%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV776-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n026.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 09:00:32 AM UTC 2026
% Result : Unsatisfiable 20.66s 21.76s
% Output : Refutation 22.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 496
% Syntax : Number of formulae : 993 ( 325 unt; 0 typ; 0 def)
% Number of atoms : 2059 ( 668 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 12270 ( 922 ~;1066 |; 0 &;10282 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 74 ( 72 usr; 11 con; 0-5 aty)
% Number of variables : 3050 ( 0 ^;3050 !; 0 ?;3050 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Event_Oknows_decl,type,
c_Event_Oknows: $i > $i > $i ).
thf(c_Message_Oagent_OSpy_decl,type,
c_Message_Oagent_OSpy: $i ).
thf(c_List_Oappend_decl,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i > $i ).
thf(tc_Event_Oevent_decl,type,
tc_Event_Oevent: $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_Event_Oevent_ONotes_decl,type,
c_Event_Oevent_ONotes: $i > $i > $i ).
thf(v_A_decl,type,
v_A: $i ).
thf(v_X_decl,type,
v_X: $i ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_Event_Obad_decl,type,
c_Event_Obad: $i ).
thf(tc_Message_Oagent_decl,type,
tc_Message_Oagent: $i ).
thf(c_Set_Oinsert_decl,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(tc_Message_Omsg_decl,type,
tc_Message_Omsg: $i ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_HOL_Oord__class_Oless_decl,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(tc_bool_decl,type,
tc_bool: $i ).
thf(class_HOL_Oord_decl,type,
class_HOL_Oord: $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_List_Olinorder__class_Osorted_decl,type,
c_List_Olinorder__class_Osorted: $i > $i > $o ).
thf(c_List_OtakeWhile_decl,type,
c_List_OtakeWhile: $i > $i > $i > $i ).
thf(c_Message_Omsg_OMPair_decl,type,
c_Message_Omsg_OMPair: $i > $i > $i ).
thf(c_List_Oset_decl,type,
c_List_Oset: $i > $i > $i ).
thf(c_List_Oremove1_decl,type,
c_List_Oremove1: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_List_Ofilter_decl,type,
c_List_Ofilter: $i > $i > $i > $i ).
thf(c_List_Oreplicate_decl,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(c_List_Odistinct_decl,type,
c_List_Odistinct: $i > $i > $o ).
thf(c_List_Orev_decl,type,
c_List_Orev: $i > $i > $i ).
thf(c_List_Olist__update_decl,type,
c_List_Olist__update: $i > $i > $i > $i > $i ).
thf(c_Event_Oevent_OGets_decl,type,
c_Event_Oevent_OGets: $i > $i > $i ).
thf(c_List_Oremdups_decl,type,
c_List_Oremdups: $i > $i > $i ).
thf(c_Message_OinvKey_decl,type,
c_Message_OinvKey: $i > $i ).
thf(c_Message_Omsg_OCrypt_decl,type,
c_Message_Omsg_OCrypt: $i > $i > $i ).
thf(c_Message_Omsg_OKey_decl,type,
c_Message_Omsg_OKey: $i > $i ).
thf(c_List_Orotate1_decl,type,
c_List_Orotate1: $i > $i > $i ).
thf(c_Message_Oparts_decl,type,
c_Message_Oparts: $i > $i ).
thf(c_Event_Oevent_OSays_decl,type,
c_Event_Oevent_OSays: $i > $i > $i > $i ).
thf(c_List_OdropWhile_decl,type,
c_List_OdropWhile: $i > $i > $i > $i ).
thf(c_List_Osko__List__XtakeWhile__eq__all__conv__1__1_decl,type,
c_List_Osko__List__XtakeWhile__eq__all__conv__1__1: $i > $i > $i > $i ).
thf(c_List_Osko__List__XtakeWhile__cong__1__1_decl,type,
c_List_Osko__List__XtakeWhile__cong__1__1: $i > $i > $i > $i > $i ).
thf(c_Message_Oanalz_decl,type,
c_Message_Oanalz: $i > $i ).
thf(c_Public_OshrK_decl,type,
c_Public_OshrK: $i > $i ).
thf(c_Message_Osynth_decl,type,
c_Message_Osynth: $i > $i ).
thf(c_List_Obutlast_decl,type,
c_List_Obutlast: $i > $i > $i ).
thf(c_List_Osko__List__XCons__eq__append__conv__1__1_decl,type,
c_List_Osko__List__XCons__eq__append__conv__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_List_Otl_decl,type,
c_List_Otl: $i > $i > $i ).
thf(c_List_Osko__List__Xsplit__list__first__prop__iff__1__5_decl,type,
c_List_Osko__List__Xsplit__list__first__prop__iff__1__5: $i > $i > $i > $i ).
thf(c_Event_OinitState_decl,type,
c_Event_OinitState: $i > $i ).
thf(c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1_decl,type,
c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1: $i > $i > $i > $i ).
thf(c_List_Osko__List__Xsplit__list__last__prop__iff__1__5_decl,type,
c_List_Osko__List__Xsplit__list__last__prop__iff__1__5: $i > $i > $i > $i ).
thf(c_List_Osko__List__Xappend__eq__Cons__conv__1__1_decl,type,
c_List_Osko__List__Xappend__eq__Cons__conv__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_List_Ohd_decl,type,
c_List_Ohd: $i > $i > $i ).
thf(c_Event_Oused_decl,type,
c_Event_Oused: $i > $i ).
thf(c_List_Olist__inter_decl,type,
c_List_Olist__inter: $i > $i > $i > $i ).
thf(c_Message_Osko__Message__Xanalz__insert__eq__I__1__1_decl,type,
c_Message_Osko__Message__Xanalz__insert__eq__I__1__1: $i > $i > $i ).
thf(c_List_Osplice_decl,type,
c_List_Osplice: $i > $i > $i > $i ).
thf(c_List_Oconcat__map_decl,type,
c_List_Oconcat__map: $i > $i > $i > $i > $i ).
thf(c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1_decl,type,
c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1: $i > $i > $i > $i ).
thf(c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2_decl,type,
c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2: $i > $i > $i > $i ).
thf(c_List_Olast_decl,type,
c_List_Olast: $i > $i > $i ).
thf(c_Message_Oagent_OServer_decl,type,
c_Message_Oagent_OServer: $i ).
thf(c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1_decl,type,
c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1: $i > $i > $i > $i ).
thf(c_List_Osko__List__XtakeWhile__append2__1__1_decl,type,
c_List_Osko__List__XtakeWhile__append2__1__1: $i > $i > $i > $i ).
thf(c_NS__Shared__Mirabelle_Ons__sharedp_decl,type,
c_NS__Shared__Mirabelle_Ons__sharedp: $i > $o ).
thf(c_List_Olength__unique_decl,type,
c_List_Olength__unique: $i > $i > $i ).
thf(346,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(1322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(221,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__eq_0) ).
thf(1036,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(430,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Osynth @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__synthD_0) ).
thf(1501,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ c_Message_Osynth @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(354,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__analz_0) ).
thf(1337,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(415,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_OtakeWhile ) ) @ c_List_Oset ) @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__takeWhileD_1) ).
thf(1469,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_OtakeWhile ) ) @ c_List_Oset ) @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(279,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).
thf(1168,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Gets_0) ).
thf(1237,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( C @ c_Message_Omsg_OKey ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I43_J_0) ).
thf(628,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( C @ c_Message_Omsg_OKey ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(11,axiom,
tc_nat @ class_HOL_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(518,plain,
tc_nat @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma1_0) ).
thf(941,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ ( B @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ ( A @ c_Message_Omsg_OKey @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( A @ c_Message_Omsg_OKey @ c_Set_Oinsert ) ) @ ( C @ ( B @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I5_J_0) ).
thf(1179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ ( B @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ ( A @ c_Message_Omsg_OKey @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( A @ c_Message_Omsg_OKey @ c_Set_Oinsert ) ) @ ( C @ ( B @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(666,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(453,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OtakeWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I1_J_0) ).
thf(1549,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OtakeWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(254,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( D @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(1110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( D @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(458,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ c_List_Oset ) @ ( E @ c_in ) ) )
| ( E @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ ( B @ ( A @ c_List_OtakeWhile ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__append1_0) ).
thf(1559,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ c_List_Oset ) @ ( E @ c_in ) ) )
| ( E @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ ( B @ ( A @ c_List_OtakeWhile ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(252,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).
thf(1105,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(299,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_usedI_0) ).
thf(1211,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(387,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ c_List_Olist_ONil ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
!= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
thf(1406,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ c_List_Olist_ONil ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
!= ( D @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(77,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( E @ ( D @ c_Event_Oevent_OGets ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I4_J_0) ).
thf(683,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( E @ ( D @ c_Event_Oevent_OGets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ ( A @ c_List_Osko__List__XtakeWhile__cong__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( D @ ( A @ c_List_Osko__List__XtakeWhile__cong__1__1 ) ) ) @ ( D @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) )
= ( C @ ( B @ ( D @ c_List_OtakeWhile ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__cong_1) ).
thf(730,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ ( A @ c_List_Osko__List__XtakeWhile__cong__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( D @ ( A @ c_List_Osko__List__XtakeWhile__cong__1__1 ) ) ) @ ( D @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) )
= ( C @ ( B @ ( D @ c_List_OtakeWhile ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(405,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth_0) ).
thf(1443,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(484,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(1618,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(204,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(994,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(385,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
| ( A = D )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1401,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
| ( A = D )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(395,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( D @ ( A @ c_Event_Oknows ) @ ( C @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Says_0) ).
thf(1422,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( D @ ( A @ c_Event_Oknows ) @ ( C @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(451,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Ofilter ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__filterD_2) ).
thf(1544,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Ofilter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(472,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__in__used_0) ).
thf(1591,plain,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(155,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( A @ c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__first__prop__iff_6) ).
thf(878,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( A @ c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(446,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( D @ c_in ) ) )
| ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile__eq__Nil__conv_0) ).
thf(1533,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( D @ c_in ) ) )
| ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(402,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ohd ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd_Osimps_0) ).
thf(1437,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ohd ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(423,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono_0) ).
thf(1486,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(223,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_0) ).
thf(1041,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( D @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__knows_0) ).
thf(861,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( D @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(428,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__conj__parts_0) ).
thf(1497,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(240,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__analz__Spy_0) ).
thf(1078,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(480,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Obutlast ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).
thf(1608,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Obutlast ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(341,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_2) ).
thf(1310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(715,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(320,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
thf(1260,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_1) ).
thf(945,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(233,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oconcat__map ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Oconcat__map ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_concat__map_Osimps_I2_J_0) ).
thf(1063,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oconcat__map ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Oconcat__map ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(363,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(1354,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(410,axiom,
tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__in__bad_0) ).
thf(1458,plain,
tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(128,axiom,
! [A: $i] :
( ( A @ c_Public_OshrK @ c_Message_OinvKey )
= ( A @ c_Public_OshrK ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__shrK_0) ).
thf(814,plain,
! [A: $i] :
( ( A @ c_Public_OshrK @ c_Message_OinvKey )
= ( A @ c_Public_OshrK ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(349,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__subset__iff_0) ).
thf(1327,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(356,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__iff_1) ).
thf(1342,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_OdropWhile ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__dropWhile_0) ).
thf(747,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_OdropWhile ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__hd__tl_0) ).
thf(913,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Orev ) )
= ( C @ ( B @ ( A @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__replicate_0) ).
thf(829,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Orev ) )
= ( C @ ( B @ ( A @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(292,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).
thf(1196,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(262,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= E )
| ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_2) ).
thf(1127,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= E )
| ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(465,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( C @ c_Event_Oevent_ONotes ) @ c_in ) ) )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Notes__imp__knows__Spy_0) ).
thf(1576,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( C @ c_Event_Oevent_ONotes ) @ c_in ) ) )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(841,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(482,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( C @ ( A @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Notes_0) ).
thf(1613,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( C @ ( A @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(495,axiom,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).
thf(1645,plain,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(418,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( B @ ( A @ c_List_Obutlast ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_0) ).
thf(1475,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( B @ ( A @ c_List_Obutlast ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oset ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__is__subset_0) ).
thf(782,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oset ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(404,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__spies_0) ).
thf(1441,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(477,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma2_0) ).
thf(1601,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(378,axiom,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__parts_0) ).
thf(1386,plain,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(565,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(369,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Otl ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl_Osimps_I1_J_0) ).
thf(1366,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Otl ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(437,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert_0) ).
thf(1518,plain,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(1265,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(486,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
thf(1623,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(421,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( C @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Says_0) ).
thf(1482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( C @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(388,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1409,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(570,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(399,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(1430,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(335,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Crypt_0) ).
thf(1298,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(322,axiom,
tc_Event_Oevent @ c_List_Olist_ONil @ c_NS__Shared__Mirabelle_Ons__sharedp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONil_0) ).
thf(1264,plain,
tc_Event_Oevent @ c_List_Olist_ONil @ c_NS__Shared__Mirabelle_Ons__sharedp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( D @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__insert__eq_0) ).
thf(1191,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( D @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ c_in ) ) )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1132,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(542,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_1) ).
thf(587,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ c_List_Osko__List__XtakeWhile__cong__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( D @ ( A @ c_List_Osko__List__XtakeWhile__cong__1__1 ) ) ) @ ( D @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) )
= ( C @ ( B @ ( D @ c_List_OtakeWhile ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__cong_2) ).
thf(838,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ c_List_Osko__List__XtakeWhile__cong__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( D @ ( A @ c_List_Osko__List__XtakeWhile__cong__1__1 ) ) ) @ ( D @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) )
= ( C @ ( B @ ( D @ c_List_OtakeWhile ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(434,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_Message_Osynth )
= ( B @ c_Message_Oanalz @ c_Message_Osynth ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fake__analz__eq_0) ).
thf(1511,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_Message_Osynth )
= ( B @ c_Message_Oanalz @ c_Message_Osynth ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(751,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(559,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( B @ c_List_Oremdups ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__remdups_0) ).
thf(638,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( B @ c_List_Oremdups ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(375,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(1379,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
thf(1347,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev ) @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oconcat__map ) ) ) )
= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_concat__map_Osimps_I1_J_0) ).
thf(1013,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oconcat__map ) ) ) )
= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(157,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).
thf(881,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_Message_Osynth @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__mono_0) ).
thf(1115,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_Message_Oanalz @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(462,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ c_List_Oset ) @ ( A @ ( C @ ( B @ c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1 ) ) @ c_in ) ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_2) ).
thf(1568,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ c_List_Oset ) @ ( A @ ( C @ ( B @ c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1 ) ) @ c_in ) ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(367,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( A @ c_List_Oset ) @ c_lessequals ) ) )
| ~ ( D @ ( E @ ( C @ c_in ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oset ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__update__subsetI_0) ).
thf(1362,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( A @ c_List_Oset ) @ c_lessequals ) ) )
| ~ ( D @ ( E @ ( C @ c_in ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oset ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(249,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_1) ).
thf(1100,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(1232,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ c_List_Oset ) @ ( A @ ( C @ ( B @ c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2 ) ) @ c_in ) ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_4) ).
thf(1087,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ c_List_Oset ) @ ( A @ ( C @ ( B @ c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2 ) ) @ c_in ) ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(435,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1514,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(104,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(756,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(408,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( B @ ( B @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_List_Olast ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__in__set_0) ).
thf(1450,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( B @ ( B @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_List_Olast ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(271,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(1151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(806,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(329,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ ( B @ c_Message_Osko__Message__Xanalz__insert__eq__I__1__1 ) @ c_in ) ) )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__eq__I_0) ).
thf(1283,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ ( B @ c_Message_Osko__Message__Xanalz__insert__eq__I__1__1 ) @ c_in ) ) )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(228,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( E @ ( B @ ( A @ c_List_OtakeWhile ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__tail_0) ).
thf(1051,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( E @ ( B @ ( A @ c_List_OtakeWhile ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(167,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( A
= ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_0) ).
thf(905,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( A
= ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(425,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).
thf(1489,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
!= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(392,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C @ ( B @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1415,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C @ ( B @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(393,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__MPair_0) ).
thf(1418,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_1) ).
thf(623,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(215,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).
thf(1020,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( C @ ( B @ c_List_Oreplicate ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__replicate_0) ).
thf(574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( C @ ( B @ c_List_Oreplicate ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(467,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(1581,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(191,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( C @ c_lessequals ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__trans_0) ).
thf(966,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( C @ c_lessequals ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(301,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__subset__iff_1) ).
thf(1215,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(186,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Oset ) @ ( B @ ( A @ c_List_Oset ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__subset__Cons_0) ).
thf(956,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Oset ) @ ( B @ ( A @ c_List_Oset ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(150,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_0) ).
thf(866,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ ( A @ c_List_Olist_OCons ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OInj_0) ).
thf(1072,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(382,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I4_J_0) ).
thf(1394,plain,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(361,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Spy__spies__bad__shrK_0) ).
thf(1351,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remdups__id_0) ).
thf(660,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(202,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I9_J_0) ).
thf(988,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(400,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__used_0) ).
thf(1433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(439,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insertI_0) ).
thf(1521,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(460,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_0) ).
thf(1564,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_OinvKey )
!= ( B @ c_Message_OinvKey ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey__eq_0) ).
thf(602,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_OinvKey )
!= ( B @ c_Message_OinvKey ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(109,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_0) ).
thf(766,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp_1) ).
thf(1104,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(312,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( B @ c_Message_Oparts ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__cut__eq_0) ).
thf(1242,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( B @ c_Message_Oparts ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(238,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__analz_1) ).
thf(1074,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( B @ c_List_Oset ) @ ( D @ ( B @ ( A @ c_List_Osko__List__XtakeWhile__append2__1__1 ) ) @ c_in ) ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_OtakeWhile ) ) @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__append2_0) ).
thf(1206,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( B @ c_List_Oset ) @ ( D @ ( B @ ( A @ c_List_Osko__List__XtakeWhile__append2__1__1 ) ) @ c_in ) ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_OtakeWhile ) ) @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(7,axiom,
tc_bool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(512,plain,
tc_bool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(339,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
thf(1306,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).
thf(1199,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(534,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(235,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_1) ).
thf(1067,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(492,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz ) )
| ( ( A @ c_Message_Oanalz )
!= ( B @ c_Message_Oanalz ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__cong_0) ).
thf(1636,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz ) )
| ( ( A @ c_Message_Oanalz )
!= ( B @ c_Message_Oanalz ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(226,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_ODecrypt_0) ).
thf(1047,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(25,axiom,
tc_bool @ class_HOL_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(546,plain,
tc_bool @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__remove1_0) ).
thf(793,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_0) ).
thf(1153,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(761,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(379,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( B @ ( B @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_List_Ohd ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__in__set_0) ).
thf(1387,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( B @ ( B @ ( A @ c_List_Oset ) @ ( B @ ( A @ c_List_Ohd ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(245,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__subset__iff_1) ).
thf(1091,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_0) ).
thf(825,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(778,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(184,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__in__knows_0) ).
thf(952,plain,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(438,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__analzD_0) ).
thf(1519,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(317,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= ( B @ ( A @ c_List_Olast ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_0) ).
thf(1255,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= ( B @ ( A @ c_List_Olast ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(463,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_3) ).
thf(1570,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(131,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Public_OshrK )
!= ( B @ c_Public_OshrK ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__injective_0) ).
thf(820,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Public_OshrK )
!= ( B @ c_Public_OshrK ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ c_List_Oset ) @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( D @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_notin__set__remove1_0) ).
thf(957,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ c_List_Oset ) @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( D @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(894,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(302,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).
thf(1217,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Oremove1 ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remove1_0) ).
thf(598,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Oremove1 ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(118,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev_0) ).
thf(788,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(371,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( E @ ( D @ c_List_Oset ) @ ( E @ ( D @ ( A @ c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 ) ) @ c_in ) ) )
| ( E @ ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__last__prop__iff_3) ).
thf(1370,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( E @ ( D @ c_List_Oset ) @ ( E @ ( D @ ( A @ c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 ) ) @ c_in ) ) )
| ( E @ ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(916,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(141,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_1) ).
thf(847,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(334,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).
thf(1296,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(522,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(160,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( E @ ( D @ c_List_Oset ) @ ( E @ ( D @ ( A @ c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 ) ) @ c_in ) ) )
| ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__last__prop__iff_4) ).
thf(889,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( E @ ( D @ c_List_Oset ) @ ( E @ ( D @ ( A @ c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 ) ) @ c_in ) ) )
| ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(275,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( D @ c_in ) ) )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_Ofilter ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__empty__conv_0) ).
thf(1159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( D @ c_in ) ) )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_Ofilter ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) )
| ( B = c_Message_Oagent_OSpy )
| ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( C @ ( A @ ( B @ c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1 ) ) @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) )
| ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_ONotes ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__imp__Says__Gets__Notes__initState_0) ).
thf(1027,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) )
| ( B = c_Message_Oagent_OSpy )
| ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( C @ ( A @ ( B @ c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1 ) ) @ ( B @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) )
| ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_ONotes ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Event_OinitState @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__remdups_0) ).
thf(757,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( C @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Cons_0) ).
thf(1195,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( C @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(143,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofilter ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I1_J_0) ).
thf(852,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofilter ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(456,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OSnd_0) ).
thf(1555,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(491,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ c_NS__Shared__Mirabelle_Ons__sharedp )
| ~ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ( tc_Event_Oevent @ ( C @ ( B @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_OFake_0) ).
thf(1634,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ c_NS__Shared__Mirabelle_Ons__sharedp )
| ~ ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ( tc_Event_Oevent @ ( C @ ( B @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ c_NS__Shared__Mirabelle_Ons__sharedp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth__analz_0) ).
thf(1392,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(464,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Obutlast ) @ c_List_Oappend ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__butlast__last__id_0) ).
thf(1573,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Obutlast ) @ c_List_Oappend ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(195,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OdropWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I1_J_0) ).
thf(974,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OdropWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(366,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_ONotes ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Notes__imp__knows_0) ).
thf(1360,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_ONotes ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(319,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Gets_0) ).
thf(1259,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__idem_0) ).
thf(650,plain,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I48_J_0) ).
thf(615,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(306,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( E @ ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( E @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I12_J_0) ).
thf(1227,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( E @ ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( E @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( D @ ( C @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__notin__initState_0) ).
thf(1096,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(449,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(1540,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
= ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups_Osimps_I2_J_1) ).
thf(869,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
= ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( C @ ( B @ c_List_Ofilter ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1__filter__not_0) ).
thf(610,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( C @ ( B @ c_List_Ofilter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(117,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_1) ).
thf(783,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(3,negated_conjecture,
( ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( v_X @ ( v_A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_List_Oappend ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
!= ( tc_Message_Omsg @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( v_X @ c_Set_Oinsert ) ) ) )
| ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( v_X @ ( v_A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_List_Oappend ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
!= ( tc_Event_Oevent @ c_List_Olist_ONil @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(499,plain,
( ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( v_X @ ( v_A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_List_Oappend ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
!= ( tc_Message_Omsg @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( v_X @ c_Set_Oinsert ) ) ) )
| ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( v_X @ ( v_A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_List_Oappend ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
!= ( tc_Event_Oevent @ c_List_Olist_ONil @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(383,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_0) ).
thf(1397,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(519,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(473,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I8_J_0) ).
thf(1592,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(742,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__dropWhile_0) ).
thf(697,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(244,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(1089,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Otl ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl_Osimps_I2_J_0) ).
thf(874,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Otl ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(267,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_Ofilter ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__eq__ConsD_2) ).
thf(1143,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_Ofilter ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) @ c_List_Ohd ) )
= ( A @ ( B @ c_List_Ohd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__append_0) ).
thf(980,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) @ c_List_Ohd ) )
= ( A @ ( B @ c_List_Ohd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(470,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( E @ ( B @ c_List_Oset ) @ ( E @ ( B @ ( A @ c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 ) ) @ c_in ) ) )
| ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__first__prop__iff_4) ).
thf(1587,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( E @ ( B @ c_List_Oset ) @ ( E @ ( B @ ( A @ c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 ) ) @ c_in ) ) )
| ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(461,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( D @ ( C @ ( B @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Says_0) ).
thf(1567,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( D @ ( C @ ( B @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( C @ c_Message_Omsg_OKey ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I41_J_0) ).
thf(669,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( C @ c_Message_Omsg_OKey ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(396,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_1) ).
thf(1424,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
thf(642,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(193,axiom,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Event_Oused @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__knows__Spy__subset__used_0) ).
thf(970,plain,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Event_Oused @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(85,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_0) ).
thf(706,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( A @ ( C @ ( B @ c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1 ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_3) ).
thf(884,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( A @ ( C @ ( B @ c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1 ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(1329,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(332,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).
thf(1292,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(177,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1__append_1) ).
thf(933,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I6_J_0) ).
thf(554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OMPair ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( B @ c_List_Odistinct ) )
| ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( C @ c_List_Odistinct ) )
| ( ( A @ ( B @ c_List_Oset ) )
!= ( A @ ( C @ c_List_Oset ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__distinct__set__unique_0) ).
thf(753,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( B @ c_List_Odistinct ) )
| ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( C @ c_List_Odistinct ) )
| ( ( A @ ( B @ c_List_Oset ) )
!= ( A @ ( C @ c_List_Oset ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(412,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_List_Oappend ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
thf(1461,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( D @ c_List_Orev ) @ c_List_Oappend ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(537,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( D @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__analz__insert__eq_1) ).
thf(901,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( D @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(686,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(391,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__Crypt__subset_0) ).
thf(1414,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(526,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).
thf(1155,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(547,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(515,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(444,axiom,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oparts @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__increasing_0) ).
thf(1530,plain,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oparts @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rotate1_0) ).
thf(654,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(455,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= E )
| ( B
= ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_3) ).
thf(1552,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= E )
| ( B
= ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OdropWhile ) ) )
= ( D @ ( C @ ( A @ c_List_OdropWhile ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_0) ).
thf(1060,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OdropWhile ) ) )
= ( D @ ( C @ ( A @ c_List_OdropWhile ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
= ( C @ c_Event_Oused ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__Gets_0) ).
thf(1002,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ c_Event_Oused )
= ( C @ c_Event_Oused ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(476,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insertI_0) ).
thf(1599,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(347,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Event_OinitState @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__subset__knows_0) ).
thf(1324,plain,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Event_OinitState @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(256,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( C @ ( B @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Notes_0) ).
thf(1114,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( C @ ( B @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(647,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( B @ ( A @ c_List_Osko__List__XtakeWhile__eq__all__conv__1__1 ) ) @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__eq__all__conv_1) ).
thf(997,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( B @ ( A @ c_List_Osko__List__XtakeWhile__eq__all__conv__1__1 ) ) @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(200,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(984,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(169,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_OInj_0) ).
thf(911,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(488,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1627,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_0) ).
thf(1525,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(352,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( D @ ( C @ c_List_Obutlast ) @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( D @ ( D @ ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Obutlast ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__butlast__appendI_1) ).
thf(1333,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( D @ ( C @ c_List_Obutlast ) @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( D @ ( D @ ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Obutlast ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(295,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( A @ ( C @ ( B @ c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2 ) ) @ ( A @ ( C @ ( B @ c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1 ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_5) ).
thf(1202,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( A @ ( C @ ( B @ c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2 ) ) @ ( A @ ( C @ ( B @ c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1 ) ) @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(179,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(938,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__filter_0) ).
thf(633,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(508,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(172,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(921,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(229,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__MPair_0) ).
thf(1054,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth__analz_2) ).
thf(1170,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(330,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(1286,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ tc_fun ) @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_1) ).
thf(674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ tc_fun ) @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(1167,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(185,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
= ( C @ ( D @ ( B @ c_List_Olist__inter ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__inter_Osimps_I2_J_1) ).
thf(953,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
= ( C @ ( D @ ( B @ c_List_Olist__inter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(773,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_0) ).
thf(718,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(174,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).
thf(926,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(327,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(1278,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(265,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_0) ).
thf(1135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_0) ).
thf(618,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(303,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__subset__iff_0) ).
thf(1219,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Otl ) )
= ( C @ ( B @ ( C @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl__append2_0) ).
thf(1273,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Otl ) )
= ( C @ ( B @ ( C @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).
thf(856,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(745,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(79,axiom,
! [B: $i,A: $i] :
~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_1) ).
thf(689,plain,
! [B: $i,A: $i] :
~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(373,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(1374,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(513,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(268,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__snoc_0) ).
thf(1146,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(337,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( D @ c_in ) ) )
| ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__eq__all__conv_0) ).
thf(1301,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( D @ c_in ) ) )
| ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(474,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OInj_0) ).
thf(1595,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(490,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(1631,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(95,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(733,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(41,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( C @ ( B @ ( D @ ( F @ ( E @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__swap_0) ).
thf(584,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( C @ ( B @ ( D @ ( F @ ( E @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( C @ ( B @ ( A @ c_List_Oremove1 ) ) @ c_List_Oset ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__remove1__subset_0) ).
thf(562,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( C @ ( B @ ( A @ c_List_Oremove1 ) ) @ c_List_Oset ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(483,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).
thf(1615,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( B @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(261,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I1_J_0) ).
thf(1125,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(485,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Olast ) )
= ( B @ ( A @ c_List_Ohd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__rev_0) ).
thf(1620,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Olast ) )
= ( B @ ( A @ c_List_Ohd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rev_0) ).
thf(579,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(424,axiom,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__shrK_0) ).
thf(1488,plain,
! [B: $i,A: $i] : ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( C @ c_lessequals ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__trans_0) ).
thf(1007,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( C @ c_lessequals ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(694,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(577,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__trans_0) ).
thf(711,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(398,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( E @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( A @ ( E @ c_List_Oset ) @ ( B @ c_in ) ) )
| ~ ( A @ ( A @ ( D @ c_List_Oset ) @ ( C @ c_in ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_2) ).
thf(1428,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( E @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( A @ ( E @ c_List_Oset ) @ ( B @ c_in ) ) )
| ~ ( A @ ( A @ ( D @ c_List_Oset ) @ ( C @ c_in ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(431,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Ohd ) )
= ( C @ ( A @ c_List_Ohd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__append_1) ).
thf(1503,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Ohd ) )
= ( C @ ( A @ c_List_Ohd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(178,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OFst_0) ).
thf(936,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(572,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(1312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( B @ c_Message_Oanalz ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gen__analz__insert__eq_0) ).
thf(1239,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( B @ c_Message_Oanalz ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(804,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(84,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( E @ ( B @ ( A @ c_List_Olist__update ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).
thf(704,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( E @ ( B @ ( A @ c_List_Olist__update ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(413,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_Message_Oagent_OSpy )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Gets__imp__knows__agents_0) ).
thf(1464,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_Message_Oagent_OSpy )
| ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( C @ c_List_Oset ) @ ( A @ ( B @ c_Event_Oevent_OGets ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ ( B @ c_Event_Oknows ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
= ( C @ c_List_Olist_ONil ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ c_List_Ohd ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__dropWhile_0) ).
thf(1224,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
= ( C @ c_List_Olist_ONil ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ c_List_Ohd ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(364,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(1356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(540,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ c_Message_OinvKey @ c_Message_OinvKey )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_invKey_0) ).
thf(672,plain,
! [A: $i] :
( ( A @ c_Message_OinvKey @ c_Message_OinvKey )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rev_1) ).
thf(713,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(2,negated_conjecture,
( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) )
| ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( v_X @ ( v_A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_List_Oappend ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
!= ( tc_Message_Omsg @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( v_X @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(498,plain,
( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) )
| ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( v_X @ ( v_A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_List_Oappend ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
!= ( tc_Message_Omsg @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( v_X @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).
thf(1058,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(253,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I7_J_0) ).
thf(1107,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(1209,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_2) ).
thf(831,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_1) ).
thf(681,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(258,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oremove1 ) ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1__append_0) ).
thf(1117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oremove1 ) ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(211,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ c_in ) ) )
| ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).
thf(1011,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ c_in ) ) )
| ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(441,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Says_0) ).
thf(1524,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(360,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Osplice ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice__Nil2_0) ).
thf(1349,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Osplice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(471,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_1) ).
thf(1589,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_1) ).
thf(737,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(260,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( B @ ( D @ ( A @ c_List_Osko__List__XtakeWhile__cong__1__1 ) ) ) @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) )
= ( C @ ( B @ ( D @ c_List_OtakeWhile ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__cong_0) ).
thf(1122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( B @ ( D @ ( A @ c_List_Osko__List__XtakeWhile__cong__1__1 ) ) ) @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) )
= ( C @ ( B @ ( D @ c_List_OtakeWhile ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(426,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( A = D )
| ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__ConsD_0) ).
thf(1492,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( A = D )
| ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(478,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( B @ c_List_Oset ) @ ( A @ ( C @ ( B @ c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1 ) ) @ c_in ) ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_3) ).
thf(1603,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( B @ c_List_Oset ) @ ( A @ ( C @ ( B @ c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1 ) ) @ c_in ) ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(156,axiom,
! [A: $i] : ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shrK__in__initState_0) ).
thf(880,plain,
! [A: $i] : ( tc_Message_Omsg @ ( A @ c_Event_OinitState @ ( A @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(224,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubsetD_0) ).
thf(1043,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(374,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Olist__inter ) ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__inter_Osimps_I2_J_0) ).
thf(1376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olist__inter ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Olist__inter ) ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(403,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(1439,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(863,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(282,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orotate1 ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_0) ).
thf(1175,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orotate1 ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(127,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I5_J_0) ).
thf(811,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(416,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( F @ ( A @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( C @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Oops__parts__spies_0) ).
thf(1471,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( F @ ( A @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OMPair ) @ ( D @ c_Message_Omsg_OMPair ) @ ( C @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ ( C @ ( c_Message_Oagent_OServer @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(241,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(1080,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct1__rotate_0) ).
thf(631,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(355,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).
thf(816,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(594,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(348,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).
thf(1325,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(270,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__used_0) ).
thf(1149,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(357,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1344,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(255,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I2_J_0) ).
thf(1112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( C @ ( B @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Gets_0) ).
thf(858,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( C @ ( B @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(457,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oset ) )
= ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps_I2_J_0) ).
thf(1557,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oset ) )
= ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_OtakeWhile ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__takeWhile_0) ).
thf(552,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_OtakeWhile ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(123,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OKey )
!= ( B @ c_Message_Omsg_OKey ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I4_J_0) ).
thf(799,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Omsg_OKey )
!= ( B @ c_Message_Omsg_OKey ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(276,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) )
| ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Notes_0) ).
thf(1162,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) )
| ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(726,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(181,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(943,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(216,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ~ ( C @ ( C @ ( C @ ( B @ ( D @ c_List_Oremove1 ) ) @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__remove1_0) ).
thf(1022,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ~ ( C @ ( C @ ( C @ ( B @ ( D @ c_List_Oremove1 ) ) @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( D @ ( C @ ( B @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( D @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__Says__rev_0) ).
thf(1177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( D @ ( C @ ( B @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( D @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(376,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_0) ).
thf(1381,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(13,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(521,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(293,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( D @ ( A @ c_List_Oset ) @ ( C @ c_Set_Oinsert ) ) @ ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oset ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__update__subset__insert_0) ).
thf(1198,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( D @ ( A @ c_List_Oset ) @ ( C @ c_Set_Oinsert ) ) @ ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oset ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(188,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__parts__knows__Spy_0) ).
thf(959,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(313,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( D @ ( B @ ( C @ c_List_Oreplicate ) ) @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__replicateD_0) ).
thf(1245,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( D @ ( B @ ( C @ c_List_Oreplicate ) ) @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(406,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Oremdups ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_0) ).
thf(1445,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Oremdups ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(115,axiom,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
= ( A @ c_Message_Oanalz ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__idem_0) ).
thf(780,plain,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
= ( A @ c_Message_Oanalz ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(1015,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(201,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(563,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(419,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_1) ).
thf(1477,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ c_List_Olist_ONil @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_0) ).
thf(1102,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ c_List_Olist_ONil @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(459,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__synth_0) ).
thf(1562,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(300,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( H @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OCrypt ) @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NS3__msg__in__parts__spies_0) ).
thf(1213,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( H @ c_Message_Omsg_OMPair ) @ ( G @ c_Message_Omsg_OMPair ) @ ( F @ c_Message_Omsg_OMPair ) @ ( E @ c_Message_Omsg_OCrypt ) @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(133,axiom,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oanalz )
= ( A @ c_Message_Oparts ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__parts_0) ).
thf(827,plain,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oanalz )
= ( A @ c_Message_Oparts ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(206,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).
thf(1000,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(401,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth__eq_1) ).
thf(1435,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( C @ c_Event_Oevent_ONotes ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Notes__imp__used_0) ).
thf(1364,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( B @ c_List_Oset ) @ ( A @ ( C @ c_Event_Oevent_ONotes ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(315,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__parts__not__analz_0) ).
thf(1250,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(239,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ ( B @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( A @ c_Message_Omsg_OKey @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( A @ c_Message_Omsg_OKey @ c_Set_Oinsert ) ) @ ( C @ ( B @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pushes_I6_J_0) ).
thf(1076,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( C @ ( B @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ ( A @ c_Message_Omsg_OKey @ c_Set_Oinsert ) ) )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( D @ ( A @ c_Message_Omsg_OKey @ c_Set_Oinsert ) ) @ ( C @ ( B @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(468,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(1583,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) @ c_List_Oappend ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__dropWhile__id_0) ).
thf(1304,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) @ c_List_Oappend ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(18,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(531,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(414,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OMPair_0) ).
thf(1467,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(121,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(795,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OKey )
!= ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I42_J_0) ).
thf(663,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OKey )
!= ( C @ ( B @ c_Message_Omsg_OCrypt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(394,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth_0) ).
thf(1420,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__analz_0) ).
thf(749,plain,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(214,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
thf(1018,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(454,axiom,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__increasing_0) ).
thf(1551,plain,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(227,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(1049,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(192,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( C @ ( C @ ( E @ ( B @ c_List_Osplice ) ) @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice__Cons__Cons_0) ).
thf(968,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( C @ ( C @ ( E @ ( B @ c_List_Osplice ) ) @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(285,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__Crypt__if_1) ).
thf(1181,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(436,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(1516,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
thf(640,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(217,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(1025,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(194,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( C @ ( A @ c_List_Ofilter ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_1) ).
thf(971,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( C @ ( A @ c_List_Ofilter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(479,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(1605,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(316,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(1252,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(370,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( A @ c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__first__prop__iff_5) ).
thf(1368,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( A @ c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(445,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
thf(1531,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(422,axiom,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Server__not__bad_0) ).
thf(1484,plain,
~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OServer @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( C @ ( B @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__Gets__rev_0) ).
thf(1098,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( C @ ( B @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(452,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1547,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(776,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(236,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( E @ ( B @ c_List_Oset ) @ ( E @ ( B @ ( A @ c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 ) ) @ c_in ) ) )
| ( E @ ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__first__prop__iff_3) ).
thf(1070,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( E @ ( B @ c_List_Oset ) @ ( E @ ( B @ ( A @ c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 ) ) @ c_in ) ) )
| ( E @ ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( D @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__append_0) ).
thf(872,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( D @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(429,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( C @ c_lessequals ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__trans_0) ).
thf(1499,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( C @ c_lessequals ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(336,axiom,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Event_Oused @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_Event_Oused @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_used__nil__subset_0) ).
thf(1300,plain,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Event_Oused @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_Event_Oused @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(287,axiom,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I5_J_0) ).
thf(1186,plain,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(222,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
thf(1038,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Orev ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(344,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( A
= ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_2) ).
thf(1317,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( A
= ( C @ ( C @ ( B @ ( A @ ( E @ ( D @ c_List_Osko__List__Xappend__eq__Cons__conv__1__1 ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(242,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_1) ).
thf(1085,plain,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(808,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(263,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( A @ ( D @ c_List_Oset ) @ ( C @ c_in ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_1) ).
thf(1130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( A @ ( D @ c_List_Oset ) @ ( C @ c_in ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(544,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(321,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Key__synth__eq_1) ).
thf(1262,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(309,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(1235,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(450,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__subset_0) ).
thf(1543,plain,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oparts @ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(318,axiom,
! [B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__notin__used__empty_0) ).
thf(1257,plain,
! [B: $i,A: $i] :
~ ( tc_Message_Omsg @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_Event_Oused @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(447,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Notes_0) ).
thf(1536,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).
thf(656,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(613,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(1221,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(432,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(1506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(397,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Osynth @ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__insert_0) ).
thf(1427,plain,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Osynth @ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(372,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( C @ ( B @ ( D @ c_in ) ) )
| ( C @ ( A @ ( D @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).
thf(1372,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( C @ ( B @ ( D @ c_in ) ) )
| ( C @ ( A @ ( D @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__shrK__Decrypt_0) ).
thf(859,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ c_Public_OshrK @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(203,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( E @ ( D @ c_Event_Oevent_ONotes ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I6_J_0) ).
thf(991,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( E @ ( D @ c_Event_Oevent_ONotes ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(386,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(1404,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(365,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_OSnd_0) ).
thf(1358,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(362,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1353,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__takeWhile_0) ).
thf(600,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(469,axiom,
! [A: $i] :
( ( tc_Event_Oevent @ c_List_Olist_ONil @ ( A @ c_Event_Oknows ) )
= ( A @ c_Event_OinitState ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Nil_0) ).
thf(1585,plain,
! [A: $i] :
( ( tc_Event_Oevent @ c_List_Olist_ONil @ ( A @ c_Event_Oknows ) )
= ( A @ c_Event_OinitState ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( C @ ( B @ ( D @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).
thf(978,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( C @ ( B @ ( D @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(266,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_0) ).
thf(1140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(1,negated_conjecture,
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) )
| ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( v_X @ ( v_A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_List_Oappend ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
!= ( tc_Event_Oevent @ c_List_Olist_ONil @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(497,plain,
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( v_A @ c_in ) ) )
| ( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( v_X @ ( v_A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( tc_Event_Oevent @ c_List_Olist_ONil @ c_List_Oappend ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
!= ( tc_Event_Oevent @ c_List_Olist_ONil @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth__analz_1) ).
thf(876,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(140,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(845,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(411,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( A @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__append_0) ).
thf(1459,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( A @ c_List_Orev ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(176,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ ( B @ ( D @ c_List_OtakeWhile ) ) @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__takeWhileD_0) ).
thf(931,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ ( B @ ( D @ c_List_OtakeWhile ) ) @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(274,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( D @ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp__first_2) ).
thf(1157,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( D @ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(390,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_1) ).
thf(1412,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(759,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__Crypt__if_0) ).
thf(891,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Oanalz @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ( ( tc_Message_Omsg @ ( C @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(380,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__mono_0) ).
thf(1390,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct1__rotate_1) ).
thf(771,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(196,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(976,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__subset__iff_0) ).
thf(903,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(524,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(581,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_0) ).
thf(1448,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(288,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(1189,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(331,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( D @ ( D @ ( C @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( D @ ( D @ ( D @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__remove1_1) ).
thf(1289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( D @ ( D @ ( C @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( D @ ( D @ ( D @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(139,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(844,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(409,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(1453,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(326,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__inter ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__inter_Osimps_I1_J_0) ).
thf(1276,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__inter ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(496,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( B @ c_Message_Oanalz ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__eq_0) ).
thf(1646,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( B @ c_Message_Oanalz ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(83,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
thf(699,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(189,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_2) ).
thf(961,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) )
| ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Notes_1) ).
thf(896,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Oagent @ ( c_Event_Obad @ ( A @ c_in ) ) )
| ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_ONotes ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(493,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_List_Osko__List__XtakeWhile__append2__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_OtakeWhile ) ) @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__append2_1) ).
thf(1639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_List_Osko__List__XtakeWhile__append2__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_OtakeWhile ) ) @ ( B @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(433,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_OtakeWhile ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_0) ).
thf(1508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OtakeWhile ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_OtakeWhile ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(65,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(652,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(489,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_1) ).
thf(1629,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(440,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(1523,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Set_Oinsert ) ) @ ( A @ ( B @ c_Message_Osko__Message__Xanalz__insert__eq__I__1__1 ) @ c_in ) ) )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__insert__eq__I_1) ).
thf(963,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Set_Oinsert ) ) @ ( A @ ( B @ c_Message_Osko__Message__Xanalz__insert__eq__I__1__1 ) @ c_in ) ) )
| ( ( tc_Message_Omsg @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Message_Oanalz )
= ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(10,axiom,
tc_bool @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(517,plain,
tc_bool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( D @ c_in ) ) )
| ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_Ofilter ) ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__id__conv_0) ).
thf(1030,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( D @ c_in ) ) )
| ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_Ofilter ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(510,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
thf(1294,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Orev ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(175,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__last__prop__iff_6) ).
thf(929,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(340,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth_OCrypt_0) ).
thf(1308,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( C @ ( A @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_Message_Omsg @ ( C @ c_Message_Osynth @ ( B @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts_OBody_0) ).
thf(1193,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ ( C @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_2) ).
thf(763,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( D @ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp__last_2) ).
thf(899,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( D @ ( D @ ( D @ ( D @ ( C @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(549,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(225,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__mono_0) ).
thf(1045,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ c_Message_Osynth @ ( A @ c_Message_Osynth @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I49_J_0) ).
thf(620,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OMPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(494,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olength__unique ) )
= ( C @ ( B @ c_List_Olength__unique ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__unique_Osimps_I2_J_0) ).
thf(1642,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olength__unique ) )
= ( C @ ( B @ c_List_Olength__unique ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
thf(1280,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(466,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Ohd ) )
= ( B @ ( A @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__rev_0) ).
thf(1578,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Ohd ) )
= ( B @ ( A @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(136,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_2) ).
thf(833,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__used_1) ).
thf(950,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(307,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( B
= ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_1) ).
thf(1229,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( B
= ( C @ ( E @ ( C @ ( E @ ( D @ ( B @ ( A @ c_List_Osko__List__XCons__eq__append__conv__1__1 ) ) ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(487,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__into__used_0) ).
thf(1625,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( C @ c_Event_OinitState @ c_Message_Oparts @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(130,axiom,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Osynth )
= ( A @ c_Message_Osynth ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__idem_0) ).
thf(818,plain,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Osynth )
= ( A @ c_Message_Osynth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__cut_0) ).
thf(854,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(420,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_0) ).
thf(1480,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(443,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
| ( ( C @ ( A @ ( B @ c_List_OdropWhile ) ) )
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( A
!= ( C @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( A @ ( B @ c_List_OtakeWhile ) ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_2) ).
thf(1527,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ hAPP ) @ hBOOL )
| ( ( C @ ( A @ ( B @ c_List_OdropWhile ) ) )
= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) )
| ( A
!= ( C @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( A @ ( B @ c_List_OtakeWhile ) ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(1148,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(314,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(1248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OKey )
!= ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I40_J_0) ).
thf(790,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Message_Omsg_OKey )
!= ( C @ ( B @ c_Message_Omsg_OMPair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(343,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(1314,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(427,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ ( B @ c_List_Obutlast ) @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__butlastD_0) ).
thf(1495,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ ( B @ c_List_Obutlast ) @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(353,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__into__parts_0) ).
thf(1335,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MPair__synth_1) ).
thf(1056,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( A @ ( C @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(220,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( C @ ( C @ ( C @ ( D @ c_List_Otl ) @ ( B @ c_List_Osplice ) ) @ ( C @ ( D @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_1) ).
thf(1033,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Osplice ) ) )
= ( C @ ( C @ ( C @ ( C @ ( D @ c_List_Otl ) @ ( B @ c_List_Osplice ) ) @ ( C @ ( D @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_OFst_0) ).
thf(1165,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( C @ ( A @ c_Message_Omsg_OMPair ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(796,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(159,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OdropWhile ) ) )
= ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_1) ).
thf(886,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OdropWhile ) ) )
= ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_Message_Oagent_OSpy )
| ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( C @ ( A @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Gets_0) ).
thf(1172,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_Message_Oagent_OSpy )
| ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( C @ ( A @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(389,axiom,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__partsD_0) ).
thf(1410,plain,
! [B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ c_Message_Oparts @ ( A @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).
thf(635,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(417,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( C @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__Spy__analz__bad_0) ).
thf(1473,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ ( C @ c_Public_OshrK @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ~ ( tc_Message_Oagent @ ( c_Event_Obad @ ( C @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(234,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__list__last__prop__iff_5) ).
thf(1065,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ c_List_Oset ) @ ( E @ ( E @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(358,axiom,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__increasing_0) ).
thf(1346,plain,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(481,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_1) ).
thf(1610,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_1) ).
thf(1093,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(728,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(324,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(1268,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oremdups ) )
= ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Ofilter ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__filter_0) ).
thf(596,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oremdups ) )
= ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Ofilter ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(168,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ c_List_Oset ) @ ( E @ c_in ) ) )
| ( E @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OdropWhile ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_OdropWhile ) ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile__append1_0) ).
thf(908,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ c_List_Oset ) @ ( E @ c_in ) ) )
| ( E @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_OdropWhile ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_OdropWhile ) ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_List_Osko__List__XtakeWhile__eq__all__conv__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__eq__all__conv_2) ).
thf(723,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_List_Osko__List__XtakeWhile__eq__all__conv__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_OtakeWhile ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(850,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(691,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(384,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).
thf(1399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(259,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OKey @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_parts__insert__Key_0) ).
thf(1120,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_Set_Oinsert ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Omsg_OKey @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__id__iff__distinct_0) ).
thf(607,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(377,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).
thf(1384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(448,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(1537,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(475,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( D @ ( B @ c_List_Obutlast ) @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( D @ ( D @ ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Obutlast ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__butlast__appendI_0) ).
thf(1597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( D @ ( B @ c_List_Obutlast ) @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( D @ ( D @ ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Obutlast ) @ c_List_Oset ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(199,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Event_Oevent @ ( B @ ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I1_J_0) ).
thf(982,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Event_Oevent @ ( B @ ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
= ( C @ ( B @ c_List_Oremdups ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups_Osimps_I2_J_0) ).
thf(1004,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_in ) ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oremdups ) )
= ( C @ ( B @ c_List_Oremdups ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(351,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1331,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(345,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__synth_1) ).
thf(1320,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( C @ ( A @ c_Message_Omsg_OCrypt ) @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(210,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synth__cut_0) ).
thf(1009,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( B @ ( C @ c_Set_Oinsert ) ) @ c_Message_Osynth @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( C @ c_in ) ) )
| ( tc_Message_Omsg @ ( B @ c_Message_Osynth @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(173,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__replicate_1) ).
thf(923,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(286,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osplice ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Osimps_I1_J_0) ).
thf(1184,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osplice ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(112,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remdups_0) ).
thf(775,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(75,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_0) ).
thf(676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Message_Omsg_OCrypt ) )
!= ( D @ ( C @ c_Message_Omsg_OCrypt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(296,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz__mono__contra_I3_J_0) ).
thf(1204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Ofilter ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__filter_0) ).
thf(592,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Orev ) )
= ( C @ ( C @ ( B @ c_List_Orev ) @ ( A @ c_List_Ofilter ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(708,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(1657,plain,
$false,
inference(e,[status(thm)],[1322,1036,1501,1337,1469,1168,1237,628,518,941,1179,666,1549,1110,1559,1105,1211,1406,683,730,1443,1618,994,1401,1422,1544,1591,878,1533,1437,1486,1041,861,1497,1078,1608,1310,715,1260,945,1063,1354,1458,814,1327,1342,747,913,829,1196,1127,1576,841,1613,1645,1475,782,1441,1601,1386,565,1366,1518,1265,1623,1482,1409,570,1430,1298,1264,1191,1132,542,587,838,1511,751,559,638,1379,1347,1013,881,1115,1568,1362,1100,1232,1087,1514,756,1450,1151,806,1283,1051,905,1489,1415,1418,623,1020,574,1581,966,1215,956,866,1072,1394,1351,660,988,1433,1521,1564,602,766,1104,1242,1074,1206,512,529,1306,1199,534,1067,1636,1047,546,793,1153,761,1387,1091,825,778,952,1519,1255,1570,820,957,894,1217,598,788,1370,916,847,1296,522,889,1159,1027,757,1195,852,1555,1634,1392,1573,974,1360,1259,650,615,1227,1096,1540,869,610,783,499,1397,519,1592,742,697,1089,874,1143,980,1587,1567,669,1424,642,970,706,884,1329,1292,933,554,753,1461,537,901,686,1414,526,1155,547,515,1530,654,1552,1060,1002,1599,1324,1114,647,997,984,911,1627,1525,1333,1202,938,633,508,921,1054,1170,1286,674,1167,953,773,718,926,1278,1135,618,1219,1273,856,745,689,1374,513,1146,1301,1595,1631,733,584,562,1615,1125,1620,579,1488,1007,694,577,711,1428,1503,936,572,1312,1239,804,704,1464,1224,1356,540,672,713,498,1058,1107,1209,831,681,1117,1011,1524,1349,1589,737,1122,1492,1603,880,1043,1376,1439,863,1175,811,1471,1080,631,1339,816,594,1325,1149,1344,1112,858,1557,552,799,1162,726,943,1022,1177,1381,521,1198,959,1245,1445,780,1015,986,563,1477,1102,658,1562,1213,827,1000,1435,1364,1250,1076,1583,1304,531,1467,795,663,1420,749,1018,1551,1049,968,1181,1516,640,1025,971,1605,1252,1368,1531,1484,1098,1547,776,1070,872,1499,1300,1186,1038,1317,1085,808,1130,544,1262,1235,1543,1257,1536,656,613,1221,1506,1427,1372,859,991,1404,1358,1353,600,1585,978,1140,497,876,845,1459,931,1157,1412,759,891,1390,771,976,903,524,581,1448,1189,1289,844,1453,1276,1646,699,961,896,1639,1508,652,1629,1523,963,517,1030,568,510,1294,929,1308,1193,763,899,549,1045,620,1642,1280,1578,833,950,1229,1625,818,854,1480,735,1527,1148,1248,790,1314,1495,506,1335,1056,1033,1165,796,886,1172,1410,635,1473,532,1065,1346,1610,1093,728,1268,596,908,723,850,691,1399,1120,607,1384,1537,1597,982,1004,1331,1320,1009,923,1184,775,676,1204,592,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV776-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/15.42 % Computer : n026.cluster.edu
% 0.15/15.42 % Model : x86_64 x86_64
% 0.15/15.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/15.42 % Memory : 8046.5625MB
% 0.15/15.42 % OS : Linux 6.8.0-71-generic
% 0.15/15.43 % CPULimit : 300
% 0.15/15.43 % WCLimit : 300
% 0.15/15.43 % DateTime : Sat Sep 26 14:59:41 UTC 2026
% 0.15/15.43 % CPUTime :
% 0.15/15.43 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.29/16.28 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.06/16.82 % [INFO] Parsing done (531ms).
% 3.06/16.84 % [INFO] Running in sequential loop mode.
% 4.53/17.40 % [INFO] eprover registered as external prover.
% 4.53/17.41 % [INFO] Scanning for conjecture ...
% 5.23/17.71 % [INFO] Found a conjecture (or negated_conjecture) and 495 axioms. Running axiom selection ...
% 5.87/18.01 % [INFO] Axiom selection finished. Selected 493 axioms (removed 2 axioms).
% 7.73/18.39 % [INFO] Problem is propositional (TPTP CNF).
% 8.10/18.43 % [INFO] Type checking passed.
% 8.10/18.43 % [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 ...
% 20.66/21.75 % External prover 'e' found a proof!
% 20.66/21.75 % [INFO] Killing All external provers ...
% 20.66/21.75 % Time passed: 6114ms (effective reasoning time: 4901ms)
% 20.66/21.76 % Axioms used in derivation (493): cls_set__subset__Cons_0, clsarity_nat__HOL_Oord, cls_butlast__snoc_0, cls_Nil__is__rev__conv_1, cls_Crypt__notin__initState_0, cls_last_Osimps_0, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_parts_OBody_0, cls_takeWhile__cong_1, cls_subset__insert_1, cls_MPair__synth__analz_0, cls_last_Osimps_1, cls_shrK__in__initState_0, cls_sorted__append_2, cls_order__le__less__trans_0, cls_rev__swap_1, cls_not__parts__not__analz_0, cls_remove1__append_0, cls_Cons__eq__append__conv_2, cls_dropWhile_Osimps_I1_J_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_parts__partsD_0, cls_equalityI_0, cls_remove1_Osimps_I2_J_0, cls_insertE_0, cls_knows__Spy__Gets_0, cls_parts_OInj_0, cls_parts_OFst_0, cls_less__fun__def_1, cls_MPair__used_0, cls_Cons__eq__append__conv_5, cls_list__update__overwrite_0, cls_splice_Osimps_I2_J_1, cls_xt1_I12_J_0, cls_knows__Notes_0, cls_set__ConsD_0, cls_butlast_Osimps_I1_J_0, cls_initState__subset__knows_0, cls_in__set__butlast__appendI_1, cls_split__list__last__prop__iff_4, cls_insert__code_1, cls_dropWhile__eq__Cons__conv_0, cls_splice__Cons__Cons_0, cls_le__funD_0, cls_synth__analz__mono_0, cls_append__self__conv_0, cls_list_Oinject_0, cls_filter__is__subset_0, cls_analz__subset__iff_1, cls_Says__imp__used_0, cls_knows__Says_0, cls_tl_Osimps_I1_J_0, cls_linorder__neqE_0, cls_in__set__conv__decomp_1, clsarity_fun__Orderings_Oorder, cls_rev__singleton__conv_1, cls_distinct__filter_0, cls_insert__absorb_0, cls_analz__subset__parts_0, cls_not__Cons__self2_0, cls_remove1__filter__not_0, cls_rev__is__rev__conv_0, cls_mem__def_1, cls_msg_Osimps_I49_J_0, clsarity_nat__Orderings_Olinorder, cls_msg_Osimps_I6_J_1, cls_Says__imp__parts__knows__Spy_0, cls_set__update__subsetI_0, cls_distinct__rev_1, cls_split__list__first__prop__iff_5, cls_filter__eq__ConsD_2, cls_eq__Nil__appendI_0, cls_order__less__trans_0, cls_knows__subset__knows__Says_0, cls_same__append__eq_0, cls_sorted__Cons_2, cls_Gets__imp__knows__agents_0, cls_set__rev__mp_0, cls_list__update__nonempty_1, cls_insert__iff_1, cls_remdups__filter_0, cls_append__eq__Cons__conv_4, cls_Crypt__synth__eq_1, cls_analz__idem_0, cls_insert__subset_0, cls_self__append__conv_0, cls_Crypt__synth__analz_0, cls_in__set__remove1_0, cls_knows__subset__knows__Cons_0, cls_append__Cons_0, cls_distinct_Osimps_I2_J_0, cls_takeWhile__append1_0, cls_subset__insert__iff_2, cls_Key__synth__eq_1, cls_hd__append_0, cls_ns__sharedp_OFake_0, cls_synth__insert_0, cls_NS3__msg__in__parts__spies_0, cls_agent_Osimps_I5_J_0, cls_knows__Nil_0, cls_butlast_Osimps_I2_J_1, cls_set__remove1__subset_0, cls_shrK__in__knows_0, cls_filter_Osimps_I2_J_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_takeWhile__cong_0, cls_replicate__eq__replicate_0, cls_synth_OCrypt_0, cls_Says__imp__spies_0, cls_Server__not__bad_0, cls_sorted_Osimps_I3_J_1, cls_knows__Spy__Notes_1, cls_sorted__takeWhile_0, cls_linorder__not__less_0, cls_sorted__Cons_3, cls_append1__eq__conv_1, cls_parts__increasing_0, cls_sorted__append_5, cls_append__eq__append__conv2_4, cls_in__set__conv__decomp__first_2, cls_append__eq__Cons__conv_0, cls_order__less__asym_0, cls_analz__Crypt__if_1, cls_order__eq__refl_0, cls_notin__set__remove1_0, cls_filter__append_0, cls_msg_Osimps_I7_J_0, cls_order__le__less_0, cls_splice_Osimps_I2_J_0, cls_analz__cut_0, cls_linorder__antisym__conv1_0, cls_distinct_Osimps_I2_J_1, cls_linorder__antisym__conv2_0, cls_distinct_Osimps_I1_J_0, cls_psubset__eq_1, cls_synth__synthD_0, cls_order__less__asym_H_0, cls_parts__subset__iff_1, cls_insert__ident_0, cls_split__list__last__prop__iff_5, cls_in__set__conv__decomp__last_2, cls_synth_OMPair_0, cls_replicate__append__same_0, cls_rev_Osimps_I2_J_0, clsarity_bool__Orderings_Oorder, cls_filter_Osimps_I1_J_0, cls_sorted__append_3, cls_rev__singleton__conv_0, cls_takeWhile_Osimps_I1_J_0, cls_spies__Gets__rev_0, cls_lemma1_0, cls_parts__mono_0, cls_hd__append_1, cls_used__nil__subset_0, cls_psubset__trans_0, cls_distinct__remove1_0, cls_less__le__not__le_2, cls_parts__insert__MPair_0, cls_xt1_I10_J_0, cls_takeWhile__eq__all__conv_2, cls_parts__knows__Spy__subset__used_0, cls_remove1__append_1, cls_not__less__iff__gr__or__eq_0, cls_remdups_Osimps_I2_J_0, cls_remdups__id__iff__distinct_0, cls_Nil__is__append__conv_0, cls_list__update__code_I1_J_0, cls_dropWhile__eq__Cons__conv_1, cls_append__Nil2_0, cls_analz__subset__iff_0, cls_append__self__conv2_0, cls_self__append__conv2_0, cls_msg_Osimps_I40_J_0, cls_Spy__spies__bad__shrK_0, cls_subset__iff_0, cls_distinct__append_0, cls_parts_OSnd_0, cls_takeWhile__tail_0, clsarity_fun__HOL_Oord, cls_remdups__eq__nil__iff_1, cls_Cons__eq__append__conv_3, cls_event_Osimps_I6_J_0, cls_pushes_I5_J_0, cls_self__append__conv2_1, cls_analz__mono__contra_I3_J_0, cls_event_Osimps_I9_J_0, cls_sorted_Osimps_I3_J_2, cls_in__set__butlast__appendI_0, cls_filter__empty__conv_0, cls_insert__code_2, cls_in__set__replicateD_0, cls_List_Oset_Osimps_I2_J_0, cls_rev__predicate1D_0, cls_shrK__in__used_0, cls_analz__conj__parts_0, cls_msg_Osimps_I43_J_0, cls_split__list__first__prop__iff_6, cls_append__eq__append__conv2_5, cls_synth__trans_0, cls_append__eq__Cons__conv_5, cls_Says__imp__analz__Spy_0, cls_append__is__Nil__conv_2, cls_synth__analz__insert__eq_0, cls_last__in__set_0, cls_append__Nil_0, cls_event_Osimps_I3_J_0, cls_last__append_1, cls_append__butlast__last__id_0, cls_singleton__rev__conv_0, cls_set__rotate1_0, cls_xt1_I8_J_0, cls_msg_Osimps_I7_J_1, cls_rev__is__Nil__conv_0, cls_distinct__rev_0, cls_knows__Gets_0, cls_agent_Osimps_I4_J_0, cls_insert__subset_1, cls_analz_OFst_0, cls_set__eq__subset_2, cls_filter__replicate_1, cls_dropWhile__eq__Cons__conv_2, cls_set__rev_0, cls_hd__dropWhile_0, cls_linorder__linear_0, cls_replicate__app__Cons__same_0, cls_parts__insertI_0, cls_rotate__simps_0, cls_synth__increasing_0, cls_filter__replicate_0, cls_append__eq__Cons__conv_1, cls_subset__iff__psubset__eq_0, cls_analz_OInj_0, cls_ns__sharedp_ONil_0, cls_not__leE_0, cls_splice__Nil2_0, cls_analz__parts_0, cls_order__antisym_0, cls_rotate1__is__Nil__conv_0, cls_butlast__append_0, cls_pushes_I12_J_0, cls_not__Cons__self_0, cls_sorted__append_4, cls_msg_Osimps_I4_J_0, cls_self__append__conv_1, cls_rev__filter_0, cls_list__update_Osimps_I1_J_0, cls_order__trans_0, cls_in__set__butlastD_0, cls_subset__trans_0, cls_insertI1_0, cls_linorder__antisym__conv1_1, cls_psubset__insert__iff_6, cls_append__same__eq_0, cls_analz__insert__Crypt__subset_0, clsarity_bool__Orderings_Opreorder, cls_parts__cut__eq_0, cls_splice_Osimps_I1_J_0, cls_MPair__synth_1, cls_Nil__is__append__conv_1, cls_last__append_0, cls_list__update__swap_0, cls_analz__Crypt__if_0, cls_last__snoc_0, cls_mem__def_0, cls_analz__insert__cong_0, cls_msg_Osimps_I48_J_0, cls_knows__Spy__Says_0, cls_neq__Nil__conv_1, cls_sorted__Cons_0, cls_list__inter_Osimps_I1_J_0, cls_analz_ODecrypt_0, cls_distinct1__rotate_0, cls_append__assoc_0, cls_distinct__takeWhile_0, cls_concat__map_Osimps_I2_J_0, cls_subset__refl_0, cls_parts__subset__iff_0, cls_set__update__subset__insert_0, cls_event_Osimps_I2_J_1, cls_linorder__not__le_1, cls_analz__shrK__Decrypt_0, cls_split__list__last__prop__iff_6, cls_butlast__append_1, cls_synth__subset__iff_1, cls_Spy__in__bad_0, cls_not__less__iff__gr__or__eq_1, cls_Cons__eq__append__conv_0, cls_Crypt__synth__analz_1, cls_insertCI_0, cls_psubset__eq_0, cls_msg_Osimps_I42_J_0, cls_remove1_Osimps_I1_J_0, clsarity_nat__Orderings_Opreorder, cls_Notes__imp__knows__Spy_0, cls_order__le__neq__trans_0, cls_Crypt__synth__eq_0, cls_takeWhile__dropWhile__id_0, cls_event_Osimps_I7_J_0, cls_order__eq__iff_2, cls_linorder__antisym__conv3_0, cls_Notes__imp__used_0, cls_analz__mono__contra_I2_J_0, cls_insert__mono_0, cls_synth__analz__insert__eq_1, cls_less__le__not__le_1, cls_list__inter_Osimps_I2_J_0, cls_distinct__append_1, cls_Fake__analz__eq_0, cls_last__rev_0, cls_event_Osimps_I1_J_1, cls_linorder__neqE__ordered__idom_0, cls_sorted__remdups_0, cls_order__neq__le__trans_0, cls_psubset__insert__iff_0, cls_distinct__remdups__id_0, cls_synth_OInj_0, cls_synth__idem_0, cls_dropWhile__eq__Nil__conv_0, cls_tl__append2_0, cls_rev__replicate_0, cls_split__list__first__prop__iff_3, cls_subset__insertI2_0, cls_shrK__injective_0, cls_remdups__eq__nil__right__iff_1, cls_append__eq__Cons__conv_2, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_sorted_Osimps_I1_J_0, cls_psubset__subset__trans_0, cls_MPair__used_1, cls_order__antisym__conv_0, cls_psubsetD_0, cls_sorted__remove1_0, cls_rotate__simps_1, cls_distinct__dropWhile_0, cls_parts__analz_0, cls_event_Osimps_I2_J_0, cls_Crypt__notin__used__empty_0, cls_MPair__synth__analz_2, cls_analz__insert__MPair_0, cls_usedI_0, cls_parts__insert__Key_0, cls_analz__analzD_0, cls_list_Osimps_I3_J_0, cls_rev__eq__Cons__iff_1, cls_distinct_Osimps_I2_J_2, cls_parts__trans_0, cls_set__remdups_0, cls_psubset__insert__iff_3, cls_sorted__distinct__set__unique_0, cls_sorted__append_0, cls_event_Osimps_I4_J_0, cls_linorder__less__linear_0, cls_takeWhile_Osimps_I2_J_1, cls_neq__shrK_0, cls_invKey__eq_0, cls_order__less__le_2, cls_invKey__shrK_0, cls_Crypt__Spy__analz__bad_0, cls_rev__is__Nil__conv_1, cls_insert__subset_2, cls_rotate1__hd__tl_0, cls_xt1_I11_J_0, cls_subsetD_0, cls_Key__synth_0, cls_Crypt__synth_0, cls_analz_OSnd_0, cls_xt1_I6_J_0, cls_dropWhile__append1_0, cls_event_Osimps_I8_J_0, cls_dropWhile_Osimps_I2_J_1, cls_analz__mono__contra_I1_J_0, cls_event_Osimps_I1_J_2, cls_insert__absorb2_0, cls_analz__mono_0, cls_append__is__Nil__conv_1, cls_takeWhile__eq__all__conv_0, cls_analz__insert__eq_0, cls_Nil__is__rev__conv_0, cls_subset__psubset__trans_0, cls_linorder__not__le_0, cls_Cons__eq__appendI_0, cls_event_Osimps_I1_J_0, cls_Crypt__synth_1, cls_synth__subset__iff_0, cls_filter__id__conv_0, cls_MPair__synth_0, cls_append__is__Nil__conv_0, cls_knows__subset__knows__Notes_0, cls_singleton__rev__conv_1, cls_append__eq__appendI_0, cls_set__takeWhileD_1, cls_initState__into__used_0, cls_analz__increasing_0, cls_hd__in__set_0, cls_order__less__irrefl_0, cls_subset__insert_0, cls_msg_Osimps_I41_J_0, cls_Cons__eq__append__conv_4, cls_list_Oinject_1, cls_parts__insert__subset_0, cls_butlast_Osimps_I2_J_0, cls_less__fun__def_2, cls_distinct__remdups_0, cls_hd_Osimps_0, cls_knows__Spy__subset__knows__Spy__Notes_0, cls_rev__append_0, cls_analz__insert__eq__I_1, cls_Cons__eq__append__conv_1, cls_Oops__parts__spies_0, clsarity_fun__Orderings_Opreorder, cls_remove1_Osimps_I2_J_1, cls_Nil__is__append__conv_2, cls_append__replicate__commute_0, cls_set__takeWhileD_0, cls_lemma2_0, cls_insertCI_1, cls_knows__Spy__subset__knows__Spy__Says_0, cls_parts__idem_0, cls_hd__rev_0, cls_rev__swap_0, cls_analz__insertI_0, cls_concat__map_Osimps_I1_J_0, cls_sorted_Osimps_I2_J_0, cls_invKey_0, cls_knows__subset__knows__Gets_0, cls_event_Osimps_I3_J_1, cls_split__list__last__prop__iff_3, cls_tl_Osimps_I2_J_0, cls_analz__insert__eq__I_0, cls_takeWhile_Osimps_I2_J_0, cls_subset__insertI_0, cls_analz__trans_0, cls_order__less__imp__le_0, cls_Says__imp__knows_0, cls_sorted__Cons_1, cls_insert__code_0, cls_sorted__append_1, cls_rev__eq__Cons__iff_0, cls_used__Gets_0, cls_msg_Osimps_I6_J_0, cls_length__unique_Osimps_I2_J_0, cls_gen__analz__insert__eq_0, cls_psubset__insert__iff_2, cls_list__inter_Osimps_I2_J_1, cls_split__list__first__prop__iff_4, cls_in__set__remove1_1, cls_append__eq__Cons__conv_3, cls_insert__commute_0, cls_insert__iff_2, cls_takeWhile__eq__all__conv_1, cls_linorder__not__less_1, cls_append1__eq__conv_0, cls_filter_Osimps_I2_J_1, cls_takeWhile__append2_0, cls_psubset__insert__iff_7, cls_equalityE_0, cls_rev__rev__ident_0, cls_sorted__dropWhile_0, cls_distinct1__rotate_1, cls_Cons__eq__filterD_2, cls_event_Osimps_I5_J_0, cls_parts__insert__Crypt_0, cls_sorted_Osimps_I3_J_0, cls_MPair__synth__analz_1, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_less__fun__def_0, cls_knows__imp__Says__Gets__Notes__initState_0, cls_xt1_I7_J_0, cls_knows__Spy__Notes_0, cls_remdups__eq__nil__iff_0, cls_list_Osimps_I2_J_0, cls_remdups__eq__nil__right__iff_0, cls_pushes_I6_J_0, cls_knows__Spy__subset__knows__Spy__Gets_0, cls_dropWhile_Osimps_I2_J_0, cls_psubset__eq_2, cls_analz__insert_0, cls_takeWhile__cong_2, cls_synth__mono_0, cls_remdups_Osimps_I2_J_1, cls_analz__into__parts_0, cls_predicate1D_0, cls_spies__Says__rev_0, cls_synth__cut_0, cls_list__update__nonempty_0, cls_Notes__imp__knows_0, cls_takeWhile__append2_1, cls_subset__insert__iff_1
% 20.66/21.76 % No. of inferences in proof: 993
% 20.66/21.76 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6114 ms resp. 4901 ms w/o parsing
% 22.56/22.22 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.56/22.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------