type,
c_24__type__7607___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_24__type__122692___24t_decl,type,
c_24__type__122692___24t: $i > $o ).
thf(c_24__type__220___24t_decl,type,
c_24__type__220___24t: $i > $i > $i > $i > $o ).
thf(cExtLib_2eTactics_2eInjection_2eBuild__Injective___24a2_decl,type,
cExtLib_2eTactics_2eInjection_2eBuild__Injective___24a2: $i > $i > $i ).
thf(c_24__type__35252___24t_decl,type,
c_24__type__35252___24t: $i > $o ).
thf(c_24__type__2118___24t_decl,type,
c_24__type__2118___24t: $i > $i > $i > $i > $i > $i > $o ).
thf(cHList_2ehlist_2ehlist__rev_27___24a4_decl,type,
cHList_2ehlist_2ehlist__rev_27___24a4: $i > $i > $i > $i > $i ).
thf(c_24__type__16977___24t_decl,type,
c_24__type__16977___24t: $i > $i > $i > $i > $o ).
thf(c_24__lam__48310_decl,type,
c_24__lam__48310: $i ).
thf(c_24__lam__48310___24a7_decl,type,
c_24__lam__48310___24a7: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_24__type__126682___24t_decl,type,
c_24__type__126682___24t: $i > $o ).
thf(c_24__type__46515___24t_decl,type,
c_24__type__46515___24t: $i > $o ).
thf(c_24__type__99___24t_decl,type,
c_24__type__99___24t: $i > $o ).
thf(c_24__type__122692_decl,type,
c_24__type__122692: $i ).
thf(c_24__type__46531_decl,type,
c_24__type__46531: $i ).
thf(c_24__type__46451___24t_decl,type,
c_24__type__46451___24t: $i > $i > $i > $i > $o ).
thf(c_24__type__126742___24t_decl,type,
c_24__type__126742___24t: $i > $i > $i > $i > $i > $o ).
thf(c_24__type__2310___24t_decl,type,
c_24__type__2310___24t: $i > $o ).
thf(c_24__lam__46511_decl,type,
c_24__lam__46511: $i ).
thf(c_24__type__34438___24t_decl,type,
c_24__type__34438___24t: $i > $i > $i > $o ).
thf(c_24__lam__47639_decl,type,
c_24__lam__47639: $i ).
thf(c_24__lam__47639___24a2_decl,type,
c_24__lam__47639___24a2: $i > $i > $i ).
thf(c_24__type__29339___24t_decl,type,
c_24__type__29339___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_24__lam__48310___24a6_decl,type,
c_24__lam__48310___24a6: $i > $i > $i > $i > $i > $i > $i ).
thf(c_24__type__35187___24t_decl,type,
c_24__type__35187___24t: $i > $i > $i > $o ).
thf(cCoq_2eLists_2eSetoidList_2etranspose2___24a4_decl,type,
cCoq_2eLists_2eSetoidList_2etranspose2___24a4: $i > $i > $i > $i > $o ).
thf(c_24__type__46443___24t_decl,type,
c_24__type__46443___24t: $i > $i > $i > $i > $o ).
thf(c_24__type__120259___24t_decl,type,
c_24__type__120259___24t: $i > $i > $i > $i > $i > $i > $o ).
thf(c_24__type__46603___24t_decl,type,
c_24__type__46603___24t: $i > $o ).
thf(c_24__type__46603_decl,type,
c_24__type__46603: $i ).
thf(c_24__type__34711___24t_decl,type,
c_24__type__34711___24t: $i > $i > $i > $i > $o ).
thf(c_24__type__46666___24t_decl,type,
c_24__type__46666___24t: $i > $o ).
thf(c_24__type__18991___24t_decl,type,
c_24__type__18991___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_24__type__35210___24t_decl,type,
c_24__type__35210___24t: $i > $i > $i > $o ).
thf(c_24__type__17185___24t_decl,type,
c_24__type__17185___24t: $i > $i > $i > $i > $o ).
thf(c_24__type__46583_decl,type,
c_24__type__46583: $i ).
thf(c_24__type__31326___24t_decl,type,
c_24__type__31326___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(cCoq_2eLists_2eList_2ehd___24a3_decl,type,
cCoq_2eLists_2eList_2ehd___24a3: $i > $i > $i > $i ).
thf(c_24__type__2628___24t_decl,type,
c_24__type__2628___24t: $i > $i > $i > $i > $i > $o ).
thf(c_24__type__40707___24t_decl,type,
c_24__type__40707___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a1_decl,type,
c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a1: $i > $i ).
thf(c_24__type__33408___24t_decl,type,
c_24__type__33408___24t: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_24__type__2170___24t_decl,type,
c_24__type__2170___24t: $i > $i > $i > $o ).
thf(cHList_2ehlist_2ehlist__app___24a3_decl,type,
cHList_2ehlist_2ehlist__app___24a3: $i > $i > $i > $i ).
thf(cCoq_2eLists_2eList_2efold__right___24a5_decl,type,
cCoq_2eLists_2eList_2efold__right___24a5: $i > $i > $i > $i > $i > $i ).
thf(c_24__type__35336___24t_decl,type,
c_24__type__35336___24t: $i > $o ).
thf(c_24__type__6875___24t_decl,type,
c_24__type__6875___24t: $i > $i > $i > $o ).
thf(cCoq_2eLists_2eList_2eflat__map___24a4_decl,type,
cCoq_2eLists_2eList_2eflat__map___24a4: $i > $i > $i > $i > $i ).
thf(cCoq_2eLists_2eList_2efold__left___24a5_decl,type,
cCoq_2eLists_2eList_2efold__left___24a5: $i > $i > $i > $i > $i > $i ).
thf(c_24__type__46600___24a1_decl,type,
c_24__type__46600___24a1: $i > $i ).
thf(c_24__type__48237___24t_decl,type,
c_24__type__48237___24t: $i > $o ).
thf(c_24__type__48237_decl,type,
c_24__type__48237: $i ).
thf(c_24__type__46547_decl,type,
c_24__type__46547: $i ).
thf(c_24__type__37914___24t_decl,type,
c_24__type__37914___24t: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_24__type__126706___24t_decl,type,
c_24__type__126706___24t: $i > $o ).
thf(c_24__type__126706_decl,type,
c_24__type__126706: $i ).
thf(c_24__type__33790___24t_decl,type,
c_24__type__33790___24t: $i > $i > $o ).
thf(c_24__lam__46514___24a2_decl,type,
c_24__lam__46514___24a2: $i > $i > $i ).
thf(c_24__type__2533___24t_decl,type,
c_24__type__2533___24t: $i > $i > $o ).
thf(c_24__generic__case__47111_decl,type,
c_24__generic__case__47111: $i ).
thf(cCoq_2eInit_2eDatatypes_2ett_decl,type,
cCoq_2eInit_2eDatatypes_2ett: $i ).
thf(282,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( c_24__lam__47639 @ happ ) @ happ ) )
= ( B @ ( A @ c_24__lam__47639___24a2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_$_lam_47639_$a2') ).
thf(2306,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( c_24__lam__47639 @ happ ) @ happ ) )
= ( B @ ( A @ c_24__lam__47639___24a2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(263,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Add_head') ).
thf(2109,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(154,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InA_cons_tl') ).
thf(1237,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(168,axiom,
! [A: $i,B: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [C: $i] :
( ? [D: $i] :
( ( ( A @ cType___24t )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ? [E: $i] :
( ? [F: $i] :
( ( ( B @ ( A @ cCoq_2eLists_2eList_2eremovelast___24a2 ) )
= ( D @ ( A @ cCoq_2eLists_2eList_2eremovelast___24a2 ) @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
| ( ( ( B @ ( A @ cCoq_2eLists_2eList_2eremovelast___24a2 ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( D
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) )
& ( B
= ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) ) ) ) )
& ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( C @ t ) ) )
| ( ( ( B @ ( A @ cCoq_2eLists_2eList_2eremovelast___24a2 ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Lists.List.removelast') ).
thf(1315,plain,
! [A: $i,B: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [C: $i] :
( ? [D: $i] :
( ( ( A @ cType___24t )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ? [E: $i] :
( ? [F: $i] :
( ( ( B @ ( A @ cCoq_2eLists_2eList_2eremovelast___24a2 ) )
= ( D @ ( A @ cCoq_2eLists_2eList_2eremovelast___24a2 ) @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
| ( ( ( B @ ( A @ cCoq_2eLists_2eList_2eremovelast___24a2 ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( D
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) )
& ( B
= ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) ) ) ) )
& ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( C @ t ) ) )
| ( ( ( B @ ( A @ cCoq_2eLists_2eList_2eremovelast___24a2 ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(166,axiom,
! [A: $i] :
( ( A @ c_24__type__15488___24t )
<=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_15488') ).
thf(1295,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ t ) ) ) ) )
=> ( A @ c_24__type__15488___24t ) )
& ( ( A @ c_24__type__15488___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(244,axiom,
! [A: $i] :
( ( A @ c_24__type__69___24t )
<=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_69') ).
thf(1956,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) )
=> ( A @ c_24__type__69___24t ) )
& ( ( A @ c_24__type__69___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(132,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( D @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( C @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.eqlistA_rev') ).
thf(1110,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( D @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( C @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
<=> ( ( D @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
& ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.micromega.Refl.make_conj_app') ).
thf(481,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( ( D @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
& ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) ) )
& ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
=> ( ( D @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
& ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(63,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( ( D @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
| ( C @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InA_app') ).
thf(645,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( ( D @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
| ( C @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( C @ ( B @ ( A @ c_24__type__4367___24t ) ) ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( D @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
& ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Coq.Sorting.Sorted.StronglySorted') ).
thf(892,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( C @ ( B @ ( A @ c_24__type__4367___24t ) ) ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( D @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
& ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__46443___24t ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cProp___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_46443') ).
thf(2363,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cProp___24t ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__46443___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__46443___24t ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cProp___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__29339___24t ) ) ) ) ) ) ) ) )
<=> ! [J: $i] :
( ( A @ ( J @ t ) )
=> ! [K: $i] :
( ( A @ ( K @ t ) )
=> ( K @ ( J @ ( I @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_29339') ).
thf(2309,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ! [J: $i] :
( ( A @ ( J @ t ) )
=> ! [K: $i] :
( ( A @ ( K @ t ) )
=> ( K @ ( J @ ( I @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__29339___24t ) ) ) ) ) ) ) ) ) )
& ( ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__29339___24t ) ) ) ) ) ) ) ) )
=> ! [J: $i] :
( ( A @ ( J @ t ) )
=> ! [K: $i] :
( ( A @ ( K @ t ) )
=> ( K @ ( J @ ( I @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i,S: $i,T: $i,U: $i,V: $i,W: $i] :
( ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__40361___24t ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
<=> ! [X: $i] :
( ( A @ ( X @ t ) )
=> ! [Y: $i] :
( ( A @ ( Y @ t ) )
=> ( Y @ ( X @ ( W @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_40361') ).
thf(1882,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i,S: $i,T: $i,U: $i,V: $i,W: $i] :
( ( ! [X: $i] :
( ( A @ ( X @ t ) )
=> ! [Y: $i] :
( ( A @ ( Y @ t ) )
=> ( Y @ ( X @ ( W @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__40361___24t ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__40361___24t ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ! [X: $i] :
( ( A @ ( X @ t ) )
=> ! [Y: $i] :
( ( A @ ( Y @ t ) )
=> ( Y @ ( X @ ( W @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(127,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
=> ( ( E @ ( C @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.NoDupA_sind') ).
thf(1068,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
=> ( ( E @ ( C @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cType___24t )
=> ( ( B @ cType___24t )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [E: $i] :
( ? [F: $i] :
( ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( F @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) @ ( E @ ( C @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
| ( ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( D
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Lists.List.map') ).
thf(2381,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cType___24t )
=> ( ( B @ cType___24t )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [E: $i] :
( ? [F: $i] :
( ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( F @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) @ ( E @ ( C @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
| ( ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( D
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(353,axiom,
! [A: $i] :
( ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ cHList_2ehlist_2ehlist___24t ) )
=> ( A = cHList_2ehlist_2eHnil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','HList.hlist.hlist_nil_eta') ).
thf(2908,plain,
! [A: $i] :
( ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ cHList_2ehlist_2ehlist___24t ) )
=> ( A = cHList_2ehlist_2eHnil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__35233___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_35233') ).
thf(1808,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) )
=> ( C @ ( B @ ( A @ c_24__type__35233___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__35233___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cType___24t )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [E: $i] :
( ? [F: $i] :
( ( ( D @ ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__impl___24a4 ) ) ) )
<=> ( ( E @ ( B @ happ ) @ p )
=> ( D @ ( F @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__impl___24a4 ) ) ) ) ) )
& ( C
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
| ( ( ( D @ ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__impl___24a4 ) ) ) )
<=> ( D @ p ) )
& ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.micromega.Refl.make_impl') ).
thf(2527,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cType___24t )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [E: $i] :
( ? [F: $i] :
( ( ( ( E @ ( B @ happ ) @ p )
=> ( D @ ( F @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__impl___24a4 ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__impl___24a4 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__impl___24a4 ) ) ) )
=> ( ( E @ ( B @ happ ) @ p )
=> ( D @ ( F @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__impl___24a4 ) ) ) ) ) )
& ( C
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
| ( ( ( D @ p )
=> ( D @ ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__impl___24a4 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__impl___24a4 ) ) ) )
=> ( D @ p ) )
& ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__45164___24t ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_45164') ).
thf(1422,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cType___24t ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__45164___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__45164___24t ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(374,axiom,
! [A: $i] :
( ( A @ c_24__type__46603___24t )
=> ( ( cHList_2ehlist_2eHnil @ ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ happ ) @ happ ) @ p )
=> ( ! [B: $i] :
( ( B @ ciT___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cF___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( E @ ( C @ ( A @ happ ) @ happ ) @ p )
=> ( E @ ( D @ ( C @ ( B @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ happ ) @ happ ) @ p ) ) ) ) ) )
=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ p ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','HList.hlist.hlist_ind') ).
thf(3098,plain,
! [A: $i] :
( ( A @ c_24__type__46603___24t )
=> ( ( cHList_2ehlist_2eHnil @ ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ happ ) @ happ ) @ p )
=> ( ! [B: $i] :
( ( B @ ciT___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cF___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( E @ ( C @ ( A @ happ ) @ happ ) @ p )
=> ( E @ ( D @ ( C @ ( B @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ happ ) @ happ ) @ p ) ) ) ) ) )
=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__45156___24t ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_45156') ).
thf(1544,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cType___24t ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__45156___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__45156___24t ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(147,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
<=> ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InA_app_idem') ).
thf(1205,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( D @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) )
& ( ( D @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(201,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
=> ( ( D = E )
& ( B = C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.app_inj_tail') ).
thf(1591,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
=> ( ( D = E )
& ( B = C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ ciT___24t )
=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cF___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cF___24t ) )
=> ! [F: $i] :
( ( F @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ cHList_2ehlist_2eHcons___24a4 ) ) ) )
= ( F @ ( E @ ( B @ ( A @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
=> ( ( D = F )
& ( C = E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ ciT___24t )
=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cF___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cF___24t ) )
=> ! [F: $i] :
( ( F @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ cHList_2ehlist_2eHcons___24a4 ) ) ) )
= ( F @ ( E @ ( B @ ( A @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
=> ( ( D = F )
& ( C = E ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(379,plain,
~ ! [A: $i] :
( ( A @ ciT___24t )
=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cF___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cF___24t ) )
=> ! [F: $i] :
( ( F @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ cHList_2ehlist_2eHcons___24a4 ) ) ) )
= ( F @ ( E @ ( B @ ( A @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
=> ( ( D = F )
& ( C = E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(225,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.NoDup_remove_1') ).
thf(1793,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(95,axiom,
c_24True @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_COQ_TRUE') ).
thf(861,plain,
c_24True @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( ( B @ ( A @ cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2 ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ( ( C @ ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( C @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InA_eqA') ).
thf(408,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( ( B @ ( A @ cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2 ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ( ( C @ ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( C @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(113,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( ( E @ ( F @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( F @ ( C @ happ ) )
= ( F @ ( D @ happ ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.ext_in_map') ).
thf(977,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( ( E @ ( F @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( F @ ( C @ happ ) )
= ( F @ ( D @ happ ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( ( A @ cType___24t )
=> ( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ? [F: $i] :
( ? [G: $i] :
( ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2elast___24a3 ) ) )
= ( C @ ( E @ ( A @ cCoq_2eLists_2eList_2elast___24a3 ) ) ) )
& ( E
= ( G @ ( F @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( F @ t ) ) )
| ( ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2elast___24a3 ) ) )
= D )
& ( E
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) )
& ( B
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2elast___24a3 ) ) )
= C )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Lists.List.last') ).
thf(1671,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( ( A @ cType___24t )
=> ( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ? [F: $i] :
( ? [G: $i] :
( ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2elast___24a3 ) ) )
= ( C @ ( E @ ( A @ cCoq_2eLists_2eList_2elast___24a3 ) ) ) )
& ( E
= ( G @ ( F @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( F @ t ) ) )
| ( ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2elast___24a3 ) ) )
= D )
& ( E
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) )
& ( B
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2elast___24a3 ) ) )
= C )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ciT___24t )
=> ( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__hd___24a3 ) ) )
= F )
& ( C
= ( G @ ( F @ ( E @ ( D @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
& ( G @ ( E @ cHList_2ehlist_2ehlist___24t ) ) )
& ( F @ ( D @ cF___24t ) ) )
& ( E @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( D @ ciT___24t ) )
| ( ( ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__hd___24a3 ) ) )
= cCoq_2eInit_2eDatatypes_2ett )
& ( C = cHList_2ehlist_2eHnil ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_HList.hlist.hlist_hd') ).
thf(3120,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ciT___24t )
=> ( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__hd___24a3 ) ) )
= F )
& ( C
= ( G @ ( F @ ( E @ ( D @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
& ( G @ ( E @ cHList_2ehlist_2ehlist___24t ) ) )
& ( F @ ( D @ cF___24t ) ) )
& ( E @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( D @ ciT___24t ) )
| ( ( ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__hd___24a3 ) ) )
= cCoq_2eInit_2eDatatypes_2ett )
& ( C = cHList_2ehlist_2eHnil ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(364,axiom,
! [A: $i] :
( ( A @ c_24__type__122692___24t )
<=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_122692') ).
thf(3004,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ cProp___24t ) ) ) )
=> ( A @ c_24__type__122692___24t ) )
& ( ( A @ c_24__type__122692___24t )
=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ cProp___24t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ciT___24t )
=> ( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__tl___24a3 ) ) )
= G )
& ( C
= ( G @ ( F @ ( E @ ( D @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
& ( G @ ( E @ cHList_2ehlist_2ehlist___24t ) ) )
& ( F @ ( D @ cF___24t ) ) )
& ( E @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( D @ ciT___24t ) )
| ( ( ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__tl___24a3 ) ) )
= cCoq_2eInit_2eDatatypes_2ett )
& ( C = cHList_2ehlist_2eHnil ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_HList.hlist.hlist_tl') ).
thf(3135,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ciT___24t )
=> ( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__tl___24a3 ) ) )
= G )
& ( C
= ( G @ ( F @ ( E @ ( D @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
& ( G @ ( E @ cHList_2ehlist_2ehlist___24t ) ) )
& ( F @ ( D @ cF___24t ) ) )
& ( E @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( D @ ciT___24t ) )
| ( ( ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__tl___24a3 ) ) )
= cCoq_2eInit_2eDatatypes_2ett )
& ( C = cHList_2ehlist_2eHnil ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(140,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.lel_nil') ).
thf(1164,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( B @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( ? [C: $i] :
( ? [D: $i] :
( ( B
= ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
& ~ ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( C @ t ) ) )
| ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Coq.Lists.List.NoDup') ).
thf(814,plain,
! [A: $i,B: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( B @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( ? [C: $i] :
( ? [D: $i] :
( ( B
= ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
& ~ ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( C @ t ) ) )
| ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(248,axiom,
! [A: $i] :
( ( A @ c_24__type__46391___24t )
<=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ! [D: $i] :
( ( B @ ( D @ t ) )
=> ( ( C = D )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ cProp___24t ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_46391') ).
thf(1988,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ! [D: $i] :
( ( B @ ( D @ t ) )
=> ( ( C = D )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ cProp___24t ) ) ) ) )
=> ( A @ c_24__type__46391___24t ) )
& ( ( A @ c_24__type__46391___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ! [D: $i] :
( ( B @ ( D @ t ) )
=> ( ( C = D )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ cProp___24t ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(79,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
=> ( ( E @ ( C @ happ ) @ p )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.Sorted_ind') ).
thf(747,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
=> ( ( E @ ( C @ happ ) @ p )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(312,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.in_cons') ).
thf(2575,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(351,axiom,
! [A: $i] :
( ( A @ ciT___24t )
<=> ( ciT @ ( A @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_iT') ).
thf(2901,plain,
! [A: $i] :
( ( ( ciT @ ( A @ t ) )
=> ( A @ ciT___24t ) )
& ( ( A @ ciT___24t )
=> ( ciT @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(107,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__2434___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [G: $i] :
( ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ( ( G @ ( F @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( ( G @ ( F @ ( C @ happ ) @ happ ) @ p )
=> ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.eqlistA_ind') ).
thf(945,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__2434___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [G: $i] :
( ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ( ( G @ ( F @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( ( G @ ( F @ ( C @ happ ) @ happ ) @ p )
=> ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ ( cHList_2ehlist_2ehlist__rect @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__rect___24a5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_HList.hlist.hlist_rect_$a5') ).
thf(1746,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ ( cHList_2ehlist_2ehlist__rect @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__rect___24a5 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(111,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.incl_Add_inv') ).
thf(973,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(171,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( B @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= ( B @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.app_inv_tail') ).
thf(1359,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( B @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= ( B @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(256,axiom,
! [A: $i] :
( ( A @ c_24__type__122667___24t )
=> ( cHList_2ehlist_2eHnil @ ( cHList_2ehlist_2eHnil @ ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','HList.hlist.hlist_eqv_nil') ).
thf(2067,plain,
! [A: $i] :
( ( A @ c_24__type__122667___24t )
=> ( cHList_2ehlist_2eHnil @ ( cHList_2ehlist_2eHnil @ ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__prop__126684___24a7 ) ) ) ) ) ) @ p )
<=> ( ( G @ ( F @ ( B @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
& ( E @ ( D @ ( C @ ( A @ happ ) @ happ ) @ happ ) @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_prop_126684') ).
thf(1254,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ ( F @ ( B @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
& ( E @ ( D @ ( C @ ( A @ happ ) @ happ ) @ happ ) @ p ) )
=> ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__prop__126684___24a7 ) ) ) ) ) ) @ p ) )
& ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__prop__126684___24a7 ) ) ) ) ) ) @ p )
=> ( ( G @ ( F @ ( B @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
& ( E @ ( D @ ( C @ ( A @ happ ) @ happ ) @ happ ) @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ happ ) @ p )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ happ ) @ p ) ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( E @ ( D @ happ ) @ p ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.HdRel_ind') ).
thf(651,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ happ ) @ p )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ happ ) @ p ) ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( E @ ( D @ happ ) @ p ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(305,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ cType___24t )
=> ( ( B @ cType___24t )
=> ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__2118___24t ) ) ) ) ) )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( D
= ( H @ ( F @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E
= ( I @ ( G @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( I @ ( H @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
& ( G @ ( F @ ( C @ happ ) @ happ ) @ p )
& ( I @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( H @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( B @ ( G @ t ) ) )
& ( A @ ( F @ t ) ) )
| ( ( D
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( E
= ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Coq.Lists.List.Forall2') ).
thf(2491,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ cType___24t )
=> ( ( B @ cType___24t )
=> ( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__2118___24t ) ) ) ) ) )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( D
= ( H @ ( F @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E
= ( I @ ( G @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( I @ ( H @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
& ( G @ ( F @ ( C @ happ ) @ happ ) @ p )
& ( I @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( H @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( B @ ( G @ t ) ) )
& ( A @ ( F @ t ) ) )
| ( ( D
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( E
= ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(335,axiom,
! [A: $i] :
( ( A @ c_24__type__48237___24t )
<=> ( c_24__type__48237 @ ( A @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_$_type_48237') ).
thf(2763,plain,
! [A: $i] :
( ( ( c_24__type__48237 @ ( A @ t ) )
=> ( A @ c_24__type__48237___24t ) )
& ( ( A @ c_24__type__48237___24t )
=> ( c_24__type__48237 @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( c_24__lam__47646 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__47646___24a6 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_$_lam_47646_$a6') ).
thf(1628,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( c_24__lam__47646 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__47646___24a6 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( ( E @ ( C @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Forall_sind') ).
thf(724,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( ( E @ ( C @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(215,axiom,
! [A: $i] :
( ( A @ c_24__type__17521___24t )
<=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ cType___24t ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_17521') ).
thf(1709,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ cType___24t ) ) ) )
=> ( A @ c_24__type__17521___24t ) )
& ( ( A @ c_24__type__17521___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ cType___24t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(179,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ happ ) @ p )
=> ( ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ happ ) @ p ) ) ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( C @ ( B @ happ ) @ p ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Init.Datatypes.list_sind') ).
thf(1430,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ happ ) @ p )
=> ( ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ happ ) @ p ) ) ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( C @ ( B @ happ ) @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__35187___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cProp___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_35187') ).
thf(2339,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cProp___24t ) )
=> ( C @ ( B @ ( A @ c_24__type__35187___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__35187___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cProp___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__3218___24t ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cProp___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_3218') ).
thf(2269,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cProp___24t ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__3218___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__3218___24t ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cProp___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( C @ happ ) )
= ( E @ ( D @ happ ) ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Logic.FunctionalExtensionality.functional_extensionality') ).
thf(504,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( C @ happ ) )
= ( E @ ( D @ happ ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(85,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eForallOrdPairs___24a3 ) ) )
=> ( ( E @ ( C @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eForallOrdPairs___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.ForallOrdPairs_sind') ).
thf(802,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eForallOrdPairs___24a3 ) ) )
=> ( ( E @ ( C @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eForallOrdPairs___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(325,axiom,
! [A: $i] :
( ( A @ c_24__type__35336___24t )
<=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ cProp___24t )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cType___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_35336') ).
thf(2682,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ cProp___24t )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cType___24t ) ) )
=> ( A @ c_24__type__35336___24t ) )
& ( ( A @ c_24__type__35336___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ cProp___24t )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cType___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__120501___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_120501') ).
thf(1279,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( C @ ( B @ ( A @ c_24__type__120501___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__120501___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(145,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
<=> ( D @ ( C @ ( B @ ( A @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.eqlistA_altdef') ).
thf(1191,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(236,axiom,
! [A: $i] :
( ( A @ c_24__type__122667___24t )
=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ! [E: $i] :
( ( E @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ! [F: $i] :
( ( F @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ! [G: $i] :
( ( G @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( ( G @ ( F @ ( C @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
& ( E @ ( D @ ( B @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p ) )
<=> ( G @ ( E @ ( C @ ( B @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( F @ ( D @ ( C @ ( B @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','HList.hlist.equiv_hlist_app') ).
thf(1892,plain,
! [A: $i] :
( ( A @ c_24__type__122667___24t )
=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ! [E: $i] :
( ( E @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ! [F: $i] :
( ( F @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ! [G: $i] :
( ( G @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( ( G @ ( E @ ( C @ ( B @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( F @ ( D @ ( C @ ( B @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
=> ( ( G @ ( F @ ( C @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
& ( E @ ( D @ ( B @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p ) ) )
& ( ( ( G @ ( F @ ( C @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
& ( E @ ( D @ ( B @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p ) )
=> ( G @ ( E @ ( C @ ( B @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( F @ ( D @ ( C @ ( B @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
& ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.Sorted_inv') ).
thf(416,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
& ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__3988___24t ) ) ) ) )
<=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ( G @ ( F @ ( E @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_3988') ).
thf(1931,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ( G @ ( F @ ( E @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__3988___24t ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__3988___24t ) ) ) ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ( G @ ( F @ ( E @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(347,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__2533___24t ) )
<=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_2533') ).
thf(2852,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( B @ ( A @ c_24__type__2533___24t ) ) )
& ( ( B @ ( A @ c_24__type__2533___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( D @ ( A @ c_24__type__46627___24t ) ) )
=> ( ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ cHList_2ehlist_2ehlist___24t ) )
=> ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__rect___24a5 ) ) ) ) )
= ( I @ ( G @ ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__rect___24a5 ) ) ) ) @ ( I @ ( H @ ( G @ ( F @ ( C @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) ) )
& ( E
= ( I @ ( H @ ( G @ ( F @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
& ( I @ ( G @ cHList_2ehlist_2ehlist___24t ) ) )
& ( H @ ( F @ cF___24t ) ) )
& ( G @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( F @ ciT___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__rect___24a5 ) ) ) ) )
= B )
& ( E = cHList_2ehlist_2eHnil ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_HList.hlist.hlist_rect') ).
thf(2989,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( D @ ( A @ c_24__type__46627___24t ) ) )
=> ( ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ cHList_2ehlist_2ehlist___24t ) )
=> ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__rect___24a5 ) ) ) ) )
= ( I @ ( G @ ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__rect___24a5 ) ) ) ) @ ( I @ ( H @ ( G @ ( F @ ( C @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) ) )
& ( E
= ( I @ ( H @ ( G @ ( F @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
& ( I @ ( G @ cHList_2ehlist_2ehlist___24t ) ) )
& ( H @ ( F @ cF___24t ) ) )
& ( G @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( F @ ciT___24t ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__rect___24a5 ) ) ) ) )
= B )
& ( E = cHList_2ehlist_2eHnil ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( c_24__lam__47646 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__47646___24a7 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_$_lam_47646_$a7') ).
thf(1362,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( c_24__lam__47646 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__47646___24a7 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( C @ happ ) )
= ( E @ ( D @ happ ) ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.map_ext') ).
thf(475,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( C @ happ ) )
= ( E @ ( D @ happ ) ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ c_24__type__72___24t ) )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ happ ) @ p ) ) ) )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( ( F @ ( D @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ happ ) @ p ) ) ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( E @ ( D @ happ ) @ p ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InA_sind') ).
thf(756,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ c_24__type__72___24t ) )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ happ ) @ p ) ) ) )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( ( F @ ( D @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ happ ) @ p ) ) ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( E @ ( D @ happ ) @ p ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(251,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C
!= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eremovelast___24a2 ) )
= ( C @ ( A @ cCoq_2eLists_2eList_2eremovelast___24a2 ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.removelast_app') ).
thf(2027,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C
!= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eremovelast___24a2 ) )
= ( C @ ( A @ cCoq_2eLists_2eList_2eremovelast___24a2 ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eLocallySorted___24a3 ) ) )
=> ( ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eLocallySorted___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.LocallySorted_ind') ).
thf(591,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eLocallySorted___24a3 ) ) )
=> ( ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eLocallySorted___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__2663___24t ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_2663') ).
thf(2451,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__2663___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__2663___24t ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5 ) ) ) ) )
<=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ! [H: $i] :
( ( B @ ( H @ t ) )
=> ! [I: $i] :
( ( B @ ( I @ t ) )
=> ( ( G @ ( F @ ( D @ happ ) @ happ ) @ p )
=> ( ( I @ ( H @ ( C @ happ ) @ happ ) @ p )
=> ( I @ ( F @ ( E @ happ ) @ happ ) @ ( G @ ( E @ happ ) @ happ ) @ ( H @ ( G @ ( E @ happ ) @ happ ) @ ( F @ ( E @ happ ) @ happ ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Lists.SetoidList.transpose_restr2') ).
thf(1828,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ! [H: $i] :
( ( B @ ( H @ t ) )
=> ! [I: $i] :
( ( B @ ( I @ t ) )
=> ( ( G @ ( F @ ( D @ happ ) @ happ ) @ p )
=> ( ( I @ ( H @ ( C @ happ ) @ happ ) @ p )
=> ( I @ ( F @ ( E @ happ ) @ happ ) @ ( G @ ( E @ happ ) @ happ ) @ ( H @ ( G @ ( E @ happ ) @ happ ) @ ( F @ ( E @ happ ) @ happ ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5 ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5 ) ) ) ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ! [H: $i] :
( ( B @ ( H @ t ) )
=> ! [I: $i] :
( ( B @ ( I @ t ) )
=> ( ( G @ ( F @ ( D @ happ ) @ happ ) @ p )
=> ( ( I @ ( H @ ( C @ happ ) @ happ ) @ p )
=> ( I @ ( F @ ( E @ happ ) @ happ ) @ ( G @ ( E @ happ ) @ happ ) @ ( H @ ( G @ ( E @ happ ) @ happ ) @ ( F @ ( E @ happ ) @ happ ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2125___24t ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ? [G: $i] :
( ? [H: $i] :
( ( F
= ( H @ ( G @ ( B @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
& ( H @ ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
& ( G @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
& ( H @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( G @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Forall2_app_inv_l') ).
thf(514,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2125___24t ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ? [G: $i] :
( ? [H: $i] :
( ( F
= ( H @ ( G @ ( B @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
& ( H @ ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
& ( G @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
& ( H @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( G @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(137,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ( D @ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.incl_app') ).
thf(1151,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ( D @ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__29599___24t ) ) ) ) )
<=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ( G @ ( F @ ( E @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_29599') ).
thf(1581,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ( G @ ( F @ ( E @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__29599___24t ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__29599___24t ) ) ) ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ( G @ ( F @ ( E @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_24505___24a3 ) ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( A @ c_24__fix__550__v__CANONICAL__1___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( ( ( C @ ( B @ ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_24505___24a3 ) ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_case_Coq.Init.Datatypes.list$505') ).
thf(905,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_24505___24a3 ) ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( A @ c_24__fix__550__v__CANONICAL__1___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( ( ( C @ ( B @ ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_24505___24a3 ) ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(316,axiom,
! [A: $i] :
( ( A @ ( c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502 @ happ ) )
= ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_$_case_Coq.Init.Datatypes.list$46502_$a1') ).
thf(2616,plain,
! [A: $i] :
( ( A @ ( c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502 @ happ ) )
= ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__19193___24t ) ) ) ) ) ) ) ) ) ) )
<=> ! [L: $i] :
( ( A @ ( L @ t ) )
=> ! [M: $i] :
( ( A @ ( M @ t ) )
=> ( M @ ( L @ ( K @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_19193') ).
thf(1946,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( ! [L: $i] :
( ( A @ ( L @ t ) )
=> ! [M: $i] :
( ( A @ ( M @ t ) )
=> ( M @ ( L @ ( K @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__19193___24t ) ) ) ) ) ) ) ) ) ) ) )
& ( ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__19193___24t ) ) ) ) ) ) ) ) ) ) )
=> ! [L: $i] :
( ( A @ ( L @ t ) )
=> ! [M: $i] :
( ( A @ ( M @ t ) )
=> ( M @ ( L @ ( K @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(184,axiom,
! [A: $i] :
( ( A @ c_24__type__122667___24t )
<=> ( c_24__type__122667 @ ( A @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_$_type_122667') ).
thf(1465,plain,
! [A: $i] :
( ( ( c_24__type__122667 @ ( A @ t ) )
=> ( A @ c_24__type__122667___24t ) )
& ( ( A @ c_24__type__122667___24t )
=> ( c_24__type__122667 @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(123,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ( ( E @ ( C @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Exists_ind') ).
thf(1040,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ( ( E @ ( C @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [C: $i] :
( ? [D: $i] :
( ( B
= ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( C @ t ) ) )
| ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Coq.Init.Datatypes.list') ).
thf(2469,plain,
! [A: $i,B: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [C: $i] :
( ? [D: $i] :
( ( B
= ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( C @ t ) ) )
| ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(120,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
<=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
| ( D @ ( C @ ( B @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InA_cons') ).
thf(1020,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
| ( D @ ( C @ ( B @ happ ) @ happ ) @ p ) )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) )
& ( ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
| ( D @ ( C @ ( B @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(275,axiom,
! [A: $i] :
( ( A @ c_24__type__2310___24t )
<=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( B @ ( D @ t ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_2310') ).
thf(2254,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( B @ ( D @ t ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ t ) ) ) ) )
=> ( A @ c_24__type__2310___24t ) )
& ( ( A @ c_24__type__2310___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( B @ ( D @ t ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(306,axiom,
! [A: $i,B: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [C: $i] :
( ? [D: $i] :
( ( ( B @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
& ( B
= ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( C @ t ) ) )
| ( ( ( B @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Lists.List.rev') ).
thf(2508,plain,
! [A: $i,B: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [C: $i] :
( ? [D: $i] :
( ( ( B @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
& ( B
= ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( C @ t ) ) )
| ( ( ( B @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2125___24t ) ) )
=> ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Forall2_nil') ).
thf(397,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2125___24t ) ) )
=> ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(174,axiom,
! [A: $i] :
( ( A @ c_24__type__33241___24t )
<=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ( B @ ( C @ ( B @ ( A @ happ ) @ happ ) @ t ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_33241') ).
thf(1377,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ( B @ ( C @ ( B @ ( A @ happ ) @ happ ) @ t ) ) ) )
=> ( A @ c_24__type__33241___24t ) )
& ( ( A @ c_24__type__33241___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ( B @ ( C @ ( B @ ( A @ happ ) @ happ ) @ t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(99,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) ) )
<=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( ( E @ ( F @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( F @ ( C @ happ ) )
= ( F @ ( D @ happ ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.map_ext_in_iff') ).
thf(877,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( ( E @ ( F @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( F @ ( C @ happ ) )
= ( F @ ( D @ happ ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) ) ) )
& ( ( ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( ( E @ ( F @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( F @ ( C @ happ ) )
= ( F @ ( D @ happ ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2125___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( B @ ( E @ t ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_2125') ).
thf(428,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( B @ ( E @ t ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( C @ ( B @ ( A @ c_24__type__2125___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__2125___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( B @ ( E @ t ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(328,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 )
!= ( C @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.app_cons_not_nil') ).
thf(2718,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 )
!= ( C @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cExtLib_2eTactics_2eInjection_2eInjective___24t ) )
<=> ( A @ cExtLib_2eTactics_2eInjection_2eInjective___24a1 @ ( B @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_ExtLib.Tactics.Injection.Injective') ).
thf(1564,plain,
! [A: $i,B: $i] :
( ( ( A @ cExtLib_2eTactics_2eInjection_2eInjective___24a1 @ ( B @ t ) )
=> ( B @ ( A @ cExtLib_2eTactics_2eInjection_2eInjective___24t ) ) )
& ( ( B @ ( A @ cExtLib_2eTactics_2eInjection_2eInjective___24t ) )
=> ( A @ cExtLib_2eTactics_2eInjection_2eInjective___24a1 @ ( B @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__120259___24t ) ) ) ) ) )
<=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ ( F @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_120259') ).
thf(2371,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i] :
( ( A @ ( G @ t ) )
=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ ( F @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__120259___24t ) ) ) ) ) ) )
& ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__120259___24t ) ) ) ) ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ ( F @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(362,axiom,
! [A: $i] :
( ( A @ c_24__type__46603___24t )
<=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_46603') ).
thf(2979,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( A @ c_24__type__46603___24t ) )
& ( ( A @ c_24__type__46603___24t )
=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(115,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ( C @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.incl_appl') ).
thf(988,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ( C @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) )
= ( F @ ( D @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
=> ( ( A = B )
& ( C = D )
& ( E = F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inj_Coq.Init.Datatypes.cons') ).
thf(2799,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) )
= ( F @ ( D @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
=> ( ( A = B )
& ( C = D )
& ( E = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ cProp___24t )
=> ( ( ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
=> ( D @ p ) )
<=> ( D @ ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__impl___24a4 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.micromega.Refl.make_conj_impl') ).
thf(452,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ cProp___24t )
=> ( ( ( D @ ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__impl___24a4 ) ) ) )
=> ( ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
=> ( D @ p ) ) )
& ( ( ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
=> ( D @ p ) )
=> ( D @ ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__impl___24a4 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__46627___24t ) ) )
<=> ( B @ ( A @ c_24__type__46627___24a2 ) @ ( C @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_$_type_46627') ).
thf(1438,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ c_24__type__46627___24a2 ) @ ( C @ t ) )
=> ( C @ ( B @ ( A @ c_24__type__46627___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__46627___24t ) ) )
=> ( B @ ( A @ c_24__type__46627___24a2 ) @ ( C @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(138,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ( ~ ( C @ ( B @ happ ) @ p )
=> ~ ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Exists_dec_subproof0') ).
thf(1153,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ( ~ ( C @ ( B @ happ ) @ p )
=> ~ ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( D @ ( E @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
<=> ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Add_in') ).
thf(810,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( D @ ( E @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) )
& ( ( D @ ( E @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(254,axiom,
! [A: $i] :
( ( A @ c_24__type__35252___24t )
<=> ! [B: $i] :
( ( B @ cProp___24t )
=> ! [C: $i] :
( ( C @ cProp___24t )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cType___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_35252') ).
thf(2047,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cProp___24t )
=> ! [C: $i] :
( ( C @ cProp___24t )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cType___24t ) ) )
=> ( A @ c_24__type__35252___24t ) )
& ( ( A @ c_24__type__35252___24t )
=> ! [B: $i] :
( ( B @ cProp___24t )
=> ! [C: $i] :
( ( C @ cProp___24t )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cType___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ ( cHList_2ehlist_2ehlist__rev_27 @ happ ) @ happ ) @ happ ) @ happ ) )
= ( D @ ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__rev_27___24a4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_HList.hlist.hlist_rev\'_$a4') ).
thf(2093,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ ( cHList_2ehlist_2ehlist__rev_27 @ happ ) @ happ ) @ happ ) @ happ ) )
= ( D @ ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__rev_27___24a4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(331,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ happ ) @ p )
=> ( ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ happ ) @ p ) ) ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( C @ ( B @ happ ) @ p ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Init.Datatypes.list_ind') ).
thf(2737,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ happ ) @ p )
=> ( ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ happ ) @ p ) ) ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( C @ ( B @ happ ) @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(319,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
| ( B @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) )
=> ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.in_or_app') ).
thf(2641,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
| ( B @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) )
=> ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(258,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
=> ( ( ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) ) )
| ( ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.app_eq_unit') ).
thf(2083,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
=> ( ( ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) ) )
| ( ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Forall_inv_tail') ).
thf(512,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(106,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForallOrdPairs___24a3 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( C @ ( E @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( D @ ( E @ ( B @ happ ) @ happ ) @ p )
| ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
| ( D = E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.ForallOrdPairs_In') ).
thf(942,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForallOrdPairs___24a3 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( C @ ( E @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( D @ ( E @ ( B @ happ ) @ happ ) @ p )
| ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
| ( D = E ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__2177___24t ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( D @ ( C @ happ ) @ p ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Forall_impl') ).
thf(534,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__2177___24t ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( D @ ( C @ happ ) @ p ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( B @ ( A @ c_24__type__126742___24t ) ) ) ) )
=> ( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( D @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
=> ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( B
= ( F @ ( E @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( C
= ( I @ ( G @ ( F @ ( E @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
& ( D
= ( J @ ( H @ ( F @ ( E @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
& ( J @ ( I @ ( F @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
& ( H @ ( G @ ( E @ ( A @ happ ) @ happ ) @ happ ) @ p )
& ( J @ ( F @ cHList_2ehlist_2ehlist___24t ) ) )
& ( I @ ( F @ cHList_2ehlist_2ehlist___24t ) ) )
& ( H @ ( E @ cF___24t ) ) )
& ( G @ ( E @ cF___24t ) ) )
& ( F @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( E @ ciT___24t ) )
| ( ( B
= ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( C = cHList_2ehlist_2eHnil )
& ( D = cHList_2ehlist_2eHnil ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_HList.hlist.equiv_hlist') ).
thf(2232,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( B @ ( A @ c_24__type__126742___24t ) ) ) ) )
=> ( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( D @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
=> ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( B
= ( F @ ( E @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( C
= ( I @ ( G @ ( F @ ( E @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
& ( D
= ( J @ ( H @ ( F @ ( E @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
& ( J @ ( I @ ( F @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
& ( H @ ( G @ ( E @ ( A @ happ ) @ happ ) @ happ ) @ p )
& ( J @ ( F @ cHList_2ehlist_2ehlist___24t ) ) )
& ( I @ ( F @ cHList_2ehlist_2ehlist___24t ) ) )
& ( H @ ( E @ cF___24t ) ) )
& ( G @ ( E @ cF___24t ) ) )
& ( F @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( E @ ciT___24t ) )
| ( ( B
= ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( C = cHList_2ehlist_2eHnil )
& ( D = cHList_2ehlist_2eHnil ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__18991___24t ) ) ) ) ) ) ) ) ) ) )
<=> ! [L: $i] :
( ( A @ ( L @ t ) )
=> ! [M: $i] :
( ( A @ ( M @ t ) )
=> ( M @ ( L @ ( K @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_18991') ).
thf(2441,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( ! [L: $i] :
( ( A @ ( L @ t ) )
=> ! [M: $i] :
( ( A @ ( M @ t ) )
=> ( M @ ( L @ ( K @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__18991___24t ) ) ) ) ) ) ) ) ) ) ) )
& ( ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__18991___24t ) ) ) ) ) ) ) ) ) ) )
=> ! [L: $i] :
( ( A @ ( L @ t ) )
=> ! [M: $i] :
( ( A @ ( M @ t ) )
=> ( M @ ( L @ ( K @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cType___24t )
=> ( ( B @ cType___24t )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [E: $i] :
( ? [F: $i] :
( ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eflat__map___24a4 ) ) ) )
= ( F @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eflat__map___24a4 ) ) ) @ ( E @ ( C @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
& ( D
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
| ( ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eflat__map___24a4 ) ) ) )
= ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( D
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Lists.List.flat_map') ).
thf(2705,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cType___24t )
=> ( ( B @ cType___24t )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [E: $i] :
( ? [F: $i] :
( ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eflat__map___24a4 ) ) ) )
= ( F @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eflat__map___24a4 ) ) ) @ ( E @ ( C @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
& ( D
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
| ( ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eflat__map___24a4 ) ) ) )
= ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( D
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__19752___24t ) ) ) ) )
<=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ( G @ ( F @ ( E @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_19752') ).
thf(1343,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ( G @ ( F @ ( E @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__19752___24t ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__19752___24t ) ) ) ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ( G @ ( F @ ( E @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(82,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) )
=> ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.lel_trans') ).
thf(778,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) )
=> ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i] :
( ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__31326___24t ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
<=> ! [S: $i] :
( ( A @ ( S @ t ) )
=> ! [T: $i] :
( ( A @ ( T @ t ) )
=> ( T @ ( S @ ( R @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_31326') ).
thf(2541,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i] :
( ( ! [S: $i] :
( ( A @ ( S @ t ) )
=> ! [T: $i] :
( ( A @ ( T @ t ) )
=> ( T @ ( S @ ( R @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__31326___24t ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__31326___24t ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ! [S: $i] :
( ( A @ ( S @ t ) )
=> ! [T: $i] :
( ( A @ ( T @ t ) )
=> ( T @ ( S @ ( R @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(278,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.incl_tl') ).
thf(2277,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
<=> ( ( D @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
& ( C @ ( B @ happ ) @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.micromega.Refl.make_conj_cons') ).
thf(862,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( ( D @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
& ( C @ ( B @ happ ) @ p ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) ) )
& ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
=> ( ( D @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
& ( C @ ( B @ happ ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__3068___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_3068') ).
thf(1570,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
=> ( C @ ( B @ ( A @ c_24__type__3068___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__3068___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(149,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( D @ ( B @ happ ) @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.micromega.Refl.make_conj_in') ).
thf(1217,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( D @ ( B @ happ ) @ p ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( ( B @ ( A @ cCoq_2eSets_2eRelations__1_2eTransitive___24a2 ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
=> ( D @ ( C @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.Sorted_extends') ).
thf(561,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( ( B @ ( A @ cCoq_2eSets_2eRelations__1_2eTransitive___24a2 ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
=> ( D @ ( C @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__33834___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cProp___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_33834') ).
thf(1487,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cProp___24t ) )
=> ( C @ ( B @ ( A @ c_24__type__33834___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__33834___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cProp___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(294,axiom,
! [A: $i] :
( ( A @ c_24__type__46666___24t )
<=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( B @ ( A @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_46666') ).
thf(2414,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( B @ ( A @ happ ) @ cType___24t ) )
=> ( A @ c_24__type__46666___24t ) )
& ( ( A @ c_24__type__46666___24t )
=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( B @ ( A @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(250,axiom,
! [A: $i] :
( ( A @ c_24__type__122667___24t )
=> ! [B: $i] :
( ( B @ c_24__type__122692___24t )
=> ( ( cHList_2ehlist_2eHnil @ ( cHList_2ehlist_2eHnil @ ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ happ ) @ happ ) @ happ ) @ p )
=> ( ! [C: $i] :
( ( C @ ciT___24t )
=> ! [D: $i] :
( ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cF___24t ) )
=> ! [F: $i] :
( ( F @ ( C @ cF___24t ) )
=> ! [G: $i] :
( ( G @ ( D @ cHList_2ehlist_2ehlist___24t ) )
=> ! [H: $i] :
( ( H @ ( D @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( F @ ( E @ ( C @ ( A @ happ ) @ happ ) @ happ ) @ p )
=> ( ( H @ ( G @ ( D @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
=> ( ( H @ ( G @ ( D @ ( B @ happ ) @ happ ) @ happ ) @ p )
=> ( H @ ( F @ ( D @ ( C @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( G @ ( E @ ( D @ ( C @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( D @ ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ happ ) @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ) )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( E @ ( D @ ( C @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
=> ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','HList.hlist.equiv_hlist_ind') ).
thf(2015,plain,
! [A: $i] :
( ( A @ c_24__type__122667___24t )
=> ! [B: $i] :
( ( B @ c_24__type__122692___24t )
=> ( ( cHList_2ehlist_2eHnil @ ( cHList_2ehlist_2eHnil @ ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ happ ) @ happ ) @ happ ) @ p )
=> ( ! [C: $i] :
( ( C @ ciT___24t )
=> ! [D: $i] :
( ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cF___24t ) )
=> ! [F: $i] :
( ( F @ ( C @ cF___24t ) )
=> ! [G: $i] :
( ( G @ ( D @ cHList_2ehlist_2ehlist___24t ) )
=> ! [H: $i] :
( ( H @ ( D @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( F @ ( E @ ( C @ ( A @ happ ) @ happ ) @ happ ) @ p )
=> ( ( H @ ( G @ ( D @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
=> ( ( H @ ( G @ ( D @ ( B @ happ ) @ happ ) @ happ ) @ p )
=> ( H @ ( F @ ( D @ ( C @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( G @ ( E @ ( D @ ( C @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( D @ ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ happ ) @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ) )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( E @ ( D @ ( C @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
=> ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(175,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cCoq_2eSets_2eRelations__1_2eTransitive___24a2 ) )
<=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( D @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ( E @ ( C @ ( B @ happ ) @ happ ) @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Sets.Relations_1.Transitive') ).
thf(1387,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( D @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ( E @ ( C @ ( B @ happ ) @ happ ) @ p ) ) ) ) ) )
=> ( B @ ( A @ cCoq_2eSets_2eRelations__1_2eTransitive___24a2 ) ) )
& ( ( B @ ( A @ cCoq_2eSets_2eRelations__1_2eTransitive___24a2 ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( D @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ( E @ ( C @ ( B @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(238,axiom,
! [A: $i] :
( ( A @ c_24__type__3185___24t )
<=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_3185') ).
thf(1900,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ cProp___24t ) ) ) )
=> ( A @ c_24__type__3185___24t ) )
& ( ( A @ c_24__type__3185___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ cProp___24t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(360,axiom,
! [A: $i] :
( ( A @ ciT___24t )
=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) )
=> ( C
= ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__tl___24a3 ) ) @ ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__hd___24a3 ) ) @ ( B @ ( A @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','HList.hlist.hlist_cons_eta') ).
thf(2958,plain,
! [A: $i] :
( ( A @ ciT___24t )
=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) )
=> ( C
= ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__tl___24a3 ) ) @ ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__hd___24a3 ) ) @ ( B @ ( A @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__1966___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( E @ ( B @ happ ) @ ( F @ t ) )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ happ ) @ ( F @ ( E @ ( D @ ( C @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_1966') ).
thf(1365,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( E @ ( B @ happ ) @ ( F @ t ) )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ happ ) @ ( F @ ( E @ ( D @ ( C @ happ ) @ happ ) @ happ ) @ t ) ) ) ) )
=> ( C @ ( B @ ( A @ c_24__type__1966___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__1966___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( E @ ( B @ happ ) @ ( F @ t ) )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ happ ) @ ( F @ ( E @ ( D @ ( C @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(297,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) )
=> ( E @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.lel_cons_cons') ).
thf(2433,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) )
=> ( E @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(245,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ? [E: $i] :
( ? [F: $i] :
( ( D
= ( F @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
& ( C
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Add_split') ).
thf(1968,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ? [E: $i] :
( ? [F: $i] :
( ( D
= ( F @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
& ( C
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(183,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( C
= ( G @ ( F @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
& ( F @ ( D @ ( B @ happ ) @ happ ) @ p )
& ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( F @ t ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InA_split') ).
thf(1457,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( C
= ( G @ ( F @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
& ( F @ ( D @ ( B @ happ ) @ happ ) @ p )
& ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( F @ t ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(22,axiom,
~ ( c_24False @ p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_COQ_FALSE') ).
thf(461,plain,
~ ( c_24False @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(366,axiom,
! [A: $i] :
( ( A @ c_24__type__48237___24t )
<=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ ( B @ ( ciT @ cCoq_2eLists_2eList_2erev___24a2 ) @ cHList_2ehlist_2ehlist___24t ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_48237') ).
thf(3028,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ ( B @ ( ciT @ cCoq_2eLists_2eList_2erev___24a2 ) @ cHList_2ehlist_2ehlist___24t ) ) ) )
=> ( A @ c_24__type__48237___24t ) )
& ( ( A @ c_24__type__48237___24t )
=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ ( B @ ( ciT @ cCoq_2eLists_2eList_2erev___24a2 ) @ cHList_2ehlist_2ehlist___24t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(146,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2125___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__17419___24t ) ) )
=> ( ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ happ ) @ happ ) @ p )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( B @ ( F @ t ) )
=> ! [G: $i] :
( ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [H: $i] :
( ( H @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( C @ happ ) @ happ ) @ p )
=> ( ( H @ ( G @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ( ( H @ ( G @ ( D @ happ ) @ happ ) @ p )
=> ( H @ ( F @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ happ ) @ happ ) @ p ) ) ) ) ) ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Forall2_sind') ).
thf(1195,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2125___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__17419___24t ) ) )
=> ( ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ happ ) @ happ ) @ p )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( B @ ( F @ t ) )
=> ! [G: $i] :
( ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [H: $i] :
( ( H @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( C @ happ ) @ happ ) @ p )
=> ( ( H @ ( G @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ( ( H @ ( G @ ( D @ happ ) @ happ ) @ p )
=> ( H @ ( F @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ happ ) @ happ ) @ p ) ) ) ) ) ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(90,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( B @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.incl_refl') ).
thf(842,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( B @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(336,axiom,
! [A: $i] :
( ( A @ c_24__type__46547___24t )
<=> ( c_24__type__46547 @ ( A @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_$_type_46547') ).
thf(2769,plain,
! [A: $i] :
( ( ( c_24__type__46547 @ ( A @ t ) )
=> ( A @ c_24__type__46547___24t ) )
& ( ( A @ c_24__type__46547___24t )
=> ( c_24__type__46547 @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ~ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.NoDup_remove_2') ).
thf(852,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ~ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cHList_2ehlist_2ehlist__app @ happ ) @ happ ) @ happ ) )
= ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__app___24a3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_HList.hlist.hlist_app_$a3') ).
thf(2663,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cHList_2ehlist_2ehlist__app @ happ ) @ happ ) @ happ ) )
= ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__app___24a3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eLocallySorted___24a3 ) ) )
=> ( ( D @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eLocallySorted___24a3 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.LSorted_consn') ).
thf(583,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eLocallySorted___24a3 ) ) )
=> ( ( D @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eLocallySorted___24a3 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ~ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Exists_dec_subproof') ).
thf(522,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ~ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__3945___24t ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_3945') ).
thf(1762,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__3945___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__3945___24t ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__prop__126659___24a7 ) ) ) ) ) ) @ p )
<=> ( ( ( G @ ( F @ ( C @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
& ( E @ ( D @ ( B @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p ) )
=> ( G @ ( E @ ( C @ ( B @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( F @ ( D @ ( C @ ( B @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_prop_126659') ).
thf(1534,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( ( G @ ( F @ ( C @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
& ( E @ ( D @ ( B @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p ) )
=> ( G @ ( E @ ( C @ ( B @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( F @ ( D @ ( C @ ( B @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p ) )
=> ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__prop__126659___24a7 ) ) ) ) ) ) @ p ) )
& ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__prop__126659___24a7 ) ) ) ) ) ) @ p )
=> ( ( ( G @ ( F @ ( C @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
& ( E @ ( D @ ( B @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p ) )
=> ( G @ ( E @ ( C @ ( B @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( F @ ( D @ ( C @ ( B @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ( ( E @ ( C @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Exists_sind') ).
thf(615,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ( ( E @ ( C @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(151,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
<=> ( D @ ( C @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InA_altdef') ).
thf(1227,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( D @ ( C @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( D @ ( C @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__120240___24t ) ) ) ) ) )
<=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ ( F @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_120240') ).
thf(1856,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i] :
( ( A @ ( G @ t ) )
=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ ( F @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__120240___24t ) ) ) ) ) ) )
& ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__120240___24t ) ) ) ) ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ ( F @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(117,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__2434___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [G: $i] :
( ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ( ( G @ ( F @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( ( G @ ( F @ ( C @ happ ) @ happ ) @ p )
=> ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.eqlistA_sind') ).
thf(1006,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__2434___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [G: $i] :
( ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ( ( G @ ( F @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( ( G @ ( F @ ( C @ happ ) @ happ ) @ p )
=> ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.NoDupA_nil') ).
thf(499,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(161,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( B @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.rev_involutive') ).
thf(1270,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( B @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(222,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
<=> ( ~ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( B != C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.not_in_cons') ).
thf(1772,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( ~ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( B != C ) )
=> ~ ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) )
& ( ~ ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ~ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( B != C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i,S: $i,T: $i,U: $i,V: $i,W: $i] :
( ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__40707___24t ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
<=> ! [X: $i] :
( ( A @ ( X @ t ) )
=> ! [Y: $i] :
( ( A @ ( Y @ t ) )
=> ( Y @ ( X @ ( W @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_40707') ).
thf(2577,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i,O: $i,P: $i,Q: $i,R: $i,S: $i,T: $i,U: $i,V: $i,W: $i] :
( ( ! [X: $i] :
( ( A @ ( X @ t ) )
=> ! [Y: $i] :
( ( A @ ( Y @ t ) )
=> ( Y @ ( X @ ( W @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__40707___24t ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( W @ ( V @ ( U @ ( T @ ( S @ ( R @ ( Q @ ( P @ ( O @ ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__40707___24t ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ! [X: $i] :
( ( A @ ( X @ t ) )
=> ! [Y: $i] :
( ( A @ ( Y @ t ) )
=> ( Y @ ( X @ ( W @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(125,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( B @ ( B @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.lel_refl') ).
thf(1064,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( B @ ( B @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(114,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ happ ) @ p )
=> ( ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( D @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ happ ) @ p ) ) ) ) ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( C @ ( B @ happ ) @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.NoDup_ind') ).
thf(980,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ happ ) @ p )
=> ( ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( D @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ happ ) @ p ) ) ) ) ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( C @ ( B @ happ ) @ p ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__2177___24t ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( D @ ( C @ happ ) @ p ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Exists_impl') ).
thf(403,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__2177___24t ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( D @ ( C @ happ ) @ p ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(326,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__6875___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( D = B )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_6875') ).
thf(2692,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( D = B )
=> ( D @ ( C @ happ ) @ cType___24t ) ) )
=> ( C @ ( B @ ( A @ c_24__type__6875___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__6875___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( D = B )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5 ) ) ) ) )
<=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ! [H: $i] :
( ( B @ ( H @ t ) )
=> ( ( G @ ( F @ ( D @ happ ) @ happ ) @ p )
=> ( H @ ( F @ ( E @ happ ) @ happ ) @ ( G @ ( E @ happ ) @ happ ) @ ( H @ ( G @ ( E @ happ ) @ happ ) @ ( F @ ( E @ happ ) @ happ ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Lists.SetoidList.transpose_restr') ).
thf(1498,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ! [H: $i] :
( ( B @ ( H @ t ) )
=> ( ( G @ ( F @ ( D @ happ ) @ happ ) @ p )
=> ( H @ ( F @ ( E @ happ ) @ happ ) @ ( G @ ( E @ happ ) @ happ ) @ ( H @ ( G @ ( E @ happ ) @ happ ) @ ( F @ ( E @ happ ) @ happ ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5 ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5 ) ) ) ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ! [H: $i] :
( ( B @ ( H @ t ) )
=> ( ( G @ ( F @ ( D @ happ ) @ happ ) @ p )
=> ( H @ ( F @ ( E @ happ ) @ happ ) @ ( G @ ( E @ happ ) @ happ ) @ ( H @ ( G @ ( E @ happ ) @ happ ) @ ( F @ ( E @ happ ) @ happ ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cHList_2ehlist_2ehlist__tl @ happ ) @ happ ) @ happ ) )
= ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__tl___24a3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_HList.hlist.hlist_tl_$a3') ).
thf(2638,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cHList_2ehlist_2ehlist__tl @ happ ) @ happ ) @ happ ) )
= ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__tl___24a3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2125___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( F @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ? [G: $i] :
( ? [H: $i] :
( ( F
= ( H @ ( G @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
& ( E @ ( H @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
& ( D @ ( G @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
& ( H @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Forall2_app_inv_r') ).
thf(420,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2125___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( F @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ? [G: $i] :
( ? [H: $i] :
( ( F
= ( H @ ( G @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
& ( E @ ( H @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
& ( D @ ( G @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
& ( H @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(349,axiom,
! [A: $i] :
( ( A @ c_24__type__122667___24t )
=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ciT___24t )
=> ! [D: $i] :
( ( D @ ( C @ cF___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cF___24t ) )
=> ! [F: $i] :
( ( F @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ! [G: $i] :
( ( G @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( G @ ( E @ ( B @ ( C @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( F @ ( D @ ( B @ ( C @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( B @ ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
=> ( ( G @ ( F @ ( B @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
& ( E @ ( D @ ( C @ ( A @ happ ) @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','HList.hlist.equiv_hlist_Hcons') ).
thf(2877,plain,
! [A: $i] :
( ( A @ c_24__type__122667___24t )
=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ciT___24t )
=> ! [D: $i] :
( ( D @ ( C @ cF___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cF___24t ) )
=> ! [F: $i] :
( ( F @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ! [G: $i] :
( ( G @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( G @ ( E @ ( B @ ( C @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( F @ ( D @ ( B @ ( C @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( B @ ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
=> ( ( G @ ( F @ ( B @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
& ( E @ ( D @ ( C @ ( A @ happ ) @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(165,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.app_assoc_reverse') ).
thf(1292,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( C @ ( B @ happ ) @ p ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Forall_inv') ).
thf(526,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( C @ ( B @ happ ) @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
<=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InA_double_head') ).
thf(637,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) )
& ( ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(323,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) )
= ( B @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( C @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.rev_app_distr') ).
thf(2666,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) )
= ( B @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( C @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(177,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.app_nil_l') ).
thf(1419,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
<=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( C @ ( B @ happ ) @ cProp___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_2177') ).
thf(489,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( C @ ( B @ happ ) @ cProp___24t ) )
=> ( B @ ( A @ c_24__type__2177___24t ) ) )
& ( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( C @ ( B @ happ ) @ cProp___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(315,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= ( D @ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.app_assoc') ).
thf(2613,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= ( D @ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2ehd___24a3 ) ) )
= D )
& ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2ehd___24a3 ) ) )
= B )
& ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Lists.List.hd') ).
thf(2551,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2ehd___24a3 ) ) )
= D )
& ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2ehd___24a3 ) ) )
= B )
& ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(118,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( C @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.NoDup_cons') ).
thf(1016,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( C @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(139,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( B @ ( E @ t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) @ ( E @ ( B @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
<=> ? [F: $i] :
( ( D @ ( F @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( ( F @ ( C @ happ ) )
= E )
& ( A @ ( F @ t ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.in_map_iff') ).
thf(1155,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( B @ ( E @ t ) )
=> ( ( ? [F: $i] :
( ( D @ ( F @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( ( F @ ( C @ happ ) )
= E )
& ( A @ ( F @ t ) ) )
=> ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) @ ( E @ ( B @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) )
& ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) @ ( E @ ( B @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ? [F: $i] :
( ( D @ ( F @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( ( F @ ( C @ happ ) )
= E )
& ( A @ ( F @ t ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(46,axiom,
cHList_2ehlist_2ehlist__rect @ c_24__type__46580___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_HList.hlist.hlist_rect') ).
thf(547,plain,
cHList_2ehlist_2ehlist__rect @ c_24__type__46580___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(218,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) )
=> ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.lel_cons') ).
thf(1744,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) )
=> ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
<=> ( c_24False @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InA_nil') ).
thf(393,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( ( ( c_24False @ p )
=> ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) )
& ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( c_24False @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( ( B @ ( A @ cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2 ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ( ( C @ ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InfA_ltA') ).
thf(647,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( ( B @ ( A @ cCoq_2eClasses_2eRelationClasses_2eStrictOrder___24a2 ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ( ( C @ ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(193,axiom,
! [A: $i] :
( ( A @ cProp___24t )
=> ! [B: $i] :
( ( B @ cProp___24t )
=> ( ~ ( ( B @ p )
| ( A @ p ) )
=> ( ~ ( B @ p )
& ~ ( A @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Logic.Decidable.not_or') ).
thf(1530,plain,
! [A: $i] :
( ( A @ cProp___24t )
=> ! [B: $i] :
( ( B @ cProp___24t )
=> ( ~ ( ( B @ p )
| ( A @ p ) )
=> ( ~ ( B @ p )
& ~ ( A @ p ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(152,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
<=> ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InA_permute_heads') ).
thf(1231,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) )
& ( ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(196,axiom,
! [A: $i] :
( ( A @ c_24__type__87___24t )
<=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_87') ).
thf(1552,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) )
=> ( A @ c_24__type__87___24t ) )
& ( ( A @ c_24__type__87___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( ( B @ ( A @ cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2 ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( ( F @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( E @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.eqlistA_app') ).
thf(457,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( ( B @ ( A @ cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2 ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( ( F @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( E @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(341,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__33790___24t ) )
<=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ happ ) @ happ ) @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_33790') ).
thf(2813,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ happ ) @ happ ) @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) )
=> ( B @ ( A @ c_24__type__33790___24t ) ) )
& ( ( B @ ( A @ c_24__type__33790___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ happ ) @ happ ) @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(348,axiom,
! [A: $i,B: $i] :
( ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( B @ ( A @ cHList_2ehlist_2ehlist___24t ) )
=> ( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( B
= ( F @ ( E @ ( D @ ( C @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
& ( A
= ( D @ ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( F @ ( D @ cHList_2ehlist_2ehlist___24t ) ) )
& ( E @ ( C @ cF___24t ) ) )
& ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( C @ ciT___24t ) )
| ( ( B = cHList_2ehlist_2eHnil )
& ( A
= ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_HList.hlist.hlist') ).
thf(2862,plain,
! [A: $i,B: $i] :
( ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( B @ ( A @ cHList_2ehlist_2ehlist___24t ) )
=> ( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( B
= ( F @ ( E @ ( D @ ( C @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
& ( A
= ( D @ ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( F @ ( D @ cHList_2ehlist_2ehlist___24t ) ) )
& ( E @ ( C @ cF___24t ) ) )
& ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( C @ ciT___24t ) )
| ( ( B = cHList_2ehlist_2eHnil )
& ( A
= ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__19092___24t ) ) ) ) ) ) ) ) ) ) )
<=> ! [L: $i] :
( ( A @ ( L @ t ) )
=> ! [M: $i] :
( ( A @ ( M @ t ) )
=> ( M @ ( L @ ( K @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_19092') ).
thf(1241,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( ! [L: $i] :
( ( A @ ( L @ t ) )
=> ! [M: $i] :
( ( A @ ( M @ t ) )
=> ( M @ ( L @ ( K @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__19092___24t ) ) ) ) ) ) ) ) ) ) ) )
& ( ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__19092___24t ) ) ) ) ) ) ) ) ) ) )
=> ! [L: $i] :
( ( A @ ( L @ t ) )
=> ! [M: $i] :
( ( A @ ( M @ t ) )
=> ( M @ ( L @ ( K @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( ( B @ ( A @ cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2 ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
=> ( C @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.NoDupA_rev') ).
thf(541,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( ( B @ ( A @ cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2 ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
=> ( C @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(67,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( ( B @ ( A @ cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2 ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( C @ ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.In_InA') ).
thf(657,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( ( B @ ( A @ cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2 ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( C @ ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) )
=> ( E @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Relations.Relation_Operators.Lt_tl') ).
thf(558,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) )
=> ( E @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( B @ ( A @ c_24__type__1926___24t ) ) )
=> ( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [F: $i] :
( ? [G: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist__rect___24a5 ) ) ) ) )
= ( G @ ( D @ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist__rect___24a5 ) ) ) ) @ ( G @ ( F @ ( D @ happ ) @ happ ) @ happ ) ) )
& ( E
= ( G @ ( F @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( F @ t ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist__rect___24a5 ) ) ) ) )
= C )
& ( E
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Init.Datatypes.list_rect') ).
thf(1515,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( B @ ( A @ c_24__type__1926___24t ) ) )
=> ( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [F: $i] :
( ? [G: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist__rect___24a5 ) ) ) ) )
= ( G @ ( D @ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist__rect___24a5 ) ) ) ) @ ( G @ ( F @ ( D @ happ ) @ happ ) @ happ ) ) )
& ( E
= ( G @ ( F @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( F @ t ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist__rect___24a5 ) ) ) ) )
= C )
& ( E
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(141,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( C @ ( E @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( E @ ( D @ ( B @ happ ) @ happ ) @ p ) ) )
=> ( C @ ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.In_InfA') ).
thf(1167,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( C @ ( E @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( E @ ( D @ ( B @ happ ) @ happ ) @ p ) ) )
=> ( C @ ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__33408___24t ) ) ) ) ) ) ) )
<=> ! [I: $i] :
( ( A @ ( I @ t ) )
=> ! [J: $i] :
( ( A @ ( J @ t ) )
=> ( J @ ( I @ ( H @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_33408') ).
thf(2645,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i] :
( ( A @ ( I @ t ) )
=> ! [J: $i] :
( ( A @ ( J @ t ) )
=> ( J @ ( I @ ( H @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__33408___24t ) ) ) ) ) ) ) ) )
& ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__33408___24t ) ) ) ) ) ) ) )
=> ! [I: $i] :
( ( A @ ( I @ t ) )
=> ! [J: $i] :
( ( A @ ( J @ t ) )
=> ( J @ ( I @ ( H @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ( ( C = D )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( C @ happ ) )
= ( E @ ( D @ happ ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Logic.FunctionalExtensionality.equal_f') ).
thf(530,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ( ( C = D )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( C @ happ ) )
= ( E @ ( D @ happ ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(84,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ happ ) @ p )
=> ( ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( D @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ happ ) @ p ) ) ) ) ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( C @ ( B @ happ ) @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.NoDup_sind') ).
thf(794,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ happ ) @ p )
=> ( ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( D @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ happ ) @ p ) ) ) ) ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( C @ ( B @ happ ) @ p ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__2118___24t ) ) ) ) ) )
<=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ! [H: $i] :
( ( B @ ( H @ t ) )
=> ( H @ ( G @ ( F @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_2118') ).
thf(2057,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i] :
( ( A @ ( G @ t ) )
=> ! [H: $i] :
( ( B @ ( H @ t ) )
=> ( H @ ( G @ ( F @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__2118___24t ) ) ) ) ) ) )
& ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__2118___24t ) ) ) ) ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ! [H: $i] :
( ( B @ ( H @ t ) )
=> ( H @ ( G @ ( F @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__32967___24t ) ) ) ) ) ) ) )
<=> ! [I: $i] :
( ( A @ ( I @ t ) )
=> ! [J: $i] :
( ( A @ ( J @ t ) )
=> ( J @ ( I @ ( H @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_32967') ).
thf(1846,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i] :
( ( A @ ( I @ t ) )
=> ! [J: $i] :
( ( A @ ( J @ t ) )
=> ( J @ ( I @ ( H @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__32967___24t ) ) ) ) ) ) ) ) )
& ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__32967___24t ) ) ) ) ) ) ) )
=> ! [I: $i] :
( ( A @ ( I @ t ) )
=> ! [J: $i] :
( ( A @ ( J @ t ) )
=> ( J @ ( I @ ( H @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(339,axiom,
! [A: $i] :
( ( A @ c_24__type__126706___24t )
<=> ( c_24__type__126706 @ ( A @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_$_type_126706') ).
thf(2793,plain,
! [A: $i] :
( ( ( c_24__type__126706 @ ( A @ t ) )
=> ( A @ c_24__type__126706___24t ) )
& ( ( A @ c_24__type__126706___24t )
=> ( c_24__type__126706 @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__lam__2046___24a4 ) ) ) )
<=> ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_lam_2046') ).
thf(1663,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__lam__2046___24a4 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__lam__2046___24a4 ) ) ) )
=> ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(266,axiom,
! [A: $i] :
( ( A @ c_24__type__46515___24t )
<=> ! [B: $i] :
( ( B @ ciT___24t )
=> ( B @ ( A @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_46515') ).
thf(2144,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ ciT___24t )
=> ( B @ ( A @ happ ) @ cType___24t ) )
=> ( A @ c_24__type__46515___24t ) )
& ( ( A @ c_24__type__46515___24t )
=> ! [B: $i] :
( ( B @ ciT___24t )
=> ( B @ ( A @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(110,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
=> ( ( E @ ( C @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.NoDupA_ind') ).
thf(965,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
=> ( ( E @ ( C @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(157,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
| ( B = C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.in_inv') ).
thf(1251,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
| ( B = C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(150,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( ( E @ ( F @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( F @ ( C @ happ ) )
= ( F @ ( D @ happ ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.map_ext_in') ).
thf(1219,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( ( E @ ( F @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( F @ ( C @ happ ) )
= ( F @ ( D @ happ ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(162,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
=> ( ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.app_eq_nil') ).
thf(1273,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
=> ( ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(371,axiom,
! [A: $i] :
( ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [B: $i] :
( ? [C: $i] :
( ( ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a1 )
= ( C @ ( B @ c_24__lam__46514___24a2 ) ) )
& ( A
= ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( B @ ciT___24t ) )
| ( ( ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a1 )
= c_24__lam__46511 )
& ( A
= ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_case_Coq.Init.Datatypes.list$46502') ).
thf(3079,plain,
! [A: $i] :
( ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [B: $i] :
( ? [C: $i] :
( ( ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a1 )
= ( C @ ( B @ c_24__lam__46514___24a2 ) ) )
& ( A
= ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( B @ ciT___24t ) )
| ( ( ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a1 )
= c_24__lam__46511 )
& ( A
= ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(330,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) )
= ( C @ ( B @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.app_comm_cons') ).
thf(2734,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) )
= ( C @ ( B @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( B @ ( D @ ( C @ happ ) @ t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_2361') ).
thf(444,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( B @ ( D @ ( C @ happ ) @ t ) ) )
=> ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( B @ ( D @ ( C @ happ ) @ t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2211___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_2211') ).
thf(1631,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) )
=> ( C @ ( B @ ( A @ c_24__type__2211___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__2211___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__48310___24a7 ) ) ) ) ) ) )
= ( G @ ( E @ ( B @ ( C @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( F @ ( B @ ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ cHList_2ehlist_2ehlist__rev_27___24a4 ) ) ) @ c_24__generic__case__48326___24a1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_lam_48310') ).
thf(2936,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__48310___24a7 ) ) ) ) ) ) )
= ( G @ ( E @ ( B @ ( C @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( F @ ( B @ ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ cHList_2ehlist_2ehlist__rev_27___24a4 ) ) ) @ c_24__generic__case__48326___24a1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ happ ) @ p )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Forall_cons') ).
thf(412,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ happ ) @ p )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(112,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2125___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( B @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [G: $i] :
( ( G @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( C @ happ ) @ happ ) @ p )
=> ( ( G @ ( F @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ( G @ ( E @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Forall2_cons') ).
thf(975,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2125___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( B @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [G: $i] :
( ( G @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( C @ happ ) @ happ ) @ p )
=> ( ( G @ ( F @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ( G @ ( E @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( ( B @ ( A @ cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2 ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__646___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( ( D @ ( F @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( F @ ( E @ ( C @ happ ) @ happ ) @ p ) ) )
=> ( D @ ( E @ ( C @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InA_InfA') ).
thf(732,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( ( B @ ( A @ cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2 ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__646___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( ( D @ ( F @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( F @ ( E @ ( C @ happ ) @ happ ) @ p ) ) )
=> ( D @ ( E @ ( C @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [C: $i] :
( ? [D: $i] :
( ( ( B @ ( A @ cCoq_2eLists_2eList_2etl___24a2 ) )
= D )
& ( B
= ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( C @ t ) ) )
| ( ( ( B @ ( A @ cCoq_2eLists_2eList_2etl___24a2 ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Lists.List.tl') ).
thf(1615,plain,
! [A: $i,B: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [C: $i] :
( ? [D: $i] :
( ( ( B @ ( A @ cCoq_2eLists_2eList_2etl___24a2 ) )
= D )
& ( B
= ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( C @ t ) ) )
| ( ( ( B @ ( A @ cCoq_2eLists_2eList_2etl___24a2 ) )
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(176,axiom,
! [A: $i] :
( ( A @ c_24__type__46580___24t )
<=> ! [B: $i] :
( ( B @ c_24__type__46583___24t )
=> ! [C: $i] :
( ( cHList_2ehlist_2eHnil @ ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ happ ) @ happ ) @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( B @ c_24__type__46600___24t ) )
=> ! [E: $i] :
( ( E @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( E @ cHList_2ehlist_2ehlist___24t ) )
=> ( F @ ( E @ ( B @ happ ) @ happ ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_46580') ).
thf(1403,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ c_24__type__46583___24t )
=> ! [C: $i] :
( ( cHList_2ehlist_2eHnil @ ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ happ ) @ happ ) @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( B @ c_24__type__46600___24t ) )
=> ! [E: $i] :
( ( E @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( E @ cHList_2ehlist_2ehlist___24t ) )
=> ( F @ ( E @ ( B @ happ ) @ happ ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ) )
=> ( A @ c_24__type__46580___24t ) )
& ( ( A @ c_24__type__46580___24t )
=> ! [B: $i] :
( ( B @ c_24__type__46583___24t )
=> ! [C: $i] :
( ( cHList_2ehlist_2eHnil @ ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ happ ) @ happ ) @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( B @ c_24__type__46600___24t ) )
=> ! [E: $i] :
( ( E @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( E @ cHList_2ehlist_2ehlist___24t ) )
=> ( F @ ( E @ ( B @ happ ) @ happ ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( C @ ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( ( D @ ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InfA_app') ).
thf(545,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( C @ ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( ( D @ ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(98,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InA_cons_hd') ).
thf(875,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
<=> ? [D: $i] :
( ( D @ ( B @ happ ) @ p )
& ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( A @ ( D @ t ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Exists_exists') ).
thf(577,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ? [D: $i] :
( ( D @ ( B @ happ ) @ p )
& ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( A @ ( D @ t ) ) )
=> ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) ) )
& ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ? [D: $i] :
( ( D @ ( B @ happ ) @ p )
& ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( A @ ( D @ t ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__2511___24t ) ) ) ) )
<=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ( G @ ( F @ ( E @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_2511') ).
thf(1795,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ( G @ ( F @ ( E @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__2511___24t ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__2511___24t ) ) ) ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ( G @ ( F @ ( E @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(214,axiom,
! [A: $i] :
( ( A @ c_24__type__64___24t )
<=> ! [B: $i] :
( ( B @ cType___24t )
=> ( B @ ( A @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_64') ).
thf(1701,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cType___24t )
=> ( B @ ( A @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
=> ( A @ c_24__type__64___24t ) )
& ( ( A @ c_24__type__64___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ( B @ ( A @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(292,axiom,
! [A: $i] :
( ( A @ c_24__type__46603___24t )
<=> ( c_24__type__46603 @ ( A @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_$_type_46603') ).
thf(2398,plain,
! [A: $i] :
( ( ( c_24__type__46603 @ ( A @ t ) )
=> ( A @ c_24__type__46603___24t ) )
& ( ( A @ c_24__type__46603___24t )
=> ( c_24__type__46603 @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( ~ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.NoDup_remove') ).
thf(641,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( ~ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(370,axiom,
! [A: $i] :
( ( A @ c_24__type__122667___24t )
=> ! [B: $i] :
( ( B @ ciT___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cF___24t ) )
=> ! [E: $i] :
( ( E @ ( B @ cF___24t ) )
=> ! [F: $i] :
( ( F @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ! [G: $i] :
( ( G @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( E @ ( D @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ p )
=> ( ( G @ ( F @ ( C @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
=> ( G @ ( E @ ( C @ ( B @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( F @ ( D @ ( C @ ( B @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','HList.hlist.hlist_eqv_cons') ).
thf(3077,plain,
! [A: $i] :
( ( A @ c_24__type__122667___24t )
=> ! [B: $i] :
( ( B @ ciT___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cF___24t ) )
=> ! [E: $i] :
( ( E @ ( B @ cF___24t ) )
=> ! [F: $i] :
( ( F @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ! [G: $i] :
( ( G @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( E @ ( D @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ p )
=> ( ( G @ ( F @ ( C @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
=> ( G @ ( E @ ( C @ ( B @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( F @ ( D @ ( C @ ( B @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(155,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eForallOrdPairs___24a3 ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eForallOrdPairs___24a3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.FOP_cons') ).
thf(1239,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eForallOrdPairs___24a3 ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eForallOrdPairs___24a3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(130,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.incl_appr') ).
thf(1092,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(237,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.app_inv_head') ).
thf(1897,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__1926___24t ) ) )
<=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_1926') ).
thf(2425,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) )
=> ( C @ ( B @ ( A @ c_24__type__1926___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__1926___24t ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(372,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( cHList_2ehlist_2eHnil
!= ( D @ ( C @ ( B @ ( A @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_discrim_HList.hlist.Hnil$HList.hlist.Hcons') ).
thf(3091,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( cHList_2ehlist_2eHnil
!= ( D @ ( C @ ( B @ ( A @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( c_24__lam__48310 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__48310___24a6 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_$_lam_48310_$a6') ).
thf(2319,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( c_24__lam__48310 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__48310___24a6 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.Sorted_cons') ).
thf(391,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(135,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ happ ) @ p )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ happ ) @ p ) ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( E @ ( D @ happ ) @ p ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.HdRel_sind') ).
thf(1139,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ happ ) @ p )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ happ ) @ p ) ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( E @ ( D @ happ ) @ p ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(307,axiom,
! [A: $i] :
( ( A @ c_24__type__46583___24t )
<=> ( c_24__type__46583 @ ( A @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_$_type_46583') ).
thf(2521,plain,
! [A: $i] :
( ( ( c_24__type__46583 @ ( A @ t ) )
=> ( A @ c_24__type__46583___24t ) )
& ( ( A @ c_24__type__46583___24t )
=> ( c_24__type__46583 @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__17185___24t ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( B @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ ( F @ ( E @ ( D @ happ ) @ happ ) @ t ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_17185') ).
thf(2478,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( B @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ ( F @ ( E @ ( D @ happ ) @ happ ) @ t ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__17185___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__17185___24t ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( B @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ ( F @ ( E @ ( D @ happ ) @ happ ) @ t ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
<=> ( ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
| ( D = B ) ) )
& ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
<=> ( c_24False @ p ) )
& ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Lists.List.In') ).
thf(990,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( ( ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
| ( D = B ) )
=> ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) )
& ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
| ( D = B ) ) )
& ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( ( ( c_24False @ p )
=> ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) )
& ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( c_24False @ p ) )
& ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(375,axiom,
! [A: $i] :
( ( A @ c_24__type__47653___24t )
<=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_47653') ).
thf(3106,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) ) ) ) ) )
=> ( A @ c_24__type__47653___24t ) )
& ( ( A @ c_24__type__47653___24t )
=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ cType___24t )
=> ( ( B @ cType___24t )
=> ( ( E @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [F: $i] :
( ? [G: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2efold__right___24a5 ) ) ) ) )
= ( G @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2efold__right___24a5 ) ) ) ) @ ( F @ ( C @ happ ) @ happ ) ) )
& ( E
= ( G @ ( F @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( G @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( B @ ( F @ t ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2efold__right___24a5 ) ) ) ) )
= D )
& ( E
= ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Lists.List.fold_right') ).
thf(2669,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ cType___24t )
=> ( ( B @ cType___24t )
=> ( ( E @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [F: $i] :
( ? [G: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2efold__right___24a5 ) ) ) ) )
= ( G @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2efold__right___24a5 ) ) ) ) @ ( F @ ( C @ happ ) @ happ ) ) )
& ( E
= ( G @ ( F @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( G @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( B @ ( F @ t ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2efold__right___24a5 ) ) ) ) )
= D )
& ( E
= ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(343,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','HList.app_ass_trans') ).
thf(2839,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( D @ ( C @ ( B @ happ ) @ happ ) @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.HdRel_inv') ).
thf(737,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( D @ ( C @ ( B @ happ ) @ happ ) @ p ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( D @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Relations.Relation_Operators.Lt_hd') ).
thf(649,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( D @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(167,axiom,
! [A: $i] :
( ( A @ c_24__type__15450___24t )
<=> ! [B: $i] :
( ( B @ cProp___24t )
=> ( B @ ( A @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_15450') ).
thf(1307,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cProp___24t )
=> ( B @ ( A @ happ ) @ cType___24t ) )
=> ( A @ c_24__type__15450___24t ) )
& ( ( A @ c_24__type__15450___24t )
=> ! [B: $i] :
( ( B @ cProp___24t )
=> ( B @ ( A @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(148,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p )
=> ( ( E @ ( C @ happ ) @ p )
=> ( ( E @ ( D @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.StronglySorted_sind') ).
thf(1209,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p )
=> ( ( E @ ( C @ happ ) @ p )
=> ( ( E @ ( D @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ cType___24t )
=> ( ( B @ cType___24t )
=> ( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [F: $i] :
( ? [G: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2efold__left___24a5 ) ) ) ) )
= ( F @ ( E @ ( C @ happ ) @ happ ) @ ( G @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2efold__left___24a5 ) ) ) ) ) )
& ( D
= ( G @ ( F @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( G @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( B @ ( F @ t ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2efold__left___24a5 ) ) ) ) )
= E )
& ( D
= ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Lists.List.fold_left') ).
thf(2721,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ cType___24t )
=> ( ( B @ cType___24t )
=> ( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [F: $i] :
( ? [G: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2efold__left___24a5 ) ) ) ) )
= ( F @ ( E @ ( C @ happ ) @ happ ) @ ( G @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2efold__left___24a5 ) ) ) ) ) )
& ( D
= ( G @ ( F @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( G @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( B @ ( F @ t ) ) )
| ( ( ( E @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2efold__left___24a5 ) ) ) ) )
= E )
& ( D
= ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(367,axiom,
! [A: $i] :
( ( A @ c_24__type__46686___24t )
<=> ! [B: $i] :
( ( B @ ciT___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cF___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_46686') ).
thf(3038,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ ciT___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cF___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) ) ) ) ) )
=> ( A @ c_24__type__46686___24t ) )
& ( ( A @ c_24__type__46686___24t )
=> ! [B: $i] :
( ( B @ ciT___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cF___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cHList_2ehlist_2ehlist__hd @ happ ) @ happ ) @ happ ) )
= ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__hd___24a3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_HList.hlist.hlist_hd_$a3') ).
thf(2422,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cHList_2ehlist_2ehlist__hd @ happ ) @ happ ) @ happ ) )
= ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__hd___24a3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(185,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.in_split') ).
thf(1471,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__46600___24t ) )
<=> ( A @ c_24__type__46600___24a1 @ ( B @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_$_type_46600') ).
thf(2757,plain,
! [A: $i,B: $i] :
( ( ( A @ c_24__type__46600___24a1 @ ( B @ t ) )
=> ( B @ ( A @ c_24__type__46600___24t ) ) )
& ( ( B @ ( A @ c_24__type__46600___24t ) )
=> ( A @ c_24__type__46600___24a1 @ ( B @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( C @ ( B @ ( A @ c_24__type__16977___24t ) ) ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D @ ( B @ happ ) @ p )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Coq.Lists.List.Exists') ).
thf(2289,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( C @ ( B @ ( A @ c_24__type__16977___24t ) ) ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D @ ( B @ happ ) @ p )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(301,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__35210___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_35210') ).
thf(2461,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) )
=> ( C @ ( B @ ( A @ c_24__type__35210___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__35210___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(354,axiom,
! [A: $i] :
( ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [B: $i] :
( ( B @ ( A @ cHList_2ehlist_2ehlist___24t ) )
=> ( B
= ( B @ ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','HList.hlist.hlist_eta') ).
thf(2911,plain,
! [A: $i] :
( ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [B: $i] :
( ( B @ ( A @ cHList_2ehlist_2ehlist___24t ) )
=> ( B
= ( B @ ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(133,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__2434___24t ) )
=> ( ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( C @ happ ) @ happ ) @ p ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ( ( F @ ( E @ ( C @ happ ) @ happ ) @ p )
=> ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Add_ind') ).
thf(1112,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__2434___24t ) )
=> ( ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( C @ happ ) @ happ ) @ p ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ( ( F @ ( E @ ( C @ happ ) @ happ ) @ p )
=> ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ happ ) @ p )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Exists_cons_hd') ).
thf(890,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ happ ) @ p )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(270,axiom,
! [A: $i] :
( ( A @ c_24__type__122692___24t )
<=> ( c_24__type__122692 @ ( A @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_$_type_122692') ).
thf(2180,plain,
! [A: $i] :
( ( ( c_24__type__122692 @ ( A @ t ) )
=> ( A @ c_24__type__122692___24t ) )
& ( ( A @ c_24__type__122692___24t )
=> ( c_24__type__122692 @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( D @ ( B @ happ ) @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Forall_forall') ).
thf(609,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( D @ ( B @ happ ) @ p ) ) )
=> ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p ) )
& ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( D @ ( B @ happ ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= ( C @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( B
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= C )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Init.Datatypes.app') ).
thf(2111,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= ( C @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( B
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= C )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( A @ cHList_2ehlist_2ehlist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__app___24a3 ) ) )
= ( G @ ( F @ ( E @ ( D @ ( B @ ( A @ c_24__lam__47646___24a6 ) ) ) ) ) ) )
& ( C
= ( G @ ( F @ ( E @ ( D @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
& ( G @ ( E @ cHList_2ehlist_2ehlist___24t ) ) )
& ( F @ ( D @ cF___24t ) ) )
& ( E @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( D @ ciT___24t ) )
| ( ( ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__app___24a3 ) ) )
= ( B @ ( A @ c_24__lam__47639___24a2 ) ) )
& ( C = cHList_2ehlist_2eHnil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_HList.hlist.hlist_app') ).
thf(3150,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( A @ cHList_2ehlist_2ehlist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__app___24a3 ) ) )
= ( G @ ( F @ ( E @ ( D @ ( B @ ( A @ c_24__lam__47646___24a6 ) ) ) ) ) ) )
& ( C
= ( G @ ( F @ ( E @ ( D @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
& ( G @ ( E @ cHList_2ehlist_2ehlist___24t ) ) )
& ( F @ ( D @ cF___24t ) ) )
& ( E @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( D @ ciT___24t ) )
| ( ( ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__app___24a3 ) ) )
= ( B @ ( A @ c_24__lam__47639___24a2 ) ) )
& ( C = cHList_2ehlist_2eHnil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(344,axiom,
! [A: $i,B: $i] :
( ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 )
= ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inj_Coq.Init.Datatypes.nil') ).
thf(2842,plain,
! [A: $i,B: $i] :
( ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 )
= ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ~ ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Forall_dec_subproof0') ).
thf(399,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ~ ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(213,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
| ( B @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.in_app_or') ).
thf(1699,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
| ( B @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( C @ ( B @ ( A @ c_24__type__2663___24t ) ) ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
& ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Coq.Sorting.Sorted.Sorted') ).
thf(827,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( C @ ( B @ ( A @ c_24__type__2663___24t ) ) ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
& ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(83,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__2434___24t ) )
=> ( ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( C @ happ ) @ happ ) @ p ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ( ( F @ ( E @ ( C @ happ ) @ happ ) @ p )
=> ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Add_sind') ).
thf(780,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__2434___24t ) )
=> ( ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( C @ happ ) @ happ ) @ p ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ( ( F @ ( E @ ( C @ happ ) @ happ ) @ p )
=> ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(143,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2125___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__17419___24t ) ) )
=> ( ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ happ ) @ happ ) @ p )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( B @ ( F @ t ) )
=> ! [G: $i] :
( ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [H: $i] :
( ( H @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( C @ happ ) @ happ ) @ p )
=> ( ( H @ ( G @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ( ( H @ ( G @ ( D @ happ ) @ happ ) @ p )
=> ( H @ ( F @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ happ ) @ happ ) @ p ) ) ) ) ) ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Forall2_ind') ).
thf(1176,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2125___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__17419___24t ) ) )
=> ( ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ happ ) @ happ ) @ p )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( B @ ( F @ t ) )
=> ! [G: $i] :
( ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [H: $i] :
( ( H @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( C @ happ ) @ happ ) @ p )
=> ( ( H @ ( G @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ( ( H @ ( G @ ( D @ happ ) @ happ ) @ p )
=> ( H @ ( F @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ happ ) @ happ ) @ p ) ) ) ) ) ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i] :
( ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__121389___24t ) ) ) ) ) ) ) ) ) ) ) ) ) )
<=> ! [O: $i] :
( ( A @ ( O @ t ) )
=> ! [P: $i] :
( ( A @ ( P @ t ) )
=> ( P @ ( O @ ( N @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_121389') ).
thf(1477,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i,M: $i,N: $i] :
( ( ! [O: $i] :
( ( A @ ( O @ t ) )
=> ! [P: $i] :
( ( A @ ( P @ t ) )
=> ( P @ ( O @ ( N @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__121389___24t ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__121389___24t ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ! [O: $i] :
( ( A @ ( O @ t ) )
=> ! [P: $i] :
( ( A @ ( P @ t ) )
=> ( P @ ( O @ ( N @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
=> ( D
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.map_eq_nil') ).
thf(438,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
=> ( D
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(227,axiom,
! [A: $i] :
( ( A @ ( c_24__generic__case__48326 @ happ ) )
= ( A @ c_24__generic__case__48326___24a1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_$_generic_case_48326_$a1') ).
thf(1805,plain,
! [A: $i] :
( ( A @ ( c_24__generic__case__48326 @ happ ) )
= ( A @ c_24__generic__case__48326___24a1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(257,axiom,
! [A: $i] :
( ( A @ c_24__type__48333___24t )
<=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ ( C @ ( B @ ( ciT @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_48333') ).
thf(2069,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ ( C @ ( B @ ( ciT @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) ) ) ) ) )
=> ( A @ c_24__type__48333___24t ) )
& ( ( A @ c_24__type__48333___24t )
=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ ( C @ ( B @ ( ciT @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(126,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.HdRel_cons') ).
thf(1066,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(192,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) )
=> ( E @ ( D @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.lel_tail') ).
thf(1528,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) )
=> ( E @ ( D @ ( A @ cCoq_2eLists_2eList_2elel___24a3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(365,axiom,
! [A: $i] :
( ( A @ c_24__type__46531___24t )
<=> ! [B: $i] :
( ( B @ ciT___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ ( C @ cHList_2ehlist_2ehlist___24t ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_46531') ).
thf(3016,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ ciT___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ ( C @ cHList_2ehlist_2ehlist___24t ) ) ) ) )
=> ( A @ c_24__type__46531___24t ) )
& ( ( A @ c_24__type__46531___24t )
=> ! [B: $i] :
( ( B @ ciT___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ ( C @ cHList_2ehlist_2ehlist___24t ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( C @ ( B @ ( A @ c_24__type__3945___24t ) ) ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
& ~ ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Coq.Lists.SetoidList.NoDupA') ).
thf(563,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( C @ ( B @ ( A @ c_24__type__3945___24t ) ) ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
& ~ ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.incl_tran') ).
thf(722,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__46627___24t ) ) )
<=> ! [D: $i] :
( ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( D @ cHList_2ehlist_2ehlist___24t ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ cType___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_46627') ).
thf(2914,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( D @ cHList_2ehlist_2ehlist___24t ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ cType___24t ) ) )
=> ( C @ ( B @ ( A @ c_24__type__46627___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__46627___24t ) ) )
=> ! [D: $i] :
( ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( D @ cHList_2ehlist_2ehlist___24t ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ cType___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(260,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Add_app') ).
thf(2096,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(265,axiom,
! [A: $i] :
( ( A @ c_24__type__126682___24t )
<=> ! [B: $i] :
( ( B @ c_24__type__122667___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ! [F: $i] :
( ( F @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ! [G: $i] :
( ( G @ ( D @ cHList_2ehlist_2ehlist___24t ) )
=> ! [H: $i] :
( ( H @ ( D @ cHList_2ehlist_2ehlist___24t ) )
=> ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ ( H @ ( F @ ( D @ ( C @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( G @ ( E @ ( D @ ( C @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( D @ ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ cExtLib_2eTactics_2eInjection_2eInjective___24t ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_126682') ).
thf(2124,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ c_24__type__122667___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ! [F: $i] :
( ( F @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ! [G: $i] :
( ( G @ ( D @ cHList_2ehlist_2ehlist___24t ) )
=> ! [H: $i] :
( ( H @ ( D @ cHList_2ehlist_2ehlist___24t ) )
=> ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ ( H @ ( F @ ( D @ ( C @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( G @ ( E @ ( D @ ( C @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( D @ ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ cExtLib_2eTactics_2eInjection_2eInjective___24t ) ) ) ) ) ) ) ) )
=> ( A @ c_24__type__126682___24t ) )
& ( ( A @ c_24__type__126682___24t )
=> ! [B: $i] :
( ( B @ c_24__type__122667___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ! [F: $i] :
( ( F @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ! [G: $i] :
( ( G @ ( D @ cHList_2ehlist_2ehlist___24t ) )
=> ! [H: $i] :
( ( H @ ( D @ cHList_2ehlist_2ehlist___24t ) )
=> ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ ( H @ ( F @ ( D @ ( C @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( G @ ( E @ ( D @ ( C @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( D @ ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ cExtLib_2eTactics_2eInjection_2eInjective___24t ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__7607___24t ) ) ) ) ) ) ) ) ) ) )
<=> ! [L: $i] :
( ( A @ ( L @ t ) )
=> ! [M: $i] :
( ( A @ ( M @ t ) )
=> ( M @ ( L @ ( K @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_7607') ).
thf(2005,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( ! [L: $i] :
( ( A @ ( L @ t ) )
=> ! [M: $i] :
( ( A @ ( M @ t ) )
=> ( M @ ( L @ ( K @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__7607___24t ) ) ) ) ) ) ) ) ) ) ) )
& ( ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__7607___24t ) ) ) ) ) ) ) ) ) ) )
=> ! [L: $i] :
( ( A @ ( L @ t ) )
=> ! [M: $i] :
( ( A @ ( M @ t ) )
=> ( M @ ( L @ ( K @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__72___24t ) )
<=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( C @ ( B @ happ ) @ cProp___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_72') ).
thf(1076,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( C @ ( B @ happ ) @ cProp___24t ) )
=> ( B @ ( A @ c_24__type__72___24t ) ) )
& ( ( B @ ( A @ c_24__type__72___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( C @ ( B @ happ ) @ cProp___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(69,axiom,
cHList_2ehlist_2ehlist__hd @ c_24__type__46547___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_HList.hlist.hlist_hd') ).
thf(663,plain,
cHList_2ehlist_2ehlist__hd @ c_24__type__46547___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( B @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Lists.List.incl') ).
thf(548,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( B @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) )
=> ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) ) )
& ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( B @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(136,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
<=> ? [E: $i] :
( ( D @ ( E @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( E @ ( C @ ( B @ happ ) @ happ ) @ p )
& ( A @ ( E @ t ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InA_alt') ).
thf(1145,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ? [E: $i] :
( ( D @ ( E @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( E @ ( C @ ( B @ happ ) @ happ ) @ p )
& ( A @ ( E @ t ) ) )
=> ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ? [E: $i] :
( ( D @ ( E @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( E @ ( C @ ( B @ happ ) @ happ ) @ p )
& ( A @ ( E @ t ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(119,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p )
=> ( ( D @ ( C @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.SSorted_cons') ).
thf(1018,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p )
=> ( ( D @ ( C @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(311,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( D @ ( C @ ( B @ ( A @ c_24__type__2628___24t ) ) ) ) )
=> ( ( A @ ( C @ t ) )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( ? [E: $i] :
( ? [F: $i] :
( ( D
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( C @ ( B @ happ ) @ happ ) @ p )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
| ( D
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Coq.Sorting.Sorted.HdRel') ).
thf(2564,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( D @ ( C @ ( B @ ( A @ c_24__type__2628___24t ) ) ) ) )
=> ( ( A @ ( C @ t ) )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( ? [E: $i] :
( ? [F: $i] :
( ( D
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( C @ ( B @ happ ) @ happ ) @ p )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
| ( D
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(359,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__46600___24t ) )
<=> ! [C: $i] :
( ( C @ ciT___24t )
=> ! [D: $i] :
( ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cF___24t ) )
=> ! [F: $i] :
( ( F @ ( D @ cHList_2ehlist_2ehlist___24t ) )
=> ! [G: $i] :
( ( F @ ( D @ ( A @ happ ) @ happ ) @ ( G @ t ) )
=> ( F @ ( E @ ( D @ ( C @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( D @ ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ happ ) @ happ ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_46600') ).
thf(2942,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C @ ciT___24t )
=> ! [D: $i] :
( ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cF___24t ) )
=> ! [F: $i] :
( ( F @ ( D @ cHList_2ehlist_2ehlist___24t ) )
=> ! [G: $i] :
( ( F @ ( D @ ( A @ happ ) @ happ ) @ ( G @ t ) )
=> ( F @ ( E @ ( D @ ( C @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( D @ ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ happ ) @ happ ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ) )
=> ( B @ ( A @ c_24__type__46600___24t ) ) )
& ( ( B @ ( A @ c_24__type__46600___24t ) )
=> ! [C: $i] :
( ( C @ ciT___24t )
=> ! [D: $i] :
( ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( C @ cF___24t ) )
=> ! [F: $i] :
( ( F @ ( D @ cHList_2ehlist_2ehlist___24t ) )
=> ! [G: $i] :
( ( F @ ( D @ ( A @ happ ) @ happ ) @ ( G @ t ) )
=> ( F @ ( E @ ( D @ ( C @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( D @ ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ happ ) @ happ ) @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ t ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( C @ ( B @ ( A @ c_24__type__3259___24t ) ) ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForallOrdPairs___24a3 ) ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eForallOrdPairs___24a3 ) ) )
& ( E @ ( D @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Coq.Lists.List.ForallOrdPairs') ).
thf(1025,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( C @ ( B @ ( A @ c_24__type__3259___24t ) ) ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForallOrdPairs___24a3 ) ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eForallOrdPairs___24a3 ) ) )
& ( E @ ( D @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(71,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eLocallySorted___24a3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.LSorted_cons1') ).
thf(705,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eLocallySorted___24a3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
<=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ ( B @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_646') ).
thf(707,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ ( B @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( B @ ( A @ c_24__type__646___24t ) ) )
& ( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ ( B @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( ( B @ ( A @ cCoq_2eSets_2eRelations__1_2eTransitive___24a2 ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
=> ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.Sorted_StronglySorted') ).
thf(414,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( ( B @ ( A @ cCoq_2eSets_2eRelations__1_2eTransitive___24a2 ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
=> ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(242,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
<=> ( ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
| ( B @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.in_app_iff') ).
thf(1941,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( ( ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
| ( B @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) )
=> ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) )
& ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( C @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
| ( B @ ( D @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
=> ( ( E @ ( C @ happ ) @ p )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.Sorted_sind') ).
thf(739,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
=> ( ( E @ ( C @ happ ) @ p )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__3259___24t ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_3259') ).
thf(1780,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__3259___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__3259___24t ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(160,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) )
= ( B @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.rev_unit') ).
thf(1267,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) )
= ( B @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(346,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ~ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.in_nil') ).
thf(2850,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ~ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( ( A @ cType___24t )
=> ( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ? [F: $i] :
( ? [G: $i] :
( ( ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
<=> ( ( E @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
& ( D @ ( B @ happ ) @ p ) ) )
& ( E
= ( G @ ( F @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( F @ t ) ) )
| ( ( ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
<=> ( D @ ( B @ happ ) @ p ) )
& ( E
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) )
& ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( ( ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
<=> ( c_24True @ p ) )
& ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.micromega.Refl.make_conj') ).
thf(2192,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( ( A @ cType___24t )
=> ( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ? [F: $i] :
( ? [G: $i] :
( ( ( ( E @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
& ( D @ ( B @ happ ) @ p ) )
=> ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) ) )
& ( ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
=> ( ( E @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
& ( D @ ( B @ happ ) @ p ) ) )
& ( E
= ( G @ ( F @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( F @ t ) ) )
| ( ( ( D @ ( B @ happ ) @ p )
=> ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) ) )
& ( ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
=> ( D @ ( B @ happ ) @ p ) )
& ( E
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) )
& ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( ( ( c_24True @ p )
=> ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) ) )
& ( ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
=> ( c_24True @ p ) )
& ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ ( cHList_2ehlist_2ehlist__app @ happ ) @ happ ) @ happ ) @ happ ) )
= ( D @ ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_HList.hlist.hlist_app_$a4') ).
thf(887,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ ( cHList_2ehlist_2ehlist__app @ happ ) @ happ ) @ happ ) @ happ ) )
= ( D @ ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__2628___24t ) ) ) ) )
<=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ( G @ ( F @ ( E @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_2628') ).
thf(2747,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ( G @ ( F @ ( E @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__2628___24t ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__2628___24t ) ) ) ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ( G @ ( F @ ( E @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(268,axiom,
! [A: $i] :
( ( A @ c_24__type__99___24t )
<=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_99') ).
thf(2165,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ cProp___24t ) ) ) )
=> ( A @ c_24__type__99___24t ) )
& ( ( A @ c_24__type__99___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ cProp___24t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(144,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
<=> ( ( D @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
| ( C @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InA_app_iff') ).
thf(1186,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( ( ( D @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
| ( C @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) )
& ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( ( D @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
| ( C @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) @ ( B @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.map_app') ).
thf(441,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) @ ( B @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
<=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
| ( C @ ( B @ happ ) @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Exists_cons') ).
thf(717,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
| ( C @ ( B @ happ ) @ p ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) ) )
& ( ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
| ( C @ ( B @ happ ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( C @ ( B @ ( A @ c_24__type__3218___24t ) ) ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
& ( D @ ( B @ happ ) @ p )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Coq.Lists.List.Forall') ).
thf(1869,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( C @ ( B @ ( A @ c_24__type__3218___24t ) ) ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( C
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
& ( D @ ( B @ happ ) @ p )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(89,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Relations.Relation_Operators.Lt_nil') ).
thf(840,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(153,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ( D @ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.incl_cons') ).
thf(1235,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( ( D @ ( C @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) )
=> ( D @ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eincl___24a3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( c_24True @ ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__impl___24a4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.micromega.Refl.make_impl_true') ).
thf(463,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( c_24True @ ( C @ ( B @ ( A @ cCoq_2emicromega_2eRefl_2emake__impl___24a4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__47646___24a7 ) ) ) ) ) ) )
= ( G @ ( F @ ( B @ ( D @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( E @ ( B @ ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( C @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_lam_47646') ).
thf(3095,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__47646___24a7 ) ) ) ) ) ) )
= ( G @ ( F @ ( B @ ( D @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( E @ ( B @ ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( C @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(224,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.app_nil_end') ).
thf(1790,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__46451___24t ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cProp___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_46451') ).
thf(2224,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cProp___24t ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__46451___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__46451___24t ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cProp___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(122,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( ( F @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.eqlistA_cons') ).
thf(1038,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( ( F @ ( E @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( c_24__lam__46514 @ happ ) @ happ ) @ happ ) )
= ( C @ ( B @ ( A @ c_24__lam__46514___24a3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_$_lam_46514_$a3') ).
thf(585,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( c_24__lam__46514 @ happ ) @ happ ) @ happ ) )
= ( C @ ( B @ ( A @ c_24__lam__46514___24a3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(52,axiom,
cHList_2ehlist_2ehlist__app @ c_24__type__47653___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_HList.hlist.hlist_app') ).
thf(576,plain,
cHList_2ehlist_2ehlist__app @ c_24__type__47653___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(209,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( ( B
!= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
=> ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2elast___24a3 ) ) @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eremovelast___24a2 ) @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.app_removelast_last') ).
thf(1658,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( ( B
!= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
=> ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2elast___24a3 ) ) @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eremovelast___24a2 ) @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( D @ ( C @ ( B @ ( A @ c_24__type__3988___24t ) ) ) ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( C
= ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D
= ( H @ ( F @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( H @ ( G @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
& ( F @ ( E @ ( B @ happ ) @ happ ) @ p )
& ( H @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( F @ t ) ) )
& ( A @ ( E @ t ) ) )
| ( ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( D
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Coq.Lists.SetoidList.eqlistA') ).
thf(2322,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( D @ ( C @ ( B @ ( A @ c_24__type__3988___24t ) ) ) ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
=> ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( C
= ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D
= ( H @ ( F @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( H @ ( G @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eeqlistA___24a4 ) ) ) )
& ( F @ ( E @ ( B @ happ ) @ happ ) @ p )
& ( H @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( F @ t ) ) )
& ( A @ ( E @ t ) ) )
| ( ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( D
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__159676___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( B = D )
=> ( D @ ( C @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_159676') ).
thf(1749,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( B = D )
=> ( D @ ( C @ happ ) @ cProp___24t ) ) )
=> ( C @ ( B @ ( A @ c_24__type__159676___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__159676___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( B = D )
=> ( D @ ( C @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(131,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eLocallySorted___24a3 ) ) )
=> ( ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eLocallySorted___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.LocallySorted_sind') ).
thf(1094,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eLocallySorted___24a3 ) ) )
=> ( ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eLocallySorted___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__220___24t ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_220') ).
thf(2030,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__220___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__220___24t ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(358,axiom,
! [A: $i] :
( ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [B: $i] :
( ( B @ ( A @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( cHList_2ehlist_2eHnil @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) )
= c_24__generic__case__47111 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','HList.hlist.hlist_app_nil_r') ).
thf(2939,plain,
! [A: $i] :
( ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [B: $i] :
( ( B @ ( A @ cHList_2ehlist_2ehlist___24t ) )
=> ( ( cHList_2ehlist_2eHnil @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) )
= c_24__generic__case__47111 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(94,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( D @ ( E @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) @ ( E @ ( C @ happ ) @ ( B @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.in_map') ).
thf(859,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( D @ ( E @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) @ ( E @ ( C @ happ ) @ ( B @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(170,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ happ ) @ p )
=> ( ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ happ ) @ p ) ) ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( C @ ( B @ happ ) @ p ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.rev_ind') ).
thf(1353,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ happ ) @ p )
=> ( ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ happ ) @ p ) ) ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( C @ ( B @ happ ) @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__34438___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_34438') ).
thf(2279,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( C @ ( B @ ( A @ c_24__type__34438___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__34438___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Forall_nil') ).
thf(497,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(276,axiom,
! [A: $i] :
( ( A @ ( c_24__lam__46511 @ happ ) )
= ( A @ c_24__lam__46511___24a1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_$_lam_46511_$a1') ).
thf(2266,plain,
! [A: $i] :
( ( A @ ( c_24__lam__46511 @ happ ) )
= ( A @ c_24__lam__46511___24a1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(298,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ happ ) @ p )
=> ( ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( B @ happ ) @ p )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( B @ happ ) @ p ) ) ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( C @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( B @ happ ) @ p ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.rev_list_ind') ).
thf(2435,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ happ ) @ p )
=> ( ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( B @ happ ) @ p )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( B @ happ ) @ p ) ) ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( C @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( B @ happ ) @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( C @ ( B @ happ ) @ p )
=> ~ ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Forall_dec_subproof') ).
thf(539,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( C @ ( B @ happ ) @ p )
=> ~ ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2125___24t ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [G: $i] :
( ( G @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ( ( G @ ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ( G @ ( F @ ( B @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Forall2_app') ).
thf(524,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2125___24t ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [G: $i] :
( ( G @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ( ( G @ ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) )
=> ( G @ ( F @ ( B @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall2___24a5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2etranspose2___24a4 ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( B @ ( G @ t ) )
=> ! [H: $i] :
( ( B @ ( H @ t ) )
=> ( ( H @ ( G @ ( C @ happ ) @ happ ) @ p )
=> ( H @ ( E @ ( D @ happ ) @ happ ) @ ( F @ ( D @ happ ) @ happ ) @ ( G @ ( F @ ( D @ happ ) @ happ ) @ ( E @ ( D @ happ ) @ happ ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Lists.SetoidList.transpose2') ).
thf(2347,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( B @ ( G @ t ) )
=> ! [H: $i] :
( ( B @ ( H @ t ) )
=> ( ( H @ ( G @ ( C @ happ ) @ happ ) @ p )
=> ( H @ ( E @ ( D @ happ ) @ happ ) @ ( F @ ( D @ happ ) @ happ ) @ ( G @ ( F @ ( D @ happ ) @ happ ) @ ( E @ ( D @ happ ) @ happ ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2etranspose2___24a4 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2etranspose2___24a4 ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( B @ ( G @ t ) )
=> ! [H: $i] :
( ( B @ ( H @ t ) )
=> ( ( H @ ( G @ ( C @ happ ) @ happ ) @ p )
=> ( H @ ( E @ ( D @ happ ) @ happ ) @ ( F @ ( D @ happ ) @ happ ) @ ( G @ ( F @ ( D @ happ ) @ happ ) @ ( E @ ( D @ happ ) @ happ ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( D @ ( C @ ( B @ ( A @ c_24__type__2511___24t ) ) ) ) )
=> ( ( A @ ( C @ t ) )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( ? [E: $i] :
( ? [F: $i] :
( ( D
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( F @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
| ? [E: $i] :
( ? [F: $i] :
( ( D
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( C @ ( B @ happ ) @ happ ) @ p )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Coq.Lists.SetoidList.InA') ).
thf(1126,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( D @ ( C @ ( B @ ( A @ c_24__type__2511___24t ) ) ) ) )
=> ( ( A @ ( C @ t ) )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( ? [E: $i] :
( ? [F: $i] :
( ( D
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( F @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
| ? [E: $i] :
( ? [F: $i] :
( ( D
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( C @ ( B @ happ ) @ happ ) @ p )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(356,axiom,
! [A: $i] :
( ( A @ c_24__type__46547___24t )
<=> ! [B: $i] :
( ( B @ ciT___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ ( B @ cF___24t ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_46547') ).
thf(2924,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ ciT___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ ( B @ cF___24t ) ) ) ) )
=> ( A @ c_24__type__46547___24t ) )
& ( ( A @ c_24__type__46547___24t )
=> ! [B: $i] :
( ( B @ ciT___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ cHList_2ehlist_2ehlist___24t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ ( B @ cF___24t ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__2434___24t ) )
<=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_2434') ).
thf(465,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( B @ ( A @ c_24__type__2434___24t ) ) )
& ( ( B @ ( A @ c_24__type__2434___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( D @ ( C @ ( B @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__prop__126660___24a7 ) ) ) ) ) ) @ p )
<=> ( ( G @ ( E @ ( C @ ( B @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( F @ ( D @ ( C @ ( B @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
=> ( ( G @ ( F @ ( C @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
& ( E @ ( D @ ( B @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_prop_126660') ).
thf(1649,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ ( E @ ( C @ ( B @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( F @ ( D @ ( C @ ( B @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
=> ( ( G @ ( F @ ( C @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
& ( E @ ( D @ ( B @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p ) ) )
=> ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__prop__126660___24a7 ) ) ) ) ) ) @ p ) )
& ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__prop__126660___24a7 ) ) ) ) ) ) @ p )
=> ( ( G @ ( E @ ( C @ ( B @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( F @ ( D @ ( C @ ( B @ cHList_2ehlist_2ehlist__app___24a4 ) ) ) @ ( C @ ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
=> ( ( G @ ( F @ ( C @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p )
& ( E @ ( D @ ( B @ ( A @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ p ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(129,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( ( E @ ( C @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Forall_ind') ).
thf(1084,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ happ ) @ p )
=> ( ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( ( E @ ( C @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(332,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( ( B = C )
=> ( C = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Logic.EqdepFacts.internal_eq_sym_internal') ).
thf(2743,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( ( B = C )
=> ( C = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(304,axiom,
ciT @ cType___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_iT') ).
thf(2490,plain,
ciT @ cType___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(164,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 )
!= ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.nil_cons') ).
thf(1289,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 )
!= ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(91,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eForallOrdPairs___24a3 ) ) )
=> ( ( E @ ( C @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eForallOrdPairs___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.ForallOrdPairs_ind') ).
thf(844,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( ( E @ ( B @ ( A @ cCoq_2eLists_2eList_2eForallOrdPairs___24a3 ) ) )
=> ( ( E @ ( C @ happ ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eForallOrdPairs___24a3 ) ) )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(233,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','HList.app_nil_r_trans') ).
thf(1866,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__37914___24t ) ) ) ) ) ) )
<=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_37914') ).
thf(2775,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ happ ) @ cType___24t ) )
=> ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__37914___24t ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__37914___24t ) ) ) ) ) ) )
=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(217,axiom,
! [A: $i] :
( ( A @ c_24__type__15477___24t )
<=> ! [B: $i] :
( ( B @ cProp___24t )
=> ! [C: $i] :
( ( C @ ( B @ cExtLib_2eTactics_2eInjection_2eInjective___24t ) )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_15477') ).
thf(1734,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cProp___24t )
=> ! [C: $i] :
( ( C @ ( B @ cExtLib_2eTactics_2eInjection_2eInjective___24t ) )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( A @ c_24__type__15477___24t ) )
& ( ( A @ c_24__type__15477___24t )
=> ! [B: $i] :
( ( B @ cProp___24t )
=> ! [C: $i] :
( ( C @ ( B @ cExtLib_2eTactics_2eInjection_2eInjective___24t ) )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(352,axiom,
cHList_2ehlist_2eHnil @ ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ cHList_2ehlist_2ehlist___24t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_HList.hlist.Hnil') ).
thf(2907,plain,
cHList_2ehlist_2eHnil @ ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ cHList_2ehlist_2ehlist___24t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ c_24__lam__46511___24a1 )
= cHList_2ehlist_2eHnil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_lam_46511') ).
thf(588,plain,
! [A: $i] :
( ( A @ c_24__lam__46511___24a1 )
= cHList_2ehlist_2eHnil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cType___24t )
=> ( ( B @ cType___24t )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [E: $i] :
( ? [F: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_2435694___24a4 ) ) ) )
= ( F @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) @ ( E @ ( C @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
| ( ( ( D @ ( C @ ( B @ ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_2435694___24a4 ) ) ) )
= ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( D
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_case_Coq.Init.Datatypes.list$35694') ).
thf(1721,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cType___24t )
=> ( ( B @ cType___24t )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [E: $i] :
( ? [F: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_2435694___24a4 ) ) ) )
= ( F @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) @ ( E @ ( C @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
| ( ( ( D @ ( C @ ( B @ ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_2435694___24a4 ) ) ) )
= ( B @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( D
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__16977___24t ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cProp___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_16977') ).
thf(2098,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cProp___24t ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__16977___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__16977___24t ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cProp___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__29901___24t ) ) ) ) ) )
<=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ ( F @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_29901') ).
thf(1639,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i] :
( ( A @ ( G @ t ) )
=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ ( F @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__29901___24t ) ) ) ) ) ) )
& ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__29901___24t ) ) ) ) ) )
=> ! [G: $i] :
( ( A @ ( G @ t ) )
=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ ( F @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(124,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.HdRel_nil') ).
thf(1062,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eHdRel___24a4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cType___24t )
=> ( ( A @ ( B @ t ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( C
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D
= ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( G @ ( F @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
& ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
| ? [E: $i] :
( ( C = E )
& ( D
= ( E @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Coq.Lists.List.Add') ).
thf(2823,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cType___24t )
=> ( ( A @ ( B @ t ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( C
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D
= ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( G @ ( F @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
& ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
| ? [E: $i] :
( ( C = E )
& ( D
= ( E @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Exists_cons_tl') ).
thf(401,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__2177___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eExists___24a3 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ c_24__fix__550__v__CANONICAL__1___24a3 ) ) )
= ( C @ ( E @ ( A @ c_24__fix__550__v__CANONICAL__1___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( B
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( ( ( C @ ( B @ ( A @ c_24__fix__550__v__CANONICAL__1___24a3 ) ) )
= C )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_fix_550_v_CANONICAL_1') ).
thf(2152,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ c_24__fix__550__v__CANONICAL__1___24a3 ) ) )
= ( C @ ( E @ ( A @ c_24__fix__550__v__CANONICAL__1___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( B
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( ( ( C @ ( B @ ( A @ c_24__fix__550__v__CANONICAL__1___24a3 ) ) )
= C )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(291,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( ( B @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
<=> ( B @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.in_rev') ).
thf(2394,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( ( ( B @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( B @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) )
& ( ( B @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ( B @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( C @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.NoDupA_cons') ).
thf(510,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ~ ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__114118___24t ) ) ) ) ) ) )
<=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_114118') ).
thf(1607,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ happ ) @ cType___24t ) )
=> ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__114118___24t ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__114118___24t ) ) ) ) ) ) )
=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(210,axiom,
( ( cHList_2ehlist_2eHnil @ ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ cHList_2ehlist_2ehlist__rev___24a2 ) )
= cHList_2ehlist_2eHnil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','HList.hlist.hlist_rev_nil') ).
thf(1661,plain,
( ( cHList_2ehlist_2eHnil @ ( ciT @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ cHList_2ehlist_2ehlist__rev___24a2 ) )
= cHList_2ehlist_2eHnil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2erev__append___24a3 ) ) )
= ( C @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( A @ cCoq_2eLists_2eList_2erev__append___24a3 ) ) ) )
& ( B
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2erev__append___24a3 ) ) )
= C )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Lists.List.rev_append') ).
thf(1444,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2erev__append___24a3 ) ) )
= ( C @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( A @ cCoq_2eLists_2eList_2erev__append___24a3 ) ) ) )
& ( B
= ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( D @ t ) ) )
| ( ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2erev__append___24a3 ) ) )
= C )
& ( B
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cHList_2ehlist_2ehlist__rev_27 @ happ ) @ happ ) @ happ ) )
= ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__rev_27___24a3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_HList.hlist.hlist_rev\'_$a3') ).
thf(1512,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cHList_2ehlist_2ehlist__rev_27 @ happ ) @ happ ) @ happ ) )
= ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__rev_27___24a3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 )
!= ( D @ ( C @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons') ).
thf(2302,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 )
!= ( D @ ( C @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(199,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502 @ happ ) @ happ ) )
= ( B @ ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_$_case_Coq.Init.Datatypes.list$46502_$a2') ).
thf(1578,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502 @ happ ) @ happ ) )
= ( B @ ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_2446502___24a2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p )
=> ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.StronglySorted_Sorted') ).
thf(410,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p )
=> ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eSorted___24a3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( D @ ( C @ ( B @ ( A @ c_24__type__19752___24t ) ) ) ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) )
=> ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( C
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D
= ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( G @ ( F @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) )
& ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( C
= ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D
= ( H @ ( F @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( H @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( F @ ( E @ ( B @ happ ) @ happ ) @ p )
& ( A @ ( F @ t ) ) )
& ( A @ ( E @ t ) ) )
| ? [E: $i] :
( ? [F: $i] :
( ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( D
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Coq.Relations.Relation_Operators.Ltl') ).
thf(2587,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( D @ ( C @ ( B @ ( A @ c_24__type__19752___24t ) ) ) ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) )
=> ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( C
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D
= ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( G @ ( F @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) )
& ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
| ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( C
= ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( D
= ( H @ ( F @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( H @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( F @ ( E @ ( B @ happ ) @ happ ) @ p )
& ( A @ ( F @ t ) ) )
& ( A @ ( E @ t ) ) )
| ? [E: $i] :
( ? [F: $i] :
( ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) )
& ( D
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p )
=> ( ( E @ ( C @ happ ) @ p )
=> ( ( E @ ( D @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Sorting.Sorted.StronglySorted_ind') ).
thf(867,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__72___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ p )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p )
=> ( ( E @ ( C @ happ ) @ p )
=> ( ( E @ ( D @ ( B @ happ ) @ ( A @ cCoq_2eLists_2eList_2eForall___24a3 ) ) @ p )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eStronglySorted___24a3 ) ) @ p )
=> ( D @ ( C @ happ ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( A @ cHList_2ehlist_2ehlist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__rev_27___24a3 ) ) )
= ( G @ ( F @ ( E @ ( D @ ( B @ ( A @ c_24__lam__48310___24a6 ) ) ) ) ) ) )
& ( C
= ( G @ ( F @ ( E @ ( D @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
& ( G @ ( E @ cHList_2ehlist_2ehlist___24t ) ) )
& ( F @ ( D @ cF___24t ) ) )
& ( E @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( D @ ciT___24t ) )
| ( ( ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__rev_27___24a3 ) ) )
= ( B @ ( A @ c_24__lam__47639___24a2 ) ) )
& ( C = cHList_2ehlist_2eHnil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_HList.hlist.hlist_rev\'') ).
thf(3062,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( A @ cHList_2ehlist_2ehlist___24t ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__rev_27___24a3 ) ) )
= ( G @ ( F @ ( E @ ( D @ ( B @ ( A @ c_24__lam__48310___24a6 ) ) ) ) ) ) )
& ( C
= ( G @ ( F @ ( E @ ( D @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
& ( G @ ( E @ cHList_2ehlist_2ehlist___24t ) ) )
& ( F @ ( D @ cF___24t ) ) )
& ( E @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( D @ ciT___24t ) )
| ( ( ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__rev_27___24a3 ) ) )
= ( B @ ( A @ c_24__lam__47639___24a2 ) ) )
& ( C = cHList_2ehlist_2eHnil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(93,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
<=> ( ( C @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
& ~ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.NoDup_cons_iff') ).
thf(854,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( ( C @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
& ~ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) )
=> ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) ) )
& ( ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( ( C @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
& ~ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(247,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ( E @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Add_cons') ).
thf(1986,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ( E @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(180,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.in_eq') ).
thf(1436,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(104,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ c_24__type__72___24t ) )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ happ ) @ p ) ) ) )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( ( F @ ( D @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ happ ) @ p ) ) ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( E @ ( D @ happ ) @ p ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InA_ind') ).
thf(918,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ c_24__type__72___24t ) )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ happ ) @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ happ ) @ p ) ) ) )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( ( F @ ( D @ happ ) @ p )
=> ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ happ ) @ p ) ) ) ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( E @ ( D @ happ ) @ p ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(271,axiom,
! [A: $i] :
( ( A @ c_24__type__46531___24t )
<=> ( c_24__type__46531 @ ( A @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_$_type_46531') ).
thf(2186,plain,
! [A: $i] :
( ( ( c_24__type__46531 @ ( A @ t ) )
=> ( A @ c_24__type__46531___24t ) )
& ( ( A @ c_24__type__46531___24t )
=> ( c_24__type__46531 @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(142,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ? [D: $i] :
( ( C @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
& ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.Add_inv') ).
thf(1172,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
=> ? [D: $i] :
( ( C @ ( D @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
& ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__2434___24t ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ happ ) @ p ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [G: $i] :
( ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) )
=> ( ( F @ ( E @ ( C @ happ ) @ happ ) @ p )
=> ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Relations.Relation_Operators.Ltl_sind') ).
thf(664,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__2434___24t ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ happ ) @ p ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [G: $i] :
( ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) )
=> ( ( F @ ( E @ ( C @ happ ) @ happ ) @ p )
=> ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( G @ ( E @ ( C @ ( A @ cHList_2ehlist_2eHcons___24a4 ) ) ) )
= ( H @ ( F @ ( D @ ( B @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
=> ( ( A = B )
& ( C = D )
& ( E = F )
& ( G = H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inj_HList.hlist.Hcons') ).
thf(2961,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( G @ ( E @ ( C @ ( A @ cHList_2ehlist_2eHcons___24a4 ) ) ) )
= ( H @ ( F @ ( D @ ( B @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) )
=> ( ( A = B )
& ( C = D )
& ( E = F )
& ( G = H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__34711___24t ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_34711') ).
thf(2404,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__34711___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__34711___24t ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(109,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ( ( D @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
<=> ( ~ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( C @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.NoDup_Add') ).
thf(960,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eAdd___24a4 ) ) ) )
=> ( ( ( ~ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( C @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) ) )
=> ( D @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) ) )
& ( ( D @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( ~ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2eIn___24a3 ) ) @ p )
& ( C @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( C @ ( B @ ( A @ c_24__type__34711___24t ) ) ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eLocallySorted___24a3 ) ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( C
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
& ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eLocallySorted___24a3 ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
& ( A @ ( D @ t ) ) )
| ? [D: $i] :
( ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( A @ ( D @ t ) ) )
| ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Coq.Sorting.Sorted.LocallySorted') ).
thf(2619,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ cType___24t )
=> ( ( B @ ( C @ ( B @ ( A @ c_24__type__34711___24t ) ) ) )
=> ( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( C @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eLocallySorted___24a3 ) ) )
=> ( ? [D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( C
= ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
& ( F @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eSorting_2eSorted_2eLocallySorted___24a3 ) ) )
& ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) ) )
& ( A @ ( E @ t ) ) )
& ( A @ ( D @ t ) ) )
| ? [D: $i] :
( ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) )
& ( A @ ( D @ t ) ) )
| ( C
= ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ( A @ cProp___24t )
=> ( ( B @ ( A @ cExtLib_2eTactics_2eInjection_2eInjective___24t ) )
=> ? [C: $i] :
( ( B
= ( C @ ( A @ cExtLib_2eTactics_2eInjection_2eBuild__Injective___24a2 ) ) )
& ( ( A @ p )
=> ( C @ p ) )
& ( C @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_ExtLib.Tactics.Injection.Injective') ).
thf(2040,plain,
! [A: $i,B: $i] :
( ( A @ cProp___24t )
=> ( ( B @ ( A @ cExtLib_2eTactics_2eInjection_2eInjective___24t ) )
=> ? [C: $i] :
( ( B
= ( C @ ( A @ cExtLib_2eTactics_2eInjection_2eBuild__Injective___24a2 ) ) )
& ( ( A @ p )
=> ( C @ p ) )
& ( C @ cProp___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(108,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__2434___24t ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ happ ) @ p ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [G: $i] :
( ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) )
=> ( ( F @ ( E @ ( C @ happ ) @ happ ) @ p )
=> ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Relations.Relation_Operators.Ltl_ind') ).
thf(955,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ c_24__type__2434___24t ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( C @ happ ) @ happ ) @ p ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( D @ ( B @ happ ) @ happ ) @ p )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [G: $i] :
( ( G @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( G @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [F: $i] :
( ( F @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( F @ ( E @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) )
=> ( ( F @ ( E @ ( C @ happ ) @ happ ) @ p )
=> ( F @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( B @ ( A @ cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4 ) ) ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__17419___24t ) ) )
<=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_17419') ).
thf(2783,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( C @ ( B @ ( A @ c_24__type__17419___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__17419___24t ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( E @ ( B @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2etranspose___24a4 ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( B @ ( G @ t ) )
=> ( G @ ( E @ ( D @ happ ) @ happ ) @ ( F @ ( D @ happ ) @ happ ) @ ( G @ ( F @ ( D @ happ ) @ happ ) @ ( E @ ( D @ happ ) @ happ ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Lists.SetoidList.transpose') ).
thf(1816,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( B @ ( G @ t ) )
=> ( G @ ( E @ ( D @ happ ) @ happ ) @ ( F @ ( D @ happ ) @ happ ) @ ( G @ ( F @ ( D @ happ ) @ happ ) @ ( E @ ( D @ happ ) @ happ ) @ ( C @ happ ) @ happ ) @ p ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2etranspose___24a4 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2etranspose___24a4 ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ! [G: $i] :
( ( B @ ( G @ t ) )
=> ( G @ ( E @ ( D @ happ ) @ happ ) @ ( F @ ( D @ happ ) @ happ ) @ ( G @ ( F @ ( D @ happ ) @ happ ) @ ( E @ ( D @ happ ) @ happ ) @ ( C @ happ ) @ happ ) @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__lam__46514___24a3 ) ) )
= ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__tl___24a3 ) ) @ ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__hd___24a3 ) ) @ ( B @ ( A @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_lam_46514') ).
thf(1495,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__lam__46514___24a3 ) ) )
= ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__tl___24a3 ) ) @ ( C @ ( B @ ( A @ cHList_2ehlist_2ehlist__hd___24a3 ) ) @ ( B @ ( A @ cHList_2ehlist_2eHcons___24a4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(159,axiom,
! [A: $i] :
( ( A @ c_24__type__46686___24t )
<=> ( c_24__type__46686 @ ( A @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_$_type_46686') ).
thf(1261,plain,
! [A: $i] :
( ( ( c_24__type__46686 @ ( A @ t ) )
=> ( A @ c_24__type__46686___24t ) )
& ( ( A @ c_24__type__46686___24t )
=> ( c_24__type__46686 @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(345,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( c_24__lam__46514 @ happ ) @ happ ) )
= ( B @ ( A @ c_24__lam__46514___24a2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_$_lam_46514_$a2') ).
thf(2847,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( c_24__lam__46514 @ happ ) @ happ ) )
= ( B @ ( A @ c_24__lam__46514___24a2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( D @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.NoDupA_split') ).
thf(528,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( D @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__34447___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_34447') ).
thf(1976,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( C @ ( B @ ( A @ c_24__type__34447___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__34447___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ ( C @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( ( B @ ( A @ cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2 ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( D @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.NoDupA_swap') ).
thf(459,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ( ( B @ ( A @ cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2 ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( D @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) )
=> ( D @ ( C @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) @ ( E @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eNoDupA___24a3 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(240,axiom,
! [A: $i] :
( ( A @ c_24__type__47653___24t )
<=> ( c_24__type__47653 @ ( A @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$tdef_$_type_47653') ).
thf(1925,plain,
! [A: $i] :
( ( ( c_24__type__47653 @ ( A @ t ) )
=> ( A @ c_24__type__47653___24t ) )
& ( ( A @ c_24__type__47653___24t )
=> ( c_24__type__47653 @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__4367___24t ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ cProp___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_4367') ).
thf(1597,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ cProp___24t ) ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__4367___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__4367___24t ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ cProp___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) @ ( D @ ( C @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.map_cons') ).
thf(501,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( E @ ( D @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) @ ( D @ ( C @ happ ) @ ( B @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ c_24__type__2177___24t ) )
=> ( ( ~ ( B @ ( D @ happ ) @ p )
| ( B @ ( D @ happ ) @ p ) )
=> ( ~ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
=> ( ~ ( C @ ( D @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
| ~ ( B @ ( D @ happ ) @ p ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.micromega.Refl.not_make_conj_cons') ).
thf(607,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( C @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ( A @ c_24__type__2177___24t ) )
=> ( ~ ( C @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( D @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
=> ( ~ ( C @ ( D @ ( A @ cCoq_2emicromega_2eRefl_2emake__conj___24a3 ) ) )
| ~ ( B @ ( D @ happ ) @ p ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_2435694___24a4 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.micromega.Tauto.map_simpl') ).
thf(486,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ c_24__case__Coq_2eInit_2eDatatypes_2elist_2435694___24a4 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(105,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.NoDup_nil') ).
thf(940,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(350,axiom,
! [A: $i] :
( ( A @ c_24__type__126706___24t )
<=> ! [B: $i] :
( ( B @ c_24__type__122667___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ciT___24t )
=> ! [E: $i] :
( ( E @ ( D @ cF___24t ) )
=> ! [F: $i] :
( ( F @ ( D @ cF___24t ) )
=> ! [G: $i] :
( ( G @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ! [H: $i] :
( ( H @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ ( H @ ( F @ ( C @ ( D @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( G @ ( E @ ( C @ ( D @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( C @ ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ cExtLib_2eTactics_2eInjection_2eInjective___24t ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_126706') ).
thf(2881,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ c_24__type__122667___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ciT___24t )
=> ! [E: $i] :
( ( E @ ( D @ cF___24t ) )
=> ! [F: $i] :
( ( F @ ( D @ cF___24t ) )
=> ! [G: $i] :
( ( G @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ! [H: $i] :
( ( H @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ ( H @ ( F @ ( C @ ( D @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( G @ ( E @ ( C @ ( D @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( C @ ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ cExtLib_2eTactics_2eInjection_2eInjective___24t ) ) ) ) ) ) ) ) )
=> ( A @ c_24__type__126706___24t ) )
& ( ( A @ c_24__type__126706___24t )
=> ! [B: $i] :
( ( B @ c_24__type__122667___24t )
=> ! [C: $i] :
( ( C @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [D: $i] :
( ( D @ ciT___24t )
=> ! [E: $i] :
( ( E @ ( D @ cF___24t ) )
=> ! [F: $i] :
( ( F @ ( D @ cF___24t ) )
=> ! [G: $i] :
( ( G @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ! [H: $i] :
( ( H @ ( C @ cHList_2ehlist_2ehlist___24t ) )
=> ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ ( H @ ( F @ ( C @ ( D @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( G @ ( E @ ( C @ ( D @ cHList_2ehlist_2eHcons___24a4 ) ) ) @ ( C @ ( D @ ( ciT @ cCoq_2eInit_2eDatatypes_2econs___24a3 ) ) @ ( B @ cHList_2ehlist_2eequiv__hlist___24a4 ) ) ) @ cExtLib_2eTactics_2eInjection_2eInjective___24t ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
<=> ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.SetoidList.InA_rev') ).
thf(659,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ c_24__type__646___24t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( D @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) )
& ( ( D @ ( A @ cCoq_2eLists_2eList_2erev___24a2 ) @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eSetoidList_2eInA___24a4 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) @ ( B @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( D @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.NoDup_map_inv') ).
thf(543,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2361___24t ) ) )
=> ! [D: $i] :
( ( D @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( D @ ( C @ ( B @ ( A @ cCoq_2eLists_2eList_2emap___24a4 ) ) ) @ ( B @ cCoq_2eLists_2eList_2eNoDup___24a2 ) )
=> ( D @ ( A @ cCoq_2eLists_2eList_2eNoDup___24a2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(49,axiom,
cHList_2ehlist_2ehlist__tl @ c_24__type__46531___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_HList.hlist.hlist_tl') ).
thf(560,plain,
cHList_2ehlist_2ehlist__tl @ c_24__type__46531___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(80,axiom,
cHList_2ehlist_2ehlist__rev_27 @ c_24__type__48333___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_HList.hlist.hlist_rev\'') ).
thf(755,plain,
cHList_2ehlist_2ehlist__rev_27 @ c_24__type__48333___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(368,axiom,
! [A: $i] :
( ( A @ c_24__type__46583___24t )
<=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cType___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_46583') ).
thf(3052,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cType___24t ) ) )
=> ( A @ c_24__type__46583___24t ) )
& ( ( A @ c_24__type__46583___24t )
=> ! [B: $i] :
( ( B @ ( ciT @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ! [C: $i] :
( ( C @ ( B @ cHList_2ehlist_2ehlist___24t ) )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cType___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( c_24__lam__48310 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__48310___24a7 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_$_lam_48310_$a7') ).
thf(2106,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( c_24__lam__48310 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__48310___24a7 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(239,axiom,
! [A: $i] :
( ( A @ c_24__type__15463___24t )
<=> ! [B: $i] :
( ( B @ cProp___24t )
=> ! [C: $i] :
( ( C @ cProp___24t )
=> ( ( ( B @ p )
=> ( C @ p ) )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ ( B @ cExtLib_2eTactics_2eInjection_2eInjective___24t ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_15463') ).
thf(1912,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cProp___24t )
=> ! [C: $i] :
( ( C @ cProp___24t )
=> ( ( ( B @ p )
=> ( C @ p ) )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ ( B @ cExtLib_2eTactics_2eInjection_2eInjective___24t ) ) ) ) )
=> ( A @ c_24__type__15463___24t ) )
& ( ( A @ c_24__type__15463___24t )
=> ! [B: $i] :
( ( B @ cProp___24t )
=> ! [C: $i] :
( ( C @ cProp___24t )
=> ( ( ( B @ p )
=> ( C @ p ) )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ ( B @ cExtLib_2eTactics_2eInjection_2eInjective___24t ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(269,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Lists.List.app_nil_r') ).
thf(2177,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ ( A @ cCoq_2eInit_2eDatatypes_2elist___24t ) )
=> ( ( A @ cCoq_2eInit_2eDatatypes_2enil___24a1 @ ( B @ ( A @ cCoq_2eInit_2eDatatypes_2eapp___24a3 ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2170___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cProp___24t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_2170') ).
thf(2655,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cProp___24t ) )
=> ( C @ ( B @ ( A @ c_24__type__2170___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__2170___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cProp___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(3661,plain,
$false,
inference(e,[status(thm)],[2306,2109,1237,1315,1295,1956,1110,481,645,892,2363,2309,1882,1068,2381,2908,1808,2527,1422,3098,1544,1205,1591,379,1793,861,408,977,1671,3120,3004,3135,1164,814,1988,747,2575,2901,945,1746,973,1359,2067,1254,651,2491,2763,1628,724,1709,1430,2339,2269,504,802,2682,1279,1191,1892,416,1931,2852,2989,1362,475,756,2027,591,2451,1828,514,1151,1581,905,2616,1946,1465,1040,2469,1020,2254,2508,397,1377,877,428,2718,1564,2371,2979,988,2799,452,1438,1153,810,2047,2093,2737,2641,2083,512,942,534,2232,2441,2705,1343,778,2541,2277,862,1570,1217,561,1487,2414,2015,1387,1900,2958,1365,2433,1968,1457,461,3028,1195,842,2769,852,2663,583,522,1762,1534,615,1227,1856,1006,499,1270,1772,2577,1064,980,403,2692,1498,2638,420,2877,1292,526,637,2666,1419,489,2613,2551,1016,1155,547,1744,393,647,1530,1231,1552,457,2813,2862,1241,541,657,558,1515,1167,2645,530,794,2057,1846,2793,1663,2144,965,1251,1219,1273,3079,2734,444,1631,2936,412,975,732,1615,1403,545,875,577,1795,1701,2398,641,3077,1239,1092,1897,2425,3091,2319,391,1139,2521,2478,990,3106,2669,2839,737,649,1307,1209,2721,3038,2422,1471,2757,2289,2461,2911,1112,890,2180,609,2111,3150,2842,399,1699,827,780,1176,1477,438,1805,2069,1066,1528,3016,563,722,2914,2096,2124,2005,1076,663,548,1145,1018,2564,2942,1025,705,707,414,1941,739,1780,1267,2850,2192,887,2747,2165,1186,441,717,1869,840,1235,463,3095,1790,2224,1038,585,576,1658,2322,1749,1094,2030,2939,859,1353,2279,497,2266,2435,539,524,2347,1126,2924,465,1649,1084,2743,2490,1289,844,1866,2775,1734,2907,588,1721,2098,1639,1062,2823,401,2152,2394,510,1607,1661,1444,1512,2302,1578,410,2587,867,3062,854,1986,1436,918,2186,1172,664,2961,2404,960,2619,2040,955,2783,1816,1495,1261,2847,528,1976,459,1925,1597,501,607,486,940,2881,659,543,560,755,3052,2106,1912,2177,2655]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV631+1 : TPTP v9.3.1. Released v9.3.0.
% 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
% 0.13/0.40 % Computer : n003.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 11:26:54 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.83/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.91/1.84 % [INFO] Parsing done (843ms).
% 3.91/1.85 % [INFO] Running in sequential loop mode.
% 4.62/2.12 % [INFO] eprover registered as external prover.
% 4.62/2.13 % [INFO] Scanning for conjecture ...
% 5.93/2.45 % [INFO] Found a conjecture (or negated_conjecture) and 3117 axioms. Running axiom selection ...
% 7.92/3.04 % [INFO] Axiom selection finished. Selected 376 axioms (removed 2741 axioms).
% 9.45/3.54 % [INFO] Problem is first-order (TPTP FOF).
% 9.45/3.60 % [INFO] Type checking passed.
% 9.80/3.60 % [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 ...
% 41.87/12.57 % External prover 'e' found a proof!
% 41.87/12.58 % [INFO] Killing All external provers ...
% 41.87/12.58 % Time passed: 12031ms (effective reasoning time: 10720ms)
% 41.87/12.58 % 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)>
% 41.87/12.58 % Axioms used in derivation (376): Coq.Lists.List.Exists_dec_subproof, Coq.Lists.SetoidList.InA_permute_heads, $tdef_$_type_46531, Coq.Lists.List.rev_ind, $_type_35336, $_type_46603, $_type_1926, Coq.Logic.FunctionalExtensionality.functional_extensionality, Coq.Lists.List.in_eq, Coq.Sorting.Sorted.LSorted_cons1, Coq.Lists.SetoidList.eqlistA_sind, $_type_7607, Coq.Lists.List.app_eq_nil, Coq.Lists.SetoidList.InA_cons_tl, $adef_HList.hlist.hlist_app_$a3, HList.hlist.equiv_hlist_ind, $_type_46547, $adef_$_lam_47639_$a2, Coq.Lists.List.Forall_impl, $_type_120259, Coq.Lists.List.NoDup_Add, $_type_64, Coq.Lists.List.app_eq_unit, Coq.Lists.SetoidList.eqlistA_rev, $_def_Coq.Lists.List.flat_map, Coq.Lists.List.Forall_sind, $adef_$_case_Coq.Init.Datatypes.list$46502_$a1, $_inversion_Coq.Relations.Relation_Operators.Ltl, Coq.Init.Datatypes.list_sind, Coq.Lists.List.Exists_ind, $adef_$_lam_48310_$a7, $_type_40707, $tdef_$_type_48237, Coq.Lists.SetoidList.InA_cons_hd, Coq.Lists.List.ext_in_map, Coq.micromega.Refl.not_make_conj_cons, $_typeof_HList.hlist.hlist_rect, Coq.Lists.SetoidList.eqlistA_cons, Coq.Lists.List.removelast_app, $_inversion_Coq.Init.Datatypes.list, $_prop_126659, Coq.Lists.List.app_comm_cons, Coq.Sorting.Sorted.Sorted_inv, Coq.Lists.List.in_cons, $_type_48333, $_case_Coq.Init.Datatypes.list$505, $_type_15463, $_type_2310, Coq.micromega.Refl.make_conj_impl, Coq.Lists.SetoidList.NoDupA_cons, HList.hlist.hlist_eta, $_type_2177, Coq.micromega.Refl.make_conj_in, $_inversion_Coq.Lists.List.Add, $_type_19193, $_type_3259, HList.hlist.equiv_hlist_Hcons, $_def_HList.hlist.hlist_rect, Coq.Sorting.Sorted.StronglySorted_sind, $_type_33834, $adef_$_lam_47646_$a7, $_type_48237, Coq.Logic.Decidable.not_or, $_inversion_Coq.Lists.List.Forall, Coq.Lists.List.in_app_iff, $_type_114118, Coq.Lists.List.incl_tl, HList.hlist.hlist_rev_nil, Coq.Lists.List.nil_cons, Coq.Sorting.Sorted.HdRel_ind, Coq.Lists.List.map_cons, $_typeof_HList.hlist.Hnil, Coq.Lists.List.Add_cons, Coq.Lists.List.Forall2_nil, $tdef_$_type_46627, $tdef_iT, $adef_HList.hlist.hlist_app_$a4, Coq.Sorting.Sorted.HdRel_sind, HList.hlist.hlist_nil_eta, Coq.Lists.SetoidList.InA_InfA, Coq.Lists.List.Exists_dec_subproof0, Coq.Lists.List.Forall_dec_subproof0, Coq.Sorting.Sorted.Sorted_extends, Coq.Lists.List.Forall2_app_inv_r, HList.app_nil_r_trans, Coq.Lists.List.Forall2_app, $_type_46531, $_prop_126660, _HAMMER_COQ_TRUE, $_type_29901, Coq.Lists.List.in_inv, Coq.Lists.List.in_rev, Coq.Lists.List.Exists_sind, $_type_2434, $_def_HList.hlist.hlist_tl, Coq.Lists.List.NoDup_ind, Coq.Lists.List.not_in_cons, $_type_72, $_typeof_HList.hlist.hlist_tl, $_type_3218, Coq.Sorting.Sorted.StronglySorted_Sorted, $_type_46583, $tdef_$_type_126706, Coq.Lists.List.ForallOrdPairs_sind, Coq.Lists.List.Forall2_cons, $_type_15477, $_def_Coq.Lists.SetoidList.transpose_restr2, $_type_46627, $_type_29599, Coq.Lists.List.app_inv_tail, Coq.Lists.SetoidList.InfA_app, $_def_Coq.Lists.List.map, $tdef_$_type_46600, Coq.Lists.List.app_nil_r, $_inversion_Coq.Sorting.Sorted.Sorted, Coq.Lists.List.NoDup_map_inv, $_def_Coq.Lists.List.last, $_type_45156, Coq.micromega.Refl.make_impl_true, $_type_18991, Coq.Relations.Relation_Operators.Ltl_sind, $_type_45164, $_inversion_Coq.Lists.List.Exists, $_typeof_HList.hlist.hlist_app, Coq.Lists.List.Exists_cons_hd, $_lam_46514, $_type_120501, Coq.Lists.List.Forall2_sind, $tdef_$_type_122667, HList.hlist.hlist_app_nil_r, Coq.Lists.SetoidList.InA_split, Coq.Lists.List.Exists_cons, $adef_$_lam_48310_$a6, Coq.Lists.SetoidList.NoDupA_nil, $_case_Coq.Init.Datatypes.list$35694, Coq.Lists.List.NoDup_cons_iff, $_def_Coq.Lists.SetoidList.transpose_restr, Coq.Lists.SetoidList.InfA_ltA, $_typeof_HList.hlist.hlist_rev', $adef_HList.hlist.hlist_rev'_$a4, Coq.Lists.List.app_nil_end, $_type_99, Coq.micromega.Refl.make_conj_app, $_type_3988, $_type_3068, $_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons, $_lam_48310, Coq.Lists.SetoidList.NoDupA_swap, Coq.Lists.SetoidList.InA_ind, $_inversion_Coq.Lists.List.Forall2, $_type_16977, $_inversion_HList.hlist.hlist, $_type_17521, Coq.Lists.List.ForallOrdPairs_In, $_type_126706, $_inversion_ExtLib.Tactics.Injection.Injective, $_case_Coq.Init.Datatypes.list$46502, Coq.Relations.Relation_Operators.Lt_nil, $adef_$_lam_46514_$a3, Coq.Lists.List.in_or_app, $_type_3945, Coq.Lists.SetoidList.NoDupA_rev, $_inversion_Coq.Lists.SetoidList.NoDupA, $_type_46600, Coq.Sorting.Sorted.Sorted_ind, Coq.Lists.List.Add_app, HList.app_ass_trans, $_type_33408, $adef_$_case_Coq.Init.Datatypes.list$46502_$a2, Coq.Lists.List.app_assoc_reverse, HList.hlist.hlist_ind, Coq.Sorting.Sorted.LocallySorted_sind, Coq.Lists.List.rev_involutive, $_inversion_Coq.Sorting.Sorted.LocallySorted, $_def_Coq.Sets.Relations_1.Transitive, Coq.Sorting.Sorted.LSorted_consn, $_inj_HList.hlist.Hcons, Coq.Lists.List.lel_trans, Coq.Lists.SetoidList.InA_app, $_def_Coq.Lists.List.fold_left, $_def_HList.hlist.hlist_rev', _HAMMER_COQ_FALSE, $_type_15488, $tdef_$_type_46547, $_type_35210, Coq.Sorting.Sorted.StronglySorted_ind, $_type_46666, $_type_126682, Coq.Lists.List.Exists_cons_tl, Coq.Lists.List.Forall_inv_tail, Coq.Lists.List.lel_tail, Coq.Lists.List.incl_cons, $_type_33241, $_type_159676, Coq.Lists.List.in_app_or, $_def_HList.hlist.hlist_hd, $_type_121389, $_type_1966, Coq.Lists.List.Exists_exists, $_def_Coq.Lists.List.hd, Coq.Sorting.Sorted.Sorted_cons, $_def_Coq.Lists.SetoidList.transpose2, $_type_2170, Coq.Lists.List.rev_app_distr, $_type_17419, HList.hlist.equiv_hlist_app, $_type_35187, $_type_46391, $_type_34438, $_typeof_iT, $_type_46515, Coq.Lists.List.in_map, Coq.Lists.SetoidList.InA_double_head, Coq.Lists.List.ForallOrdPairs_ind, Coq.Lists.List.in_split, Coq.Lists.List.Forall_nil, Coq.Lists.List.Add_sind, $_def_Coq.micromega.Refl.make_impl, Coq.Lists.List.map_ext, Coq.Lists.List.rev_list_ind, $tdef_ExtLib.Tactics.Injection.Injective, $_type_2628, Coq.Lists.List.in_nil, Coq.Lists.List.incl_refl, $adef_$_generic_case_48326_$a1, $_lam_46511, $_def_Coq.Lists.List.rev, Coq.Logic.FunctionalExtensionality.equal_f, $adef_$_lam_46511_$a1, $_typeof_HList.hlist.hlist_hd, $adef_HList.hlist.hlist_rev'_$a3, $_type_15450, $_def_Coq.Lists.SetoidList.transpose, $adef_HList.hlist.hlist_hd_$a3, $_prop_126684, $tdef_$_type_47653, Coq.Sorting.Sorted.HdRel_inv, $_type_46443, $_type_47653, $_type_31326, Coq.micromega.Refl.make_conj_cons, Coq.Lists.List.Add_in, $_type_646, Coq.Lists.List.map_eq_nil, Coq.Sorting.Sorted.Sorted_StronglySorted, Coq.Lists.SetoidList.In_InA, $_def_Coq.Lists.List.incl, $_type_35233, Coq.Lists.List.NoDup_remove_2, $_inj_Coq.Init.Datatypes.cons, Coq.Lists.SetoidList.InA_alt, $_inversion_Coq.Lists.List.NoDup, $_inversion_Coq.Sorting.Sorted.StronglySorted, $_type_2511, $_def_Coq.Lists.List.fold_right, HList.hlist.hlist_eqv_nil, $_type_19752, $_def_Coq.Lists.List.In, Coq.Lists.List.app_removelast_last, $_type_3185, Coq.Lists.List.incl_tran, Coq.Lists.List.NoDup_nil, Coq.Lists.SetoidList.eqlistA_ind, Coq.Lists.List.NoDup_remove, $_type_19092, $_type_4367, Coq.Lists.List.Forall_ind, Coq.Lists.List.in_map_iff, $_type_34711, Coq.Lists.List.Add_inv, $tdef_$_type_46686, $_type_29339, $_inversion_HList.hlist.equiv_hlist, Coq.Lists.List.app_inj_tail, $_type_2533, Coq.Lists.List.map_app, $_type_2211, Coq.Lists.List.NoDup_cons, $_inversion_Coq.Lists.SetoidList.InA, Coq.Lists.SetoidList.InA_eqA, Coq.Lists.List.NoDup_sind, $_type_35252, $tdef_$_type_46583, Coq.Logic.EqdepFacts.internal_eq_sym_internal, Coq.Lists.SetoidList.InA_app_iff, HList.hlist.hlist_cons_eta, Coq.Lists.List.incl_Add_inv, Coq.Lists.List.FOP_cons, $tdef_$_type_46603, $_def_Coq.Init.Datatypes.app, Coq.Relations.Relation_Operators.Lt_tl, Coq.Lists.List.map_ext_in, $_def_Coq.Lists.List.tl, $_type_2663, $_lam_2046, Coq.Lists.SetoidList.InA_nil, Coq.Lists.SetoidList.InA_cons, Coq.Lists.List.rev_unit, $_type_6875, $_def_Coq.Lists.List.removelast, $_type_120240, Coq.Lists.List.Forall_cons, Coq.Lists.List.Forall_forall, Coq.Lists.List.app_cons_not_nil, Coq.Sorting.Sorted.SSorted_cons, $_type_37914, $_lam_47646, $adef_$_lam_47646_$a6, Coq.Lists.SetoidList.InA_altdef, $_type_32967, Coq.Lists.SetoidList.In_InfA, Coq.Lists.List.Forall_dec_subproof, $_inj_Coq.Init.Datatypes.nil, Coq.Lists.SetoidList.InA_rev, Coq.Lists.SetoidList.eqlistA_app, $tdef_$_type_122692, Coq.Lists.List.incl_appl, $_type_2125, Coq.Sorting.Sorted.Sorted_sind, Coq.micromega.Tauto.map_simpl, Coq.Init.Datatypes.list_ind, $_type_46451, $_type_87, $_def_Coq.micromega.Refl.make_conj, $adef_HList.hlist.hlist_rect_$a5, Coq.Lists.SetoidList.NoDupA_sind, Coq.Lists.List.Forall_inv, Coq.Lists.List.app_nil_l, $_def_Coq.Init.Datatypes.list_rect, Coq.Lists.SetoidList.InA_sind, $_type_220, $_def_Coq.Lists.List.rev_append, Coq.Sorting.Sorted.LocallySorted_ind, Coq.Lists.List.map_ext_in_iff, $_type_46580, Coq.Lists.List.Exists_impl, Coq.Relations.Relation_Operators.Lt_hd, $_type_2361, Coq.Sorting.Sorted.HdRel_nil, Coq.Lists.List.NoDup_remove_1, Coq.Lists.List.app_inv_head, Coq.Lists.List.Add_split, $_type_69, $adef_HList.hlist.hlist_tl_$a3, $_fix_550_v_CANONICAL_1, Coq.Lists.List.lel_cons, Coq.Lists.List.incl_appr, $_type_17185, $adef_$_lam_46514_$a2, Coq.Lists.SetoidList.NoDupA_split, Coq.Lists.List.Forall2_app_inv_l, $_inversion_Coq.Sorting.Sorted.HdRel, Coq.Lists.List.Forall2_ind, Coq.Lists.List.incl_app, Coq.Lists.SetoidList.NoDupA_ind, Coq.Relations.Relation_Operators.Ltl_ind, Coq.Lists.List.lel_refl, $_type_46686, $_inversion_Coq.Lists.List.ForallOrdPairs, Coq.Lists.List.app_assoc, $_type_122692, $_type_2118, $_type_34447, Coq.Lists.List.lel_cons_cons, Coq.Lists.SetoidList.InA_app_idem, $_def_HList.hlist.hlist_app, Coq.Lists.List.lel_nil, Coq.Sorting.Sorted.HdRel_cons, $_type_40361, $_type_33790, $_discrim_HList.hlist.Hnil$HList.hlist.Hcons, HList.hlist.hlist_eqv_cons, Coq.Lists.List.Add_head, Coq.Lists.List.Add_ind, Coq.Lists.SetoidList.eqlistA_altdef, $_inversion_Coq.Lists.SetoidList.eqlistA
% 41.87/12.58 % No. of inferences in proof: 756
% 41.87/12.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 12031 ms resp. 10720 ms w/o parsing
% 46.34/13.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 46.34/13.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------