%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV772-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n009.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 09:00:31 AM UTC 2026
% Result : Unsatisfiable 11.71s 3.77s
% Output : Refutation 12.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 448
% Syntax : Number of formulae : 897 ( 281 unt; 0 typ; 0 def)
% Number of atoms : 1895 ( 622 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 11018 ( 838 ~; 998 |; 0 &;9182 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 77 ( 75 usr; 11 con; 0-5 aty)
% Number of variables : 2820 ( 0 ^;2820 !; 0 ?;2820 :)
% 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_OSays_decl,type,
c_Event_Oevent_OSays: $i > $i > $i > $i ).
thf(v_A_decl,type,
v_A: $i ).
thf(v_B_decl,type,
v_B: $i ).
thf(v_X_decl,type,
v_X: $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_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(c_List_Odistinct_decl,type,
c_List_Odistinct: $i > $i > $o ).
thf(c_List_Olinorder__class_Oinsort__key_decl,type,
c_List_Olinorder__class_Oinsort__key: $i > $i > $i > $i > $i > $i ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
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_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_Event_Oevent_ONotes_decl,type,
c_Event_Oevent_ONotes: $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_Orotate1_decl,type,
c_List_Orotate1: $i > $i > $i ).
thf(c_Message_Oparts_decl,type,
c_Message_Oparts: $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_Omsg_OCrypt_decl,type,
c_Message_Omsg_OCrypt: $i > $i > $i ).
thf(c_List_OdropWhile_decl,type,
c_List_OdropWhile: $i > $i > $i > $i ).
thf(c_Message_Oanalz_decl,type,
c_Message_Oanalz: $i > $i ).
thf(c_List_Obutlast_decl,type,
c_List_Obutlast: $i > $i > $i ).
thf(c_Message_Osynth_decl,type,
c_Message_Osynth: $i > $i ).
thf(c_Public_OshrK_decl,type,
c_Public_OshrK: $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_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__Xrev__induct__1__2_decl,type,
c_List_Osko__List__Xrev__induct__1__2: $i > $i > $i ).
thf(c_Event_Obad_decl,type,
c_Event_Obad: $i ).
thf(tc_Message_Oagent_decl,type,
tc_Message_Oagent: $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_List_Osko__List__Xrev__induct__1__1_decl,type,
c_List_Osko__List__Xrev__induct__1__1: $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_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_List_Oconcat__map_decl,type,
c_List_Oconcat__map: $i > $i > $i > $i > $i ).
thf(c_Event_OinitState_decl,type,
c_Event_OinitState: $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__Xrev__cases__1__1_decl,type,
c_List_Osko__List__Xrev__cases__1__1: $i > $i > $i ).
thf(c_List_Osko__List__Xrev__cases__1__2_decl,type,
c_List_Osko__List__Xrev__cases__1__2: $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_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_List_Osko__List__Xlinorder__class__Xinsort__is__Cons__1__1_decl,type,
c_List_Osko__List__Xlinorder__class__Xinsort__is__Cons__1__1: $i > $i > $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(187,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/sandbox/benchmark/theBenchmark.p',cls_parts__knows__Spy__subset__used_0) ).
thf(892,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)],[187]) ).
thf(248,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/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_0) ).
thf(1036,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)],[248]) ).
thf(154,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/sandbox/benchmark/theBenchmark.p',cls_Says__imp__knows_0) ).
thf(809,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)],[154]) ).
thf(415,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/sandbox/benchmark/theBenchmark.p',cls_sorted__Cons_2) ).
thf(1411,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)],[415]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_0) ).
thf(629,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)],[78]) ).
thf(439,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
thf(1469,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)],[439]) ).
thf(315,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/sandbox/benchmark/theBenchmark.p',cls_initState__subset__knows_0) ).
thf(1190,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)],[315]) ).
thf(132,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/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(760,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)],[132]) ).
thf(188,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/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_1) ).
thf(893,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)],[188]) ).
thf(339,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/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(1237,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)],[339]) ).
thf(169,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/sandbox/benchmark/theBenchmark.p',cls_dropWhile__append1_0) ).
thf(846,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)],[169]) ).
thf(270,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/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).
thf(1083,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)],[270]) ).
thf(217,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/sandbox/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).
thf(962,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)],[217]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(468,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(91,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/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(666,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)],[91]) ).
thf(366,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/sandbox/benchmark/theBenchmark.p',cls_distinct__append_0) ).
thf(1295,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)],[366]) ).
thf(326,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/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
thf(1211,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)],[326]) ).
thf(234,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/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_0) ).
thf(1005,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)],[234]) ).
thf(364,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Oremdups ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_0) ).
thf(1290,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)],[364]) ).
thf(429,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/sandbox/benchmark/theBenchmark.p',cls_sorted__append_3) ).
thf(1443,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)],[429]) ).
thf(229,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(994,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(419,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/sandbox/benchmark/theBenchmark.p',cls_Notes__imp__knows__Spy_0) ).
thf(1422,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)],[419]) ).
thf(295,axiom,
tc_Event_Oevent @ c_List_Olist_ONil @ c_NS__Shared__Mirabelle_Ons__sharedp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_ONil_0) ).
thf(1142,plain,
tc_Event_Oevent @ c_List_Olist_ONil @ c_NS__Shared__Mirabelle_Ons__sharedp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(511,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)],[32]) ).
thf(369,axiom,
tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Spy__in__bad_0) ).
thf(1305,plain,
tc_Message_Oagent @ ( c_Event_Obad @ ( c_Message_Oagent_OSpy @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(426,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/sandbox/benchmark/theBenchmark.p',cls_parts_OInj_0) ).
thf(1437,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)],[426]) ).
thf(174,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/sandbox/benchmark/theBenchmark.p',cls_analz__subset__iff_0) ).
thf(861,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)],[174]) ).
thf(307,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/sandbox/benchmark/theBenchmark.p',cls_used__nil__subset_0) ).
thf(1173,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)],[307]) ).
thf(301,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/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
thf(1158,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)],[301]) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',cls_psubsetD_0) ).
thf(582,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)],[60]) ).
thf(133,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/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(762,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)],[133]) ).
thf(122,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/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(741,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)],[122]) ).
thf(265,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/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Cons_0) ).
thf(1073,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)],[265]) ).
thf(179,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/sandbox/benchmark/theBenchmark.p',cls_remove1__append_1) ).
thf(873,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)],[179]) ).
thf(323,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/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1205,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)],[323]) ).
thf(1,negated_conjecture,
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( v_X @ ( v_B @ ( v_A @ c_Event_Oevent_OSays ) ) @ 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/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(449,plain,
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( v_X @ ( v_B @ ( v_A @ c_Event_Oevent_OSays ) ) @ 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)],[1]) ).
thf(292,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/sandbox/benchmark/theBenchmark.p',cls_Crypt__notin__used__empty_0) ).
thf(1137,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)],[292]) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(500,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)],[27]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',cls_sorted__dropWhile_0) ).
thf(715,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)],[109]) ).
thf(357,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/sandbox/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_1) ).
thf(1275,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)],[357]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(472,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)],[14]) ).
thf(156,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_0) ).
thf(814,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)],[156]) ).
thf(210,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/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).
thf(945,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)],[210]) ).
thf(332,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/sandbox/benchmark/theBenchmark.p',cls_Notes__imp__used_0) ).
thf(1222,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)],[332]) ).
thf(435,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/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(1458,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)],[435]) ).
thf(303,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(1164,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)],[303]) ).
thf(148,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/sandbox/benchmark/theBenchmark.p',cls_butlast__append_1) ).
thf(797,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)],[148]) ).
thf(125,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/sandbox/benchmark/theBenchmark.p',cls_filter__is__subset_0) ).
thf(747,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)],[125]) ).
thf(197,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/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(913,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)],[197]) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(898,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)],[190]) ).
thf(232,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/sandbox/benchmark/theBenchmark.p',cls_Crypt__notin__initState_0) ).
thf(1001,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)],[232]) ).
thf(406,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__filterD_2) ).
thf(1391,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)],[406]) ).
thf(428,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/sandbox/benchmark/theBenchmark.p',cls_analz__insertI_0) ).
thf(1441,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)],[428]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__decomp__last_2) ).
thf(841,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)],[167]) ).
thf(184,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/sandbox/benchmark/theBenchmark.p',cls_analz__insert__eq__I_1) ).
thf(885,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)],[184]) ).
thf(442,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/sandbox/benchmark/theBenchmark.p',cls_distinct__append_1) ).
thf(1475,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)],[442]) ).
thf(393,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/sandbox/benchmark/theBenchmark.p',cls_analz__analzD_0) ).
thf(1366,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)],[393]) ).
thf(352,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/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_1) ).
thf(1265,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)],[352]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',cls_sorted__Cons_3) ).
thf(829,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)],[162]) ).
thf(275,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/sandbox/benchmark/theBenchmark.p',cls_usedI_0) ).
thf(1095,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)],[275]) ).
thf(335,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/sandbox/benchmark/theBenchmark.p',cls_split__list__last__prop__iff_3) ).
thf(1228,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)],[335]) ).
thf(445,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/sandbox/benchmark/theBenchmark.p',cls_takeWhile__append2_1) ).
thf(1482,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)],[445]) ).
thf(347,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/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1254,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)],[347]) ).
thf(113,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(724,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(111,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/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(719,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)],[111]) ).
thf(142,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/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_2) ).
thf(785,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)],[142]) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(504,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)],[29]) ).
thf(379,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/sandbox/benchmark/theBenchmark.p',cls_analz__mono_0) ).
thf(1330,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)],[379]) ).
thf(166,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/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Notes_1) ).
thf(838,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)],[166]) ).
thf(150,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofilter ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I1_J_0) ).
thf(802,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)],[150]) ).
thf(359,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/sandbox/benchmark/theBenchmark.p',cls_sorted__append_2) ).
thf(1279,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)],[359]) ).
thf(434,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/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).
thf(1455,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)],[434]) ).
thf(206,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/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
thf(934,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)],[206]) ).
thf(316,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).
thf(1191,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)],[316]) ).
thf(259,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/sandbox/benchmark/theBenchmark.p',cls_knows__Gets_0) ).
thf(1059,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)],[259]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(1132,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(51,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/sandbox/benchmark/theBenchmark.p',cls_remove1__filter__not_0) ).
thf(559,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)],[51]) ).
thf(444,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/sandbox/benchmark/theBenchmark.p',cls_analz__insert__cong_0) ).
thf(1479,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)],[444]) ).
thf(220,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/sandbox/benchmark/theBenchmark.p',cls_split__list__last__prop__iff_5) ).
thf(969,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)],[220]) ).
thf(238,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/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(1013,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)],[238]) ).
thf(283,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(1115,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(337,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(1232,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)],[337]) ).
thf(157,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/sandbox/benchmark/theBenchmark.p',cls_remdups_Osimps_I2_J_1) ).
thf(817,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)],[157]) ).
thf(192,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/sandbox/benchmark/theBenchmark.p',cls_hd__append_0) ).
thf(902,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)],[192]) ).
thf(409,axiom,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Osynth @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__increasing_0) ).
thf(1398,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)],[409]) ).
thf(182,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/sandbox/benchmark/theBenchmark.p',cls_Says__imp__parts__knows__Spy_0) ).
thf(881,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)],[182]) ).
thf(448,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/sandbox/benchmark/theBenchmark.p',cls_analz__insert__eq_0) ).
thf(1489,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)],[448]) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(475,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)],[15]) ).
thf(23,axiom,
tc_bool @ class_HOL_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(492,plain,
tc_bool @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(130,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(756,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(144,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ c_List_Oset ) @ ( C @ c_in ) ) )
| ~ ( E @ ( D @ c_List_Odistinct ) )
| ( E @ ( A @ ( E @ ( D @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ c_List_Odistinct ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__insort_2) ).
thf(789,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ c_List_Oset ) @ ( C @ c_in ) ) )
| ~ ( E @ ( D @ c_List_Odistinct ) )
| ( E @ ( A @ ( E @ ( D @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ c_List_Odistinct ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(432,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/sandbox/benchmark/theBenchmark.p',cls_last_Osimps_1) ).
thf(1450,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)],[432]) ).
thf(64,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/sandbox/benchmark/theBenchmark.p',cls_sorted__remdups_0) ).
thf(591,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)],[64]) ).
thf(281,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/sandbox/benchmark/theBenchmark.p',cls_hd__dropWhile_0) ).
thf(1109,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)],[281]) ).
thf(164,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/sandbox/benchmark/theBenchmark.p',cls_split__list__last__prop__iff_4) ).
thf(834,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)],[164]) ).
thf(298,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/sandbox/benchmark/theBenchmark.p',cls_tl__append2_0) ).
thf(1151,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)],[298]) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).
thf(806,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)],[152]) ).
thf(255,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/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__decomp__first_2) ).
thf(1051,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)],[255]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(480,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)],[18]) ).
thf(402,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/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Notes_0) ).
thf(1383,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)],[402]) ).
thf(242,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/sandbox/benchmark/theBenchmark.p',cls_remove1__append_0) ).
thf(1020,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)],[242]) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(574,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)],[57]) ).
thf(224,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/sandbox/benchmark/theBenchmark.p',cls_split__list__first__prop__iff_3) ).
thf(981,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)],[224]) ).
thf(399,axiom,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oparts @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__increasing_0) ).
thf(1377,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)],[399]) ).
thf(100,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/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(692,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)],[100]) ).
thf(176,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/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).
thf(866,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)],[176]) ).
thf(138,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Public_OshrK )
!= ( B @ c_Public_OshrK ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shrK__injective_0) ).
thf(774,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Public_OshrK )
!= ( B @ c_Public_OshrK ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(407,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/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1394,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)],[407]) ).
thf(231,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/sandbox/benchmark/theBenchmark.p',cls_last__append_1) ).
thf(998,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)],[231]) ).
thf(424,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/sandbox/benchmark/theBenchmark.p',cls_split__list__first__prop__iff_4) ).
thf(1433,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)],[424]) ).
thf(321,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/sandbox/benchmark/theBenchmark.p',cls_analz__into__parts_0) ).
thf(1201,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)],[321]) ).
thf(305,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/sandbox/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).
thf(1169,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)],[305]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',cls_takeWhile__eq__all__conv_0) ).
thf(687,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)],[98]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1215,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)],[328]) ).
thf(79,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(634,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)],[79]) ).
thf(341,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/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).
thf(1242,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)],[341]) ).
thf(170,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/sandbox/benchmark/theBenchmark.p',cls_analz_OInj_0) ).
thf(849,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)],[170]) ).
thf(266,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orev ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).
thf(1074,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)],[266]) ).
thf(2,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(452,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)],[2]) ).
thf(200,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/sandbox/benchmark/theBenchmark.p',cls_remdups_Osimps_I2_J_0) ).
thf(920,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)],[200]) ).
thf(209,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( A
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Osko__List__Xrev__cases__1__2 ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Osko__List__Xrev__cases__1__1 ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__cases_0) ).
thf(942,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( A
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Osko__List__Xrev__cases__1__2 ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Osko__List__Xrev__cases__1__1 ) @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(40,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/sandbox/benchmark/theBenchmark.p',cls_list__update__swap_0) ).
thf(529,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)],[40]) ).
thf(202,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/sandbox/benchmark/theBenchmark.p',cls_synth__cut_0) ).
thf(925,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)],[202]) ).
thf(370,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/sandbox/benchmark/theBenchmark.p',cls_rev__append_0) ).
thf(1306,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)],[370]) ).
thf(320,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/sandbox/benchmark/theBenchmark.p',cls_in__set__butlast__appendI_1) ).
thf(1199,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)],[320]) ).
thf(382,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_1) ).
thf(1338,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)],[382]) ).
thf(372,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/sandbox/benchmark/theBenchmark.p',cls_Gets__imp__knows__agents_0) ).
thf(1311,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)],[372]) ).
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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_1) ).
thf(534,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(253,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/sandbox/benchmark/theBenchmark.p',cls_sorted__append_0) ).
thf(1047,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)],[253]) ).
thf(258,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/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).
thf(1057,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)],[258]) ).
thf(215,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/sandbox/benchmark/theBenchmark.p',cls_takeWhile__tail_0) ).
thf(957,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)],[215]) ).
thf(383,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/sandbox/benchmark/theBenchmark.p',cls_Fake__analz__eq_0) ).
thf(1343,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)],[383]) ).
thf(250,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/sandbox/benchmark/theBenchmark.p',cls_last__snoc_0) ).
thf(1042,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)],[250]) ).
thf(388,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/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(1355,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)],[388]) ).
thf(308,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/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).
thf(1174,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)],[308]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',cls_filter__append_0) ).
thf(820,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)],[158]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(1370,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)],[395]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(729,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)],[116]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(1387,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)],[404]) ).
thf(196,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I6_J_0) ).
thf(910,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)],[196]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_ONotes ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I9_J_0) ).
thf(566,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)],[54]) ).
thf(392,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/sandbox/benchmark/theBenchmark.p',cls_analz__insert_0) ).
thf(1365,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)],[392]) ).
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/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(879,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(310,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/sandbox/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
thf(1178,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)],[310]) ).
thf(37,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/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(522,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)],[37]) ).
thf(7,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/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(461,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)],[7]) ).
thf(268,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/sandbox/benchmark/theBenchmark.p',cls_set__update__subset__insert_0) ).
thf(1079,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)],[268]) ).
thf(131,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/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(757,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)],[131]) ).
thf(288,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/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(1128,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)],[288]) ).
thf(360,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/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(1281,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)],[360]) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(710,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)],[107]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(456,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)],[4]) ).
thf(222,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_1) ).
thf(974,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)],[222]) ).
thf(280,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( E @ ( D @ ( B @ ( C @ c_List_Osko__List__Xlinorder__class__Xinsort__is__Cons__1__1 ) ) ) ) @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( ( A @ ( E @ ( D @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) )
= ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insort__is__Cons_1) ).
thf(1106,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( E @ ( D @ ( B @ ( C @ c_List_Osko__List__Xlinorder__class__Xinsort__is__Cons__1__1 ) ) ) ) @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( ( A @ ( E @ ( D @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) )
= ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(198,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/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).
thf(916,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)],[198]) ).
thf(11,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(467,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(493,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)],[24]) ).
thf(325,axiom,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oanalz @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__increasing_0) ).
thf(1210,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)],[325]) ).
thf(318,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(1195,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)],[318]) ).
thf(413,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_0) ).
thf(1407,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)],[413]) ).
thf(411,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/sandbox/benchmark/theBenchmark.p',cls_List_Oset_Osimps_I2_J_0) ).
thf(1402,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)],[411]) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',cls_filter__replicate_0) ).
thf(519,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)],[36]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(1143,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)],[296]) ).
thf(349,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/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
thf(1259,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)],[349]) ).
thf(85,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( D @ ( C @ ( B @ ( E @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ c_List_Odistinct ) )
| ~ ( D @ ( D @ ( C @ c_List_Oset ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__insort_0) ).
thf(650,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( D @ ( C @ ( B @ ( E @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ c_List_Odistinct ) )
| ~ ( D @ ( D @ ( C @ c_List_Oset ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(240,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/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Notes_0) ).
thf(1017,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)],[240]) ).
thf(378,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/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Says_0) ).
thf(1328,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)],[378]) ).
thf(261,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osplice ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I1_J_0) ).
thf(1064,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osplice ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__remdups_0) ).
thf(725,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)],[114]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
thf(593,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(177,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/sandbox/benchmark/theBenchmark.p',cls_split__list__last__prop__iff_6) ).
thf(869,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)],[177]) ).
thf(390,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/sandbox/benchmark/theBenchmark.p',cls_set__ConsD_0) ).
thf(1360,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)],[390]) ).
thf(386,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/sandbox/benchmark/theBenchmark.p',cls_synth__synthD_0) ).
thf(1350,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)],[386]) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(697,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)],[102]) ).
thf(338,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/sandbox/benchmark/theBenchmark.p',cls_list__inter_Osimps_I2_J_0) ).
thf(1234,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)],[338]) ).
thf(141,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/sandbox/benchmark/theBenchmark.p',cls_rev__replicate_0) ).
thf(783,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)],[141]) ).
thf(284,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(1118,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(245,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/sandbox/benchmark/theBenchmark.p',cls_sorted__Cons_1) ).
thf(1028,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)],[245]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(488,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)],[21]) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',cls_notin__set__remove1_0) ).
thf(554,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)],[49]) ).
thf(312,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/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(1182,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)],[312]) ).
thf(436,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( D @ c_List_Olist_ONil @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) )
= ( D @ ( D @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insort__key_Osimps_I1_J_0) ).
thf(1461,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( D @ c_List_Olist_ONil @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) )
= ( D @ ( D @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',cls_psubset__trans_0) ).
thf(669,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)],[92]) ).
thf(420,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/sandbox/benchmark/theBenchmark.p',cls_hd__rev_0) ).
thf(1424,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)],[420]) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(526,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)],[39]) ).
thf(80,axiom,
! [B: $i,A: $i] :
~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).
thf(637,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)],[80]) ).
thf(249,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/sandbox/benchmark/theBenchmark.p',cls_filter__eq__ConsD_2) ).
thf(1039,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)],[249]) ).
thf(47,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_1) ).
thf(547,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)],[47]) ).
thf(418,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I5_J_0) ).
thf(1419,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)],[418]) ).
thf(104,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/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(701,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)],[104]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(515,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)],[34]) ).
thf(367,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/sandbox/benchmark/theBenchmark.p',cls_last__in__set_0) ).
thf(1297,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)],[367]) ).
thf(120,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/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(738,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)],[120]) ).
thf(87,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/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
thf(654,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)],[87]) ).
thf(112,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/sandbox/benchmark/theBenchmark.p',cls_sorted__distinct__set__unique_0) ).
thf(721,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)],[112]) ).
thf(139,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/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_0) ).
thf(779,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)],[139]) ).
thf(84,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/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(647,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)],[84]) ).
thf(351,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/sandbox/benchmark/theBenchmark.p',cls_parts__partsD_0) ).
thf(1263,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)],[351]) ).
thf(277,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/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).
thf(1099,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)],[277]) ).
thf(226,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/sandbox/benchmark/theBenchmark.p',cls_Says__imp__analz__Spy_0) ).
thf(985,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)],[226]) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',cls_takeWhile__eq__all__conv_1) ).
thf(569,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)],[55]) ).
thf(422,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/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(1429,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)],[422]) ).
thf(28,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/sandbox/benchmark/theBenchmark.p',cls_set__remove1__subset_0) ).
thf(503,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)],[28]) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(605,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)],[69]) ).
thf(375,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_1) ).
thf(1318,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)],[375]) ).
thf(271,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/sandbox/benchmark/theBenchmark.p',cls_sorted__append_5) ).
thf(1086,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)],[271]) ).
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/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(541,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(362,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/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(1286,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)],[362]) ).
thf(314,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_2) ).
thf(1187,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)],[314]) ).
thf(213,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/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_0) ).
thf(953,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)],[213]) ).
thf(438,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/sandbox/benchmark/theBenchmark.p',cls_last__rev_0) ).
thf(1466,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)],[438]) ).
thf(264,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/sandbox/benchmark/theBenchmark.p',cls_parts_OBody_0) ).
thf(1071,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)],[264]) ).
thf(244,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I1_J_0) ).
thf(1026,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)],[244]) ).
thf(304,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/sandbox/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
thf(1167,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)],[304]) ).
thf(146,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(794,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',cls_distinct__filter_0) ).
thf(586,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)],[62]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).
thf(662,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)],[89]) ).
thf(185,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/sandbox/benchmark/theBenchmark.p',cls_analz__trans_0) ).
thf(888,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)],[185]) ).
thf(358,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/sandbox/benchmark/theBenchmark.p',cls_synth__insert_0) ).
thf(1278,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)],[358]) ).
thf(291,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/sandbox/benchmark/theBenchmark.p',cls_last__append_0) ).
thf(1135,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)],[291]) ).
thf(127,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/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(750,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)],[127]) ).
thf(279,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/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(1103,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)],[279]) ).
thf(160,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/sandbox/benchmark/theBenchmark.p',cls_split__list__first__prop__iff_6) ).
thf(824,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)],[160]) ).
thf(356,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/sandbox/benchmark/theBenchmark.p',cls_knows__Says_0) ).
thf(1273,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)],[356]) ).
thf(124,axiom,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
= ( A @ c_Message_Oanalz ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__idem_0) ).
thf(745,plain,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
= ( A @ c_Message_Oanalz ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(398,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/sandbox/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_2) ).
thf(1374,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)],[398]) ).
thf(118,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/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_2) ).
thf(733,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)],[118]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(513,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)],[33]) ).
thf(297,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/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(1146,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)],[297]) ).
thf(137,axiom,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Osynth )
= ( A @ c_Message_Osynth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synth__idem_0) ).
thf(772,plain,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Osynth )
= ( A @ c_Message_Osynth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(123,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/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(743,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)],[123]) ).
thf(161,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).
thf(826,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)],[161]) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',cls_in__set__remove1_0) ).
thf(579,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)],[59]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct1__rotate_0) ).
thf(584,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)],[61]) ).
thf(299,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__inter ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__inter_Osimps_I1_J_0) ).
thf(1154,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)],[299]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(562,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(193,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/sandbox/benchmark/theBenchmark.p',cls_list__inter_Osimps_I2_J_1) ).
thf(904,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)],[193]) ).
thf(235,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/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__decomp_1) ).
thf(1007,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)],[235]) ).
thf(101,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/sandbox/benchmark/theBenchmark.p',cls_takeWhile__cong_1) ).
thf(694,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)],[101]) ).
thf(168,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_0) ).
thf(843,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)],[168]) ).
thf(287,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/sandbox/benchmark/theBenchmark.p',cls_parts__cut__eq_0) ).
thf(1125,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)],[287]) ).
thf(334,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/sandbox/benchmark/theBenchmark.p',cls_split__list__first__prop__iff_5) ).
thf(1226,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)],[334]) ).
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/sandbox/benchmark/theBenchmark.p',cls_distinct__remove1_0) ).
thf(545,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(447,axiom,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).
thf(1488,plain,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(641,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)],[82]) ).
thf(293,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/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Gets_0) ).
thf(1139,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)],[293]) ).
thf(207,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( ( A @ ( F @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) )
= ( F @ ( A @ ( F @ ( E @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insort__key_Osimps_I2_J_1) ).
thf(936,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( ( A @ ( F @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) )
= ( F @ ( A @ ( F @ ( E @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ ( D @ c_List_Olist_OCons ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(572,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)],[56]) ).
thf(340,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/sandbox/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_0) ).
thf(1239,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)],[340]) ).
thf(380,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ c_List_Oset ) @ ( A @ ( E @ ( D @ ( B @ ( C @ c_List_Osko__List__Xlinorder__class__Xinsort__is__Cons__1__1 ) ) ) ) @ c_in ) ) )
| ( ( A @ ( E @ ( D @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) )
= ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insort__is__Cons_0) ).
thf(1332,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ c_List_Oset ) @ ( A @ ( E @ ( D @ ( B @ ( C @ c_List_Osko__List__Xlinorder__class__Xinsort__is__Cons__1__1 ) ) ) ) @ c_in ) ) )
| ( ( A @ ( E @ ( D @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) )
= ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(273,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/sandbox/benchmark/theBenchmark.p',cls_takeWhile__append2_0) ).
thf(1090,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)],[273]) ).
thf(151,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/sandbox/benchmark/theBenchmark.p',cls_analz__cut_0) ).
thf(804,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)],[151]) ).
thf(333,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Otl ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I1_J_0) ).
thf(1224,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)],[333]) ).
thf(355,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/sandbox/benchmark/theBenchmark.p',cls_Crypt__synth_0) ).
thf(1271,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)],[355]) ).
thf(396,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/sandbox/benchmark/theBenchmark.p',cls_knows__subset__knows__Says_0) ).
thf(1371,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)],[396]) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(611,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)],[72]) ).
thf(143,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_0) ).
thf(787,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(108,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/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(713,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)],[108]) ).
thf(26,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/sandbox/benchmark/theBenchmark.p',cls_sorted__takeWhile_0) ).
thf(498,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)],[26]) ).
thf(437,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(1464,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)],[437]) ).
thf(211,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/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_1) ).
thf(947,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)],[211]) ).
thf(134,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/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(764,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)],[134]) ).
thf(191,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/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).
thf(900,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)],[191]) ).
thf(163,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/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_1) ).
thf(831,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)],[163]) ).
thf(96,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/sandbox/benchmark/theBenchmark.p',cls_takeWhile__eq__all__conv_2) ).
thf(681,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)],[96]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct1__rotate_1) ).
thf(736,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)],[119]) ).
thf(230,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/sandbox/benchmark/theBenchmark.p',cls_synth__subset__iff_1) ).
thf(996,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)],[230]) ).
thf(31,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( C @ ( B @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ c_List_Odistinct ) )
| ( C @ ( B @ c_List_Odistinct ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__insort_1) ).
thf(509,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( C @ ( B @ ( E @ ( D @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ c_List_Odistinct ) )
| ( C @ ( B @ c_List_Odistinct ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(427,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/sandbox/benchmark/theBenchmark.p',cls_in__set__butlast__appendI_0) ).
thf(1439,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)],[427]) ).
thf(175,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/sandbox/benchmark/theBenchmark.p',cls_filter__replicate_1) ).
thf(863,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)],[175]) ).
thf(74,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I3_J_0) ).
thf(616,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)],[74]) ).
thf(286,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/sandbox/benchmark/theBenchmark.p',cls_gen__analz__insert__eq_0) ).
thf(1122,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)],[286]) ).
thf(186,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/sandbox/benchmark/theBenchmark.p',cls_splice__Cons__Cons_0) ).
thf(890,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)],[186]) ).
thf(16,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(477,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(811,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)],[155]) ).
thf(440,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/sandbox/benchmark/theBenchmark.p',cls_initState__into__used_0) ).
thf(1471,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)],[440]) ).
thf(269,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ ( E @ ( D @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ c_List_Oset ) )
= ( E @ ( E @ ( D @ c_List_Oset ) @ ( C @ c_Set_Oinsert ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__insort_0) ).
thf(1080,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ ( E @ ( D @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) @ c_List_Oset ) )
= ( E @ ( E @ ( D @ c_List_Oset ) @ ( C @ c_Set_Oinsert ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(48,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/sandbox/benchmark/theBenchmark.p',cls_distinct__takeWhile_0) ).
thf(552,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)],[48]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).
thf(609,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)],[71]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remdups__id_0) ).
thf(621,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(483,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)],[19]) ).
thf(218,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/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_0) ).
thf(964,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)],[218]) ).
thf(136,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_ONotes ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I8_J_0) ).
thf(769,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)],[136]) ).
thf(365,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/sandbox/benchmark/theBenchmark.p',cls_Says__imp__used_0) ).
thf(1293,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)],[365]) ).
thf(282,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_1) ).
thf(1112,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)],[282]) ).
thf(306,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/sandbox/benchmark/theBenchmark.p',cls_parts__insert__Crypt_0) ).
thf(1171,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)],[306]) ).
thf(225,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/sandbox/benchmark/theBenchmark.p',cls_synth_OInj_0) ).
thf(983,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)],[225]) ).
thf(408,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OtakeWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I1_J_0) ).
thf(1396,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)],[408]) ).
thf(327,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Osplice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice__Nil2_0) ).
thf(1213,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Osplice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(183,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/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_2) ).
thf(883,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)],[183]) ).
thf(239,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/sandbox/benchmark/theBenchmark.p',cls_analz__mono__contra_I2_J_0) ).
thf(1015,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)],[239]) ).
thf(309,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/sandbox/benchmark/theBenchmark.p',cls_takeWhile__dropWhile__id_0) ).
thf(1176,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)],[309]) ).
thf(425,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/sandbox/benchmark/theBenchmark.p',cls_sorted__append_1) ).
thf(1435,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)],[425]) ).
thf(443,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/sandbox/benchmark/theBenchmark.p',cls_ns__sharedp_OFake_0) ).
thf(1477,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)],[443]) ).
thf(345,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last_Osimps_0) ).
thf(1250,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)],[345]) ).
thf(171,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/sandbox/benchmark/theBenchmark.p',cls_rotate1__hd__tl_0) ).
thf(851,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)],[171]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(1044,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)],[251]) ).
thf(343,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/sandbox/benchmark/theBenchmark.p',cls_hd__in__set_0) ).
thf(1245,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)],[343]) ).
thf(262,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/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Notes_0) ).
thf(1066,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)],[262]) ).
thf(430,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(1445,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)],[430]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(490,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(795,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(203,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/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).
thf(927,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)],[203]) ).
thf(208,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/sandbox/benchmark/theBenchmark.p',cls_knows__imp__Says__Gets__Notes__initState_0) ).
thf(939,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)],[208]) ).
thf(241,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/sandbox/benchmark/theBenchmark.p',cls_synth__analz__mono_0) ).
thf(1018,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)],[241]) ).
thf(129,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/sandbox/benchmark/theBenchmark.p',cls_sorted__remove1_0) ).
thf(754,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)],[129]) ).
thf(5,axiom,
tc_bool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(458,plain,
tc_bool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( A @ c_List_Osko__List__Xrev__induct__1__2 ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__induct_0) ).
thf(836,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( A @ c_List_Osko__List__Xrev__induct__1__2 ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(254,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/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).
thf(1049,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)],[254]) ).
thf(416,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_3) ).
thf(1413,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)],[416]) ).
thf(267,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I4_J_0) ).
thf(1076,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)],[267]) ).
thf(322,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(1203,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)],[322]) ).
thf(324,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/sandbox/benchmark/theBenchmark.p',cls_analz__subset__iff_1) ).
thf(1208,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)],[324]) ).
thf(233,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_1) ).
thf(1003,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)],[233]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(690,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)],[99]) ).
thf(300,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(1156,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)],[300]) ).
thf(221,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/sandbox/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_1) ).
thf(971,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)],[221]) ).
thf(346,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/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).
thf(1252,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)],[346]) ).
thf(394,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/sandbox/benchmark/theBenchmark.p',cls_parts__insertI_0) ).
thf(1368,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)],[394]) ).
thf(353,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/sandbox/benchmark/theBenchmark.p',cls_analz__insert__Crypt__subset_0) ).
thf(1267,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)],[353]) ).
thf(336,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/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).
thf(1230,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)],[336]) ).
thf(256,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/sandbox/benchmark/theBenchmark.p',cls_filter__empty__conv_0) ).
thf(1053,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)],[256]) ).
thf(94,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/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(673,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)],[94]) ).
thf(368,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/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(1300,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)],[368]) ).
thf(145,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/sandbox/benchmark/theBenchmark.p',cls_takeWhile__cong_2) ).
thf(791,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)],[145]) ).
thf(110,axiom,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__analz_0) ).
thf(717,plain,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1262,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(8,axiom,
tc_bool @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(463,plain,
tc_bool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Gets_0) ).
thf(808,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)],[153]) ).
thf(289,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/sandbox/benchmark/theBenchmark.p',cls_not__parts__not__analz_0) ).
thf(1130,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)],[289]) ).
thf(330,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/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(1218,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)],[330]) ).
thf(331,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/sandbox/benchmark/theBenchmark.p',cls_Notes__imp__knows_0) ).
thf(1220,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)],[331]) ).
thf(194,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/sandbox/benchmark/theBenchmark.p',cls_set__subset__Cons_0) ).
thf(907,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)],[194]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(470,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(58,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/sandbox/benchmark/theBenchmark.p',cls_filter__id__conv_0) ).
thf(576,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)],[58]) ).
thf(412,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/sandbox/benchmark/theBenchmark.p',cls_takeWhile__append1_0) ).
thf(1404,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)],[412]) ).
thf(348,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/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(1257,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)],[348]) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_1) ).
thf(703,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)],[105]) ).
thf(243,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_2) ).
thf(1023,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)],[243]) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(613,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)],[73]) ).
thf(361,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ohd ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd_Osimps_0) ).
thf(1284,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)],[361]) ).
thf(67,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/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(600,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)],[67]) ).
thf(446,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/sandbox/benchmark/theBenchmark.p',cls_length__unique_Osimps_I2_J_0) ).
thf(1485,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)],[446]) ).
thf(421,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/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(1427,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)],[421]) ).
thf(115,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/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(727,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)],[115]) ).
thf(294,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/sandbox/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
thf(1140,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)],[294]) ).
thf(236,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/sandbox/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).
thf(1008,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)],[236]) ).
thf(180,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/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(876,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)],[180]) ).
thf(173,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/sandbox/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(859,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)],[173]) ).
thf(397,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_0) ).
thf(1372,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)],[397]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_List_Orev ) )
!= ( B @ ( C @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
thf(595,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)],[66]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(465,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_1) ).
thf(627,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)],[77]) ).
thf(374,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/sandbox/benchmark/theBenchmark.p',cls_butlast__append_0) ).
thf(1316,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)],[374]) ).
thf(311,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/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_2) ).
thf(1180,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)],[311]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__id__iff__distinct_0) ).
thf(556,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rev_1) ).
thf(671,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)],[93]) ).
thf(376,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_0) ).
thf(1321,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)],[376]) ).
thf(223,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_2) ).
thf(976,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)],[223]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rev_0) ).
thf(524,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)],[38]) ).
thf(25,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/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(495,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)],[25]) ).
thf(329,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/sandbox/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(1216,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)],[329]) ).
thf(431,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Obutlast ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).
thf(1448,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)],[431]) ).
thf(433,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/sandbox/benchmark/theBenchmark.p',cls_knows__Notes_0) ).
thf(1453,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)],[433]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(931,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)],[205]) ).
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/sandbox/benchmark/theBenchmark.p',cls_rev__filter_0) ).
thf(539,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(237,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I7_J_0) ).
thf(1010,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)],[237]) ).
thf(405,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/sandbox/benchmark/theBenchmark.p',cls_parts__insert__subset_0) ).
thf(1390,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)],[405]) ).
thf(377,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/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_0) ).
thf(1326,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)],[377]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(517,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(260,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orotate1 ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_0) ).
thf(1062,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)],[260]) ).
thf(278,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/sandbox/benchmark/theBenchmark.p',cls_synth__subset__iff_0) ).
thf(1101,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)],[278]) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',cls_distinct__dropWhile_0) ).
thf(652,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)],[86]) ).
thf(342,axiom,
! [A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__subset__parts_0) ).
thf(1244,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)],[342]) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',cls_set__takeWhileD_1) ).
thf(731,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)],[117]) ).
thf(140,axiom,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oanalz )
= ( A @ c_Message_Oparts ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_analz__parts_0) ).
thf(781,plain,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oanalz )
= ( A @ c_Message_Oparts ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(63,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/sandbox/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).
thf(588,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)],[63]) ).
thf(103,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/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(699,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)],[103]) ).
thf(189,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OdropWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I1_J_0) ).
thf(896,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)],[189]) ).
thf(126,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/sandbox/benchmark/theBenchmark.p',cls_in__set__butlastD_0) ).
thf(748,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)],[126]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1030,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)],[246]) ).
thf(204,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/sandbox/benchmark/theBenchmark.p',cls_concat__map_Osimps_I1_J_0) ).
thf(929,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)],[204]) ).
thf(371,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/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
thf(1308,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)],[371]) ).
thf(317,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/sandbox/benchmark/theBenchmark.p',cls_parts__subset__iff_0) ).
thf(1193,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)],[317]) ).
thf(17,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/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(478,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)],[17]) ).
thf(97,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/sandbox/benchmark/theBenchmark.p',cls_in__set__remove1_1) ).
thf(684,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)],[97]) ).
thf(252,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(1045,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)],[252]) ).
thf(302,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/sandbox/benchmark/theBenchmark.p',cls_analz__insert__eq__I_0) ).
thf(1161,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)],[302]) ).
thf(149,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/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(800,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)],[149]) ).
thf(385,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/sandbox/benchmark/theBenchmark.p',cls_parts__trans_0) ).
thf(1348,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)],[385]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev_0) ).
thf(752,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)],[128]) ).
thf(219,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/sandbox/benchmark/theBenchmark.p',cls_concat__map_Osimps_I2_J_0) ).
thf(967,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)],[219]) ).
thf(401,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/sandbox/benchmark/theBenchmark.p',cls_dropWhile__eq__Nil__conv_0) ).
thf(1380,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)],[401]) ).
thf(172,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/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(854,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)],[172]) ).
thf(344,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/sandbox/benchmark/theBenchmark.p',cls_parts__mono_0) ).
thf(1248,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)],[344]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__idem_0) ).
thf(603,plain,
! [A: $i] :
( ( A @ c_Message_Oparts @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(212,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Orev ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
thf(950,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)],[212]) ).
thf(276,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/sandbox/benchmark/theBenchmark.p',cls_parts__subset__iff_1) ).
thf(1097,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)],[276]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(564,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)],[53]) ).
thf(199,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/sandbox/benchmark/theBenchmark.p',cls_used__Gets_0) ).
thf(918,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)],[199]) ).
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_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(506,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)],[30]) ).
thf(381,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).
thf(1335,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)],[381]) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',cls_set__takeWhileD_0) ).
thf(532,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)],[41]) ).
thf(214,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/sandbox/benchmark/theBenchmark.p',cls_synth__mono_0) ).
thf(955,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)],[214]) ).
thf(384,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/sandbox/benchmark/theBenchmark.p',cls_analz__conj__parts_0) ).
thf(1346,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)],[384]) ).
thf(391,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(1363,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)],[391]) ).
thf(373,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/sandbox/benchmark/theBenchmark.p',cls_Crypt__Spy__analz__bad_0) ).
thf(1314,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)],[373]) ).
thf(414,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/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Says_0) ).
thf(1410,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)],[414]) ).
thf(135,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/sandbox/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).
thf(767,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)],[135]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(1056,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)],[257]) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_0) ).
thf(664,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)],[90]) ).
thf(247,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( ( A @ ( F @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) )
= ( F @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_OCons ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insort__key_Osimps_I2_J_0) ).
thf(1033,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( ( A @ ( F @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olinorder__class_Oinsort__key ) ) ) ) )
= ( F @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_OCons ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(363,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/sandbox/benchmark/theBenchmark.p',cls_Says__imp__spies_0) ).
thf(1288,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)],[363]) ).
thf(319,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/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1197,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)],[319]) ).
thf(216,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(960,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)],[216]) ).
thf(441,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/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1473,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)],[441]) ).
thf(121,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remdups_0) ).
thf(740,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(227,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/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(987,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)],[227]) ).
thf(354,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/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1268,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)],[354]) ).
thf(403,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(1384,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)],[403]) ).
thf(400,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/sandbox/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
thf(1378,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)],[400]) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(644,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)],[83]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Otl ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I2_J_0) ).
thf(822,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)],[159]) ).
thf(423,axiom,
! [A: $i] :
( ( tc_Event_Oevent @ c_List_Olist_ONil @ ( A @ c_Event_Oknows ) )
= ( A @ c_Event_OinitState ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_knows__Nil_0) ).
thf(1431,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)],[423]) ).
thf(178,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( C @ ( A @ c_List_Osko__List__Xrev__induct__1__1 ) @ c_List_Olist_OCons ) ) @ ( C @ ( A @ c_List_Osko__List__Xrev__induct__1__2 ) @ c_List_Oappend ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__induct_1) ).
thf(871,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( C @ ( A @ c_List_Osko__List__Xrev__induct__1__1 ) @ c_List_Olist_OCons ) ) @ ( C @ ( A @ c_List_Osko__List__Xrev__induct__1__2 ) @ c_List_Oappend ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(410,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_3) ).
thf(1399,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)],[410]) ).
thf(285,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/sandbox/benchmark/theBenchmark.p',cls_knows__Spy__Gets_0) ).
thf(1120,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)],[285]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rotate1_0) ).
thf(607,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)],[70]) ).
thf(274,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(1093,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(76,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/sandbox/benchmark/theBenchmark.p',cls_takeWhile__cong_0) ).
thf(624,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)],[76]) ).
thf(387,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/sandbox/benchmark/theBenchmark.p',cls_hd__append_1) ).
thf(1352,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)],[387]) ).
thf(9,axiom,
tc_nat @ class_HOL_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(464,plain,
tc_nat @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(389,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/sandbox/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_0) ).
thf(1357,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)],[389]) ).
thf(6,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(459,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)],[6]) ).
thf(195,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/sandbox/benchmark/theBenchmark.p',cls_analz__mono__contra_I1_J_0) ).
thf(908,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)],[195]) ).
thf(228,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/sandbox/benchmark/theBenchmark.p',cls_sorted__append_4) ).
thf(992,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)],[228]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(486,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(201,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/sandbox/benchmark/theBenchmark.p',cls_synth__trans_0) ).
thf(923,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)],[201]) ).
thf(313,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/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(1184,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)],[313]) ).
thf(88,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/sandbox/benchmark/theBenchmark.p',cls_in__set__replicateD_0) ).
thf(659,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)],[88]) ).
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/sandbox/benchmark/theBenchmark.p',cls_remdups__filter_0) ).
thf(543,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(417,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/sandbox/benchmark/theBenchmark.p',cls_append__butlast__last__id_0) ).
thf(1416,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)],[417]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_1) ).
thf(639,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orev ) @ c_List_Orev ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_0) ).
thf(676,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)],[95]) ).
thf(272,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/sandbox/benchmark/theBenchmark.p',cls_analz__mono__contra_I3_J_0) ).
thf(1088,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)],[272]) ).
thf(106,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/sandbox/benchmark/theBenchmark.p',cls_set__update__subsetI_0) ).
thf(708,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)],[106]) ).
thf(3,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/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(454,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)],[3]) ).
thf(263,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(1069,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(1492,plain,
$false,
inference(e,[status(thm)],[892,1036,809,1411,629,1469,1190,760,893,1237,846,1083,962,468,666,1295,1211,1005,1290,1443,994,1422,1142,511,1305,1437,861,1173,1158,582,762,741,1073,873,1205,449,1137,500,715,1275,472,814,945,1222,1458,1164,797,747,913,898,1001,1391,1441,841,885,1475,1366,1265,829,1095,1228,1482,1254,724,719,785,504,1330,838,802,1279,1455,934,1191,1059,1132,559,1479,969,1013,1115,1232,817,902,1398,881,1489,475,492,756,789,1450,591,1109,834,1151,806,1051,480,1383,1020,574,981,1377,692,866,774,1394,998,1433,1201,1169,687,1215,634,1242,849,1074,452,920,942,529,925,1306,1199,1338,1311,534,1047,1057,957,1343,1042,1355,1174,820,1370,729,1387,910,566,1365,879,1178,522,461,1079,757,1128,1281,710,456,974,1106,916,467,493,1210,1195,1407,1402,519,1143,1259,650,1017,1328,1064,725,593,869,1360,1350,697,1234,783,1118,1028,488,554,1182,1461,669,1424,526,637,1039,547,1419,701,515,1297,738,654,721,779,647,1263,1099,985,569,1429,503,605,1318,1086,541,1286,1187,953,1466,1071,1026,1167,794,586,662,888,1278,1135,750,1103,824,1273,745,1374,733,513,1146,772,743,826,579,584,1154,562,904,1007,694,843,1125,1226,545,1488,641,1139,936,572,1239,1332,1090,804,1224,1271,1371,611,787,713,498,1464,947,764,900,831,681,736,996,509,1439,863,616,1122,890,477,811,1471,1080,552,609,621,483,964,769,1293,1112,1171,983,1396,1213,883,1015,1176,1435,1477,1250,851,1044,1245,1066,1445,490,795,927,939,1018,754,458,836,1049,1413,1076,1203,1208,1003,690,1156,971,1252,1368,1267,1230,1053,673,1300,791,717,1262,463,808,1130,1218,1220,907,470,576,1404,1257,703,1023,613,1284,600,1485,1427,727,1140,1008,876,859,1372,595,465,627,1316,1180,556,671,1321,976,524,495,1216,1448,1453,931,539,1010,1390,1326,517,1062,1101,652,1244,731,781,588,699,896,748,1030,929,1308,1193,478,684,1045,1161,800,1348,752,967,1380,854,1248,603,950,1097,564,918,506,1335,532,955,1346,1363,1314,1410,767,1056,664,1033,1288,1197,960,1473,740,987,1268,1384,1378,644,822,1431,871,1399,1120,607,1093,624,1352,464,1357,459,908,992,486,923,1184,659,543,1416,639,676,1088,708,454,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV772-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.43 % Computer : n009.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 14:56:30 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.64/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.08/1.01 % [INFO] Parsing done (226ms).
% 1.08/1.01 % [INFO] Running in sequential loop mode.
% 2.43/1.23 % [INFO] eprover registered as external prover.
% 2.43/1.23 % [INFO] Scanning for conjecture ...
% 2.86/1.34 % [INFO] Found a conjecture (or negated_conjecture) and 449 axioms. Running axiom selection ...
% 3.29/1.48 % [INFO] Axiom selection finished. Selected 447 axioms (removed 2 axioms).
% 4.61/1.71 % [INFO] Problem is propositional (TPTP CNF).
% 4.61/1.73 % [INFO] Type checking passed.
% 4.61/1.74 % [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 ...
% 11.71/3.76 % External prover 'e' found a proof!
% 11.71/3.76 % [INFO] Killing All external provers ...
% 11.71/3.76 % Time passed: 3209ms (effective reasoning time: 2746ms)
% 11.71/3.77 % Axioms used in derivation (447): 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_sorted__append_2, cls_parts_OBody_0, cls_takeWhile__cong_1, cls_subset__insert_1, cls_last_Osimps_1, 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_Cons__eq__append__conv_5, cls_equalityI_0, cls_remove1_Osimps_I2_J_0, cls_insertE_0, cls_knows__Spy__Gets_0, cls_parts_OInj_0, cls_less__fun__def_1, 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_insort__key_Osimps_I2_J_1, 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_rev__induct_0, cls_in__set__conv__decomp_1, clsarity_fun__Orderings_Oorder, cls_rev__singleton__conv_1, cls_Says__imp__parts__knows__Spy_0, 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, clsarity_nat__Orderings_Olinorder, 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_self__append__conv_0, cls_knows__subset__knows__Says_0, cls_same__append__eq_0, cls_sorted__Cons_2, 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_analz__idem_0, cls_insert__subset_0, cls_distinct__insort_2, cls_Gets__imp__knows__agents_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_hd__append_0, cls_ns__sharedp_OFake_0, cls_synth__insert_0, cls_filter_Osimps_I2_J_0, cls_knows__Nil_0, cls_butlast_Osimps_I2_J_1, cls_set__remove1__subset_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_takeWhile__cong_0, cls_replicate__eq__replicate_0, cls_Says__imp__spies_0, cls_sorted_Osimps_I3_J_1, cls_order__less__asym_0, 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__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_takeWhile_Osimps_I1_J_0, cls_insert__ident_0, cls_split__list__last__prop__iff_5, cls_parts__mono_0, cls_in__set__conv__decomp__last_2, cls_replicate__append__same_0, cls_rev_Osimps_I2_J_0, clsarity_bool__Orderings_Oorder, cls_filter_Osimps_I1_J_0, cls_rev__induct_1, cls_sorted__append_3, cls_rev__singleton__conv_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_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_subset__iff_0, cls_distinct__append_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_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_self__append__conv2_0, cls_insort__key_Osimps_I2_J_0, cls_insert__code_2, cls_in__set__replicateD_0, cls_List_Oset_Osimps_I2_J_0, cls_rev__predicate1D_0, cls_append__is__Nil__conv_2, cls_analz__conj__parts_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_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_set__eq__subset_2, cls_knows__Gets_0, cls_insert__subset_1, cls_filter__replicate_1, cls_dropWhile__eq__Cons__conv_2, cls_set__rev_0, cls_hd__dropWhile_0, cls_linorder__linear_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_replicate__app__Cons__same_0, cls_distinct__insort_1, 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_not__Cons__self_0, cls_sorted__append_4, 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_analz__insert__cong_0, cls_parts__cut__eq_0, cls_splice_Osimps_I1_J_0, cls_Nil__is__append__conv_1, cls_last__append_0, cls_list__update__swap_0, cls_last__snoc_0, cls_mem__def_0, cls_knows__Spy__Says_0, cls_neq__Nil__conv_1, cls_sorted__Cons_0, cls_list__inter_Osimps_I1_J_0, cls_distinct1__rotate_0, cls_append__assoc_0, cls_distinct__takeWhile_0, cls_concat__map_Osimps_I2_J_0, cls_set__insort_0, cls_subset__refl_0, cls_split__list__last__prop__iff_6, cls_parts__subset__iff_0, cls_set__update__subset__insert_0, cls_event_Osimps_I2_J_1, cls_linorder__not__le_1, 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_insertCI_0, cls_psubset__eq_0, cls_takeWhile__dropWhile__id_0, cls_remove1_Osimps_I1_J_0, clsarity_nat__Orderings_Opreorder, cls_Notes__imp__knows__Spy_0, cls_order__le__neq__trans_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_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_psubset__subset__trans_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_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_takeWhile_Osimps_I2_J_1, cls_analz__analzD_0, cls_order__less__le_2, 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_usedI_0, cls_insort__is__Cons_0, cls_Crypt__Spy__analz__bad_0, cls_rev__is__Nil__conv_1, cls_insert__subset_2, cls_rotate1__hd__tl_0, cls_subsetD_0, cls_distinct__insort_0, cls_xt1_I11_J_0, cls_Crypt__synth_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_synth__subset__iff_0, cls_filter__id__conv_0, cls_append__is__Nil__conv_0, cls_insort__is__Cons_1, 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_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, 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_insertCI_1, cls_rev__cases_0, 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_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_length__unique_Osimps_I2_J_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_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_insort__key_Osimps_I1_J_0, cls_gen__analz__insert__eq_0, clsarity_nat__Orderings_Oorder, 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_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_knows__Spy__subset__knows__Spy__Gets_0, cls_dropWhile_Osimps_I2_J_0, cls_psubset__eq_2, cls_synth__cut_0, 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_list__update__nonempty_0, cls_Notes__imp__knows_0, cls_takeWhile__append2_1, cls_subset__insert__iff_1
% 11.71/3.77 % No. of inferences in proof: 897
% 11.71/3.77 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3209 ms resp. 2746 ms w/o parsing
% 12.98/4.08 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.98/4.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------