%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV778-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:00:32 AM UTC 2026
% Result : Unsatisfiable 19.16s 6.11s
% Output : Refutation 21.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 435
% Syntax : Number of formulae : 871 ( 383 unt; 0 typ; 0 def)
% Number of atoms : 1639 ( 744 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 10650 ( 654 ~; 768 |; 0 &;9228 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 104 ( 102 usr; 9 con; 0-5 aty)
% Number of variables : 2944 ( 0 ^;2944 !; 0 ?;2944 :)
% 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_Olist_ONil_decl,type,
c_List_Olist_ONil: $i > $i ).
thf(tc_Event_Oevent_decl,type,
tc_Event_Oevent: $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_List_Orev_decl,type,
c_List_Orev: $i > $i ).
thf(c_Fun_Oinj__on_decl,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_List_Oset_decl,type,
c_List_Oset: $i > $i > $i ).
thf(c_List_Odistinct_decl,type,
c_List_Odistinct: $i > $i > $o ).
thf(c_List_Omap_decl,type,
c_List_Omap: $i > $i > $i > $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_List_Oremove1_decl,type,
c_List_Oremove1: $i > $i > $i > $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(tc_bool_decl,type,
tc_bool: $i ).
thf(c_List_Otake_decl,type,
c_List_Otake: $i > $i > $i > $i ).
thf(c_List_Oappend_decl,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_Nat_Osize__class_Osize_decl,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_List_Olist__update_decl,type,
c_List_Olist__update: $i > $i > $i > $i > $i ).
thf(c_List_Odrop_decl,type,
c_List_Odrop: $i > $i > $i > $i ).
thf(c_List_Orotate_decl,type,
c_List_Orotate: $i > $i > $i > $i ).
thf(c_List_Ofilter_decl,type,
c_List_Ofilter: $i > $i > $i > $i ).
thf(c_List_Otl_decl,type,
c_List_Otl: $i > $i > $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
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_Message_Oagent_OFriend_decl,type,
c_Message_Oagent_OFriend: $i > $i ).
thf(c_Message_Oagent_OServer_decl,type,
c_Message_Oagent_OServer: $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_List_OdropWhile_decl,type,
c_List_OdropWhile: $i > $i > $i > $i ).
thf(c_List_Olist__all2_decl,type,
c_List_Olist__all2: $i > $i > $i > $i > $i > $o ).
thf(c_Event_Oevent_OGets_decl,type,
c_Event_Oevent_OGets: $i > $i > $i ).
thf(c_Set_Oinsert_decl,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(c_List_Orotate1_decl,type,
c_List_Orotate1: $i > $i > $i ).
thf(c_List_Oremdups_decl,type,
c_List_Oremdups: $i > $i > $i ).
thf(c_List_Onull_decl,type,
c_List_Onull: $i > $i > $o ).
thf(c_fequal_decl,type,
c_fequal: $i > $i ).
thf(c_Map_Omap__upds_decl,type,
c_Map_Omap__upds: $i > $i > $i > $i > $i > $i ).
thf(class_HOL_Oord_decl,type,
class_HOL_Oord: $i > $o ).
thf(class_Divides_Osemiring__div_decl,type,
class_Divides_Osemiring__div: $i > $o ).
thf(c_Divides_Odiv__class_Omod_decl,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(c_List_Ofoldr_decl,type,
c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).
thf(c_Event_Oevent_OSays_decl,type,
c_Event_Oevent_OSays: $i > $i > $i > $i ).
thf(c_List_Olistsp_decl,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(c_List_Osublist_decl,type,
c_List_Osublist: $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_Divides_Oring__div_decl,type,
class_Divides_Oring__div: $i > $o ).
thf(c_List_Olist__all_decl,type,
c_List_Olist__all: $i > $i > $i > $o ).
thf(c_Message_Oagent_Oagent__case_decl,type,
c_Message_Oagent_Oagent__case: $i > $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(c_Message_Osko__Message__Xagent__Xcase__cong__1__1_decl,type,
c_Message_Osko__Message__Xagent__Xcase__cong__1__1: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Osetsum_decl,type,
c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).
thf(c_List_Olistsum_decl,type,
c_List_Olistsum: $i > $i > $i ).
thf(c_List_Oreplicate_decl,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(c_List_Obutlast_decl,type,
c_List_Obutlast: $i > $i > $i ).
thf(c_List_Ohd_decl,type,
c_List_Ohd: $i > $i > $i ).
thf(c_Message_Oagent_Oagent__rec_decl,type,
c_Message_Oagent_Oagent__rec: $i > $i > $i > $i > $i > $i ).
thf(c_List_Olist__ex_decl,type,
c_List_Olist__ex: $i > $i > $i > $o ).
thf(c_List_Ofoldl_decl,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(v_sko__List__XdropWhile__Xinduct__2_decl,type,
v_sko__List__XdropWhile__Xinduct__2: $i > $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(v_sko__List__Xlist__Xinduct__2_decl,type,
v_sko__List__Xlist__Xinduct__2: $i > $i ).
thf(tc_Message_Omsg_decl,type,
tc_Message_Omsg: $i ).
thf(v_sko__List__Xlist__Xinduct__1_decl,type,
v_sko__List__Xlist__Xinduct__1: $i > $i ).
thf(c_List_Olist_Olist__rec_decl,type,
c_List_Olist_Olist__rec: $i > $i > $i > $i > $i > $i ).
thf(v_sko__List__Xlist__update__Xinduct__2_decl,type,
v_sko__List__Xlist__update__Xinduct__2: $i > $i ).
thf(c_List_Olist_Olist__case_decl,type,
c_List_Olist_Olist__case: $i > $i > $i > $i > $i > $i ).
thf(v_sko__Message__Xagent__Xsplit__asm__1_decl,type,
v_sko__Message__Xagent__Xsplit__asm__1: $i > $i > $i > $i ).
thf(c_List_Olast_decl,type,
c_List_Olast: $i > $i > $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(v_sko__List__Xzip__Xinduct__1_decl,type,
v_sko__List__Xzip__Xinduct__1: $i > $i ).
thf(v_sko__List__Xzip__Xinduct__2_decl,type,
v_sko__List__Xzip__Xinduct__2: $i > $i ).
thf(v_sko__Message__Xagent__Xsplit__1_decl,type,
v_sko__Message__Xagent__Xsplit__1: $i > $i > $i > $i ).
thf(v_sko__List__Xremove1__Xinduct__1_decl,type,
v_sko__List__Xremove1__Xinduct__1: $i > $i ).
thf(v_sko__List__Xremove1__Xinduct__2_decl,type,
v_sko__List__Xremove1__Xinduct__2: $i > $i ).
thf(c_List_Olistrelp_decl,type,
c_List_Olistrelp: $i > $i > $i > $i > $o ).
thf(v_sko__List__Xlistset__Xinduct__2_decl,type,
v_sko__List__Xlistset__Xinduct__2: $i > $i ).
thf(c_List_Ofiltermap_decl,type,
c_List_Ofiltermap: $i > $i > $i > $i > $i ).
thf(v_sko__List__Xconcat__Xinduct__2_decl,type,
v_sko__List__Xconcat__Xinduct__2: $i > $i ).
thf(v_sko__List__Xtake__Xinduct__2_decl,type,
v_sko__List__Xtake__Xinduct__2: $i > $i ).
thf(v_sko__List__XremoveAll__Xinduct__1_decl,type,
v_sko__List__XremoveAll__Xinduct__1: $i > $i ).
thf(v_sko__List__XremoveAll__Xinduct__2_decl,type,
v_sko__List__XremoveAll__Xinduct__2: $i > $i ).
thf(v_sko__List__Xlast__Xinduct__1_decl,type,
v_sko__List__Xlast__Xinduct__1: $i > $i ).
thf(v_sko__List__Xlast__Xinduct__2_decl,type,
v_sko__List__Xlast__Xinduct__2: $i > $i ).
thf(v_sko__List__Xlistsum__Xinduct__2_decl,type,
v_sko__List__Xlistsum__Xinduct__2: $i > $i ).
thf(c_NS__Shared__Mirabelle_Ons__sharedp_decl,type,
c_NS__Shared__Mirabelle_Ons__sharedp: $i > $o ).
thf(c_List_Olist__inter_decl,type,
c_List_Olist__inter: $i > $i > $i > $i ).
thf(c_Event_OinitState_decl,type,
c_Event_OinitState: $i > $i ).
thf(v_sko__List__Xlist__update__Xinduct__1_decl,type,
v_sko__List__Xlist__update__Xinduct__1: $i > $i ).
thf(v_sko__List__Xlistset__Xinduct__1_decl,type,
v_sko__List__Xlistset__Xinduct__1: $i > $i ).
thf(v_sko__List__Xlistsum__Xinduct__1_decl,type,
v_sko__List__Xlistsum__Xinduct__1: $i > $i ).
thf(v_sko__List__Xmap__Xinduct__2_decl,type,
v_sko__List__Xmap__Xinduct__2: $i > $i ).
thf(v_sko__List__Xdistinct__Xinduct__2_decl,type,
v_sko__List__Xdistinct__Xinduct__2: $i > $i ).
thf(v_sko__List__XtakeWhile__Xinduct__1_decl,type,
v_sko__List__XtakeWhile__Xinduct__1: $i > $i ).
thf(v_sko__List__XtakeWhile__Xinduct__2_decl,type,
v_sko__List__XtakeWhile__Xinduct__2: $i > $i ).
thf(v_sko__List__Xfoldl__Xinduct__2_decl,type,
v_sko__List__Xfoldl__Xinduct__2: $i > $i ).
thf(v_sko__List__XdropWhile__Xinduct__1_decl,type,
v_sko__List__XdropWhile__Xinduct__1: $i > $i ).
thf(v_sko__List__Xdistinct__Xinduct__1_decl,type,
v_sko__List__Xdistinct__Xinduct__1: $i > $i ).
thf(199,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) )
| ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
thf(892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) )
| ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oset ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__is__subset_0) ).
thf(809,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)],[161]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Ohd ) )
= ( C @ ( A @ c_List_Ohd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__append_1) ).
thf(1337,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)],[395]) ).
thf(82,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(629,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( C @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Gets_0) ).
thf(1190,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)],[328]) ).
thf(349,axiom,
! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistsp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(1237,plain,
! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistsp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(207,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xlist__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinduct_0) ).
thf(909,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xlist__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(281,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( c_Message_Oagent_OSpy @ ( C @ ( B @ ( A @ c_Message_Oagent_Oagent__rec ) ) ) ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Orecs_I3_J_0) ).
thf(1083,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( c_Message_Oagent_OSpy @ ( C @ ( B @ ( A @ c_Message_Oagent_Oagent__rec ) ) ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(52,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_List_Omap ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__imp__length__eq_0) ).
thf(555,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_List_Omap ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(319,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xlast__Xinduct__2 @ ( A @ v_sko__List__Xlast__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Oinduct_1) ).
thf(1168,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xlast__Xinduct__2 @ ( A @ v_sko__List__Xlast__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ohd ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd_Osimps_0) ).
thf(760,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)],[140]) ).
thf(386,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ ( B @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__replicate_0) ).
thf(1315,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ ( B @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Oset ) @ ( B @ ( A @ c_List_Oset ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__subset__Cons_0) ).
thf(518,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)],[35]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ ( A @ c_List_Orev @ hAPP ) @ ( tc_nat @ ( B @ ( A @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__take_0) ).
thf(977,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ ( A @ c_List_Orev @ hAPP ) @ ( tc_nat @ ( B @ ( A @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(105,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( E @ ( B @ ( A @ c_List_Olist__update ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).
thf(683,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)],[105]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__drop_0) ).
thf(730,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(275,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(1068,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Otl ) )
= ( C @ ( B @ ( C @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl__append2_0) ).
thf(1205,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)],[336]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
thf(597,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(321,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
= ( C @ c_List_Olist_ONil ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ c_List_Ohd ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__dropWhile_0) ).
thf(1173,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)],[321]) ).
thf(314,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(1158,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__remdups_0) ).
thf(762,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)],[141]) ).
thf(306,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).
thf(1142,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)],[306]) ).
thf(365,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( B @ c_List_Oremdups ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_0) ).
thf(1269,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)],[365]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( B @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_0) ).
thf(614,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)],[74]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Otake ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__take_0) ).
thf(677,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Otake ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).
thf(1078,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)],[279]) ).
thf(304,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( D @ ( C @ ( B @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( D @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__Says__rev_0) ).
thf(1137,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( D @ ( C @ ( B @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( D @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rotate_1) ).
thf(533,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Olist_OCons ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).
thf(550,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)],[49]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(472,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
thf(538,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(317,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_List_Olist__all ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_2) ).
thf(1164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_List_Olist__all ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(154,axiom,
tc_bool @ class_HOL_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(797,plain,
tc_bool @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(397,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xmap__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Oinduct_0) ).
thf(1342,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xmap__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_OdropWhile ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__dropWhile_0) ).
thf(747,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_OdropWhile ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(342,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).
thf(1222,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)],[342]) ).
thf(217,axiom,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OSpy ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I6_J_0) ).
thf(930,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OSpy ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_1) ).
thf(898,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)],[202]) ).
thf(246,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = c_Message_Oagent_OSpy )
| ( ( D @ ( B @ ( F @ ( A @ ( E @ c_Message_Oagent_Oagent__case ) ) ) ) )
= ( D @ ( B @ ( G @ ( C @ ( E @ c_Message_Oagent_Oagent__case ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ ( B @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_6) ).
thf(1001,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = c_Message_Oagent_OSpy )
| ( ( D @ ( B @ ( F @ ( A @ ( E @ c_Message_Oagent_Oagent__case ) ) ) ) )
= ( D @ ( B @ ( G @ ( C @ ( E @ c_Message_Oagent_Oagent__case ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ ( B @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(175,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(841,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(265,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_1) ).
thf(1046,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)],[265]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(1359,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)],[406]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).
thf(565,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)],[56]) ).
thf(1,negated_conjecture,
( ( tc_Event_Oevent @ c_List_Olist_ONil @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
!= ( tc_Event_Oevent @ c_List_Olist_ONil @ ( tc_Event_Oevent @ c_List_Orev @ hAPP ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(436,plain,
( ( tc_Event_Oevent @ c_List_Olist_ONil @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
!= ( tc_Event_Oevent @ c_List_Olist_ONil @ ( tc_Event_Oevent @ c_List_Orev @ hAPP ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Oremove1 ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__remove1_0) ).
thf(829,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)],[169]) ).
thf(286,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = c_Message_Oagent_OServer )
| ~ ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__1 ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_6) ).
thf(1095,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = c_Message_Oagent_OServer )
| ~ ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__1 ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(269,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__asm__1 ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_10) ).
thf(1055,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__asm__1 ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(373,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ c_List_Orev @ hAPP ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rev_0) ).
thf(1287,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ c_List_Orev @ hAPP ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(119,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_List_Olistsp ) ) )
| ~ ( D @ ( C @ ( A @ c_List_Olistsp ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).
thf(719,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_List_Olistsp ) ) )
| ~ ( D @ ( C @ ( A @ c_List_Olistsp ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(150,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
thf(785,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(136,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(751,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)],[136]) ).
thf(157,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct1__rotate_1) ).
thf(802,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)],[157]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Odrop ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__drop_0) ).
thf(460,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Odrop ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Osublist ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__sublistI_0) ).
thf(587,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Osublist ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(389,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( E
= ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__asm__1 ) ) @ c_Message_Oagent_OFriend ) )
| ( E = c_Message_Oagent_OSpy )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_7) ).
thf(1323,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( E
= ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__asm__1 ) ) @ c_Message_Oagent_OFriend ) )
| ( E = c_Message_Oagent_OSpy )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(77,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Otake ) ) )
= ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Otake ) ) @ ( B @ c_List_Omap ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__map_0) ).
thf(619,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Otake ) ) )
= ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Otake ) ) @ ( B @ c_List_Omap ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__mod__geq_0) ).
thf(838,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(385,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xlistset__Xinduct__2 @ ( A @ v_sko__List__Xlistset__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listset_Oinduct_1) ).
thf(1313,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xlistset__Xinduct__2 @ ( A @ v_sko__List__Xlistset__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(369,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(1279,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)],[369]) ).
thf(271,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = c_Message_Oagent_OServer )
| ~ ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__asm__1 ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_6) ).
thf(1059,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = c_Message_Oagent_OServer )
| ~ ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__asm__1 ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(302,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_Message_Oagent_OSpy )
| ( ( tc_Event_Oevent @ ( C @ ( B @ ( A @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( C @ ( A @ c_Event_Oknows ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Gets_0) ).
thf(1132,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)],[302]) ).
thf(182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( B @ ( B @ ( D @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( B @ ( D @ ( C @ c_List_Oappend ) ) ) )
| ( A
!= ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_5) ).
thf(853,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( B @ ( B @ ( D @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( B @ ( D @ ( C @ c_List_Oappend ) ) ) )
| ( A
!= ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(283,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( E
= ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__1 ) ) @ c_Message_Oagent_OFriend ) )
| ( E = c_Message_Oagent_OSpy )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_7) ).
thf(1087,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( E
= ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__1 ) ) @ c_Message_Oagent_OFriend ) )
| ( E = c_Message_Oagent_OSpy )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(354,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Otl ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl_Osimps_I1_J_0) ).
thf(1247,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)],[354]) ).
thf(190,axiom,
tc_nat @ class_HOL_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(870,plain,
tc_nat @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( B @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(1362,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)],[407]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev @ hAPP ) @ c_List_Oappend ) ) @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
thf(1100,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Orev @ hAPP ) @ c_List_Oappend ) ) @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(347,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1232,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)],[347]) ).
thf(232,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ ( B @ ( A @ c_List_Orev @ hAPP ) @ c_List_Ohd ) )
= ( A @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__rev_0) ).
thf(969,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ ( B @ ( A @ c_List_Orev @ hAPP ) @ c_List_Ohd ) )
= ( A @ ( B @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
thf(606,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(430,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( E @ ( F @ ( B @ ( D @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ c_Message_Oagent_OFriend ) )
| ( D = c_Message_Oagent_OSpy )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Message_Oagent_Oagent__case ) ) ) ) )
= ( E @ ( D @ ( G @ ( F @ ( A @ c_Message_Oagent_Oagent__case ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_4) ).
thf(1415,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( E @ ( F @ ( B @ ( D @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ c_Message_Oagent_OFriend ) )
| ( D = c_Message_Oagent_OSpy )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Message_Oagent_Oagent__case ) ) ) ) )
= ( E @ ( D @ ( G @ ( F @ ( A @ c_Message_Oagent_Oagent__case ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ ( A @ c_List_Oappend ) ) )
= C )
| ( A
!= ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_2) ).
thf(475,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ ( A @ c_List_Oappend ) ) )
= C )
| ( A
!= ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Oremove1 ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).
thf(492,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)],[25]) ).
thf(66,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ~ ( D @ ( B @ ( G @ ( F @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append_2) ).
thf(591,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ~ ( D @ ( B @ ( G @ ( F @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(262,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osplit_1) ).
thf(1040,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(91,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( D @ ( F @ ( C @ c_List_Oappend ) ) @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) )
= ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upds__append2__drop_0) ).
thf(646,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( D @ ( F @ ( C @ c_List_Oappend ) ) @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) )
= ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Oremove1 ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remove1_0) ).
thf(514,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)],[33]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).
thf(1151,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)],[311]) ).
thf(159,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remdups_0) ).
thf(806,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_List_Oremdups ) @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(371,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( C @ ( A @ hAPP ) @ ( B @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__replicate_0) ).
thf(1283,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( C @ ( A @ hAPP ) @ ( B @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(267,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( c_Message_Oagent_OSpy @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_2) ).
thf(1051,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( c_Message_Oagent_OSpy @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(380,axiom,
! [B: $i,A: $i] :
( ( A @ tc_List_Olist @ ( B @ ( A @ c_List_Orev @ hAPP ) @ c_Nat_Osize__class_Osize ) )
= ( A @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rev_0) ).
thf(1302,plain,
! [B: $i,A: $i] :
( ( A @ tc_List_Olist @ ( B @ ( A @ c_List_Orev @ hAPP ) @ c_Nat_Osize__class_Osize ) )
= ( A @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(138,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(756,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(431,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( F @ ( A @ ( E @ c_Message_Oagent_Oagent__case ) ) ) ) )
= ( D @ ( B @ ( F @ ( C @ ( G @ c_Message_Oagent_Oagent__case ) ) ) ) ) )
| ( B = c_Message_Oagent_OServer )
| ( ( D @ ( C @ ( A @ ( B @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_3) ).
thf(1418,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( F @ ( A @ ( E @ c_Message_Oagent_Oagent__case ) ) ) ) )
= ( D @ ( B @ ( F @ ( C @ ( G @ c_Message_Oagent_Oagent__case ) ) ) ) ) )
| ( B = c_Message_Oagent_OServer )
| ( ( D @ ( C @ ( A @ ( B @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_List_Olist__all ) ) )
| ~ ( D @ ( C @ ( A @ c_List_Olist__all ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__append_2) ).
thf(623,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_List_Olist__all ) ) )
| ~ ( D @ ( C @ ( A @ c_List_Olist__all ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(485,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)],[22]) ).
thf(172,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Odrop ) ) )
= ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( B @ c_List_Omap ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__map_0) ).
thf(834,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Odrop ) ) )
= ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( B @ c_List_Omap ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(416,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(1383,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)],[416]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofiltermap ) ) ) )
= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filtermap_Osimps_I1_J_0) ).
thf(1020,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofiltermap ) ) ) )
= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(205,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( E @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofoldr ) ) ) ) )
= ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
thf(905,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( E @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofoldr ) ) ) ) )
= ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( B @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(480,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)],[21]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(687,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__snoc_0) ).
thf(1119,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)],[296]) ).
thf(402,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xdistinct__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Oinduct_0) ).
thf(1351,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xdistinct__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(244,axiom,
! [B: $i,A: $i] : ( A @ tc_List_Olist @ ( A @ tc_List_Olist @ ( B @ ( A @ c_List_Orev @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__rev_0) ).
thf(998,plain,
! [B: $i,A: $i] : ( A @ tc_List_Olist @ ( A @ tc_List_Olist @ ( B @ ( A @ c_List_Orev @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(240,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_List_Odistinct ) )
| ( A @ ( B @ ( A @ c_List_Orev @ hAPP ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rev_1) ).
thf(988,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_List_Odistinct ) )
| ( A @ ( B @ ( A @ c_List_Orev @ hAPP ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(426,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__XdropWhile__Xinduct__2 @ ( A @ v_sko__List__XdropWhile__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Oinduct_1) ).
thf(1405,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__XdropWhile__Xinduct__2 @ ( A @ v_sko__List__XdropWhile__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(334,axiom,
tc_Event_Oevent @ c_List_Olist_ONil @ c_NS__Shared__Mirabelle_Ons__sharedp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONil_0) ).
thf(1201,plain,
tc_Event_Oevent @ c_List_Olist_ONil @ c_NS__Shared__Mirabelle_Ons__sharedp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(30,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ~ ( B @ ( D @ ( A @ ( C @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( B @ ( D @ ( B @ ( A @ ( E @ c_List_Oappend ) ) @ ( D @ ( C @ ( F @ c_List_Oappend ) ) @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( F @ c_Nat_Osize__class_Osize ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append1_5) ).
thf(507,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( E @ ( F @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ~ ( B @ ( D @ ( A @ ( C @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( B @ ( D @ ( B @ ( A @ ( E @ c_List_Oappend ) ) @ ( D @ ( C @ ( F @ c_List_Oappend ) ) @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( F @ c_Nat_Osize__class_Osize ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
thf(527,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(193,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
thf(877,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(109,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
thf(692,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(290,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oremove1 ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I1_J_0) ).
thf(1104,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)],[290]) ).
thf(352,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Omap ) ) ) )
= ( F @ ( D @ ( A @ hAPP ) @ ( C @ ( F @ ( E @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Olist__update ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__update_0) ).
thf(1242,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Olist__update ) ) ) @ ( A @ c_List_Omap ) ) ) )
= ( F @ ( D @ ( A @ hAPP ) @ ( C @ ( F @ ( E @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Olist__update ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(179,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__remdups__leq_0) ).
thf(849,plain,
! [B: $i,A: $i] : ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(277,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(1074,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( D @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__append_0) ).
thf(452,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)],[8]) ).
thf(213,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( E @ c_Message_Oagent_OFriend @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_1) ).
thf(920,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( E @ c_Message_Oagent_OFriend @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
thf(529,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_List_Omap ) ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__map_0) ).
thf(546,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_List_Omap ) ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(215,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(925,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)],[215]) ).
thf(382,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_Map_Omap__upds ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upds__Nil1_0) ).
thf(1306,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_Map_Omap__upds ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(162,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( F @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ~ ( D @ ( B @ ( C @ ( A @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( D @ ( C @ ( F @ c_List_Oappend ) ) @ ( B @ ( A @ ( E @ c_List_Oappend ) ) @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( F @ c_Nat_Osize__class_Osize ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append2_5) ).
thf(810,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( F @ ( E @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ~ ( D @ ( B @ ( C @ ( A @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( D @ ( C @ ( F @ c_List_Oappend ) ) @ ( B @ ( A @ ( E @ c_List_Oappend ) ) @ ( G @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( E @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( F @ c_Nat_Osize__class_Osize ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(384,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( D @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( C @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Says_0) ).
thf(1311,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)],[384]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(714,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(512,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)],[32]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Omap ) ) ) )
= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).
thf(942,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Omap ) ) ) )
= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Odistinct ) )
| ( D @ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__map_1) ).
thf(439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Odistinct ) )
| ( D @ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).
thf(798,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(270,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(1057,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( D @ ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) )
= ( tc_Message_Omsg @ ( D @ ( A @ c_Event_Oknows ) @ ( C @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Says_0) ).
thf(1274,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)],[367]) ).
thf(418,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( D @ c_List_Olist_ONil @ ( C @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Nil_0) ).
thf(1387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( D @ c_List_Olist_ONil @ ( C @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(894,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)],[200]) ).
thf(147,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( C @ ( A @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_3) ).
thf(778,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( C @ ( A @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) )
= E )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(263,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).
thf(1042,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
thf(1355,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)],[404]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_0) ).
thf(820,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(164,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_1) ).
thf(815,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)],[164]) ).
thf(350,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1238,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)],[350]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xremove1__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Oinduct_0) ).
thf(1123,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xremove1__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(186,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Odrop ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Obutlast ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__butlast_0) ).
thf(862,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Obutlast ) @ ( A @ c_List_Odrop ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Obutlast ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(110,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( B @ ( A @ c_fequal @ c_List_Olist__all2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__eq_0) ).
thf(693,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( B @ ( A @ c_fequal @ c_List_Olist__all2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( D @ ( A @ c_List_Oset ) @ ( C @ c_Set_Oinsert ) ) @ ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Oset ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__update__subset__insert_0) ).
thf(630,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)],[83]) ).
thf(151,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(788,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(410,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( F @ ( C @ ( A @ c_List_Olistrelp ) ) ) )
| ( D @ ( D @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olistrelp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listrelp_OCons_0) ).
thf(1370,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( F @ ( C @ ( A @ c_List_Olistrelp ) ) ) )
| ( D @ ( D @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olistrelp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(178,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oset ) )
= ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps_I2_J_0) ).
thf(847,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)],[178]) ).
thf(259,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).
thf(1032,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(408,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Ofilter ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__filterD_2) ).
thf(1365,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)],[408]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__drop_0) ).
thf(625,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_Nat_Osize__class_Osize ) )
= ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(181,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).
thf(852,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(323,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= ( E @ ( F @ ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(1178,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= ( E @ ( F @ ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(1210,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)],[338]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(1027,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)],[257]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
thf(757,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).
thf(1128,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)],[300]) ).
thf(370,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( D @ ( E @ c_List_Orev @ hAPP ) @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( E @ ( B @ ( D @ ( C @ ( B @ c_List_Orev @ hAPP ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__rev1_1) ).
thf(1281,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( D @ ( E @ c_List_Orev @ hAPP ) @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( E @ ( B @ ( D @ ( C @ ( B @ c_List_Orev @ hAPP ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(420,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(1392,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)],[420]) ).
thf(250,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xremove1__Xinduct__2 @ ( A @ v_sko__List__Xremove1__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Oinduct_1) ).
thf(1012,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xremove1__Xinduct__2 @ ( A @ v_sko__List__Xremove1__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ ( A @ c_List_Orev @ hAPP ) @ ( tc_nat @ ( B @ ( A @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__drop_0) ).
thf(1106,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ ( A @ c_List_Orev @ hAPP ) @ ( tc_nat @ ( B @ ( A @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(211,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) )
= ( E @ ( F @ ( D @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Orecs_I2_J_0) ).
thf(916,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) )
= ( E @ ( F @ ( D @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Orotate ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rotate_0) ).
thf(467,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Orotate ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(377,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__all2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Nil_1) ).
thf(1296,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__all2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__dropWhile_0) ).
thf(665,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)],[98]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) )
| ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
thf(583,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Oappend ) ) @ ( A @ c_List_Olistsp ) ) )
| ( C @ ( B @ ( A @ c_List_Olistsp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).
thf(522,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(331,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Otake ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).
thf(1195,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Otake ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(427,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_List_Orev @ hAPP ) @ c_List_Olistsum ) )
= ( A @ ( B @ c_List_Olistsum ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum__rev_0) ).
thf(1407,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_List_Orev @ hAPP ) @ c_List_Olistsum ) )
= ( A @ ( B @ c_List_Olistsum ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__drop_0) ).
thf(456,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(176,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_List_Olist__ex ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_2) ).
thf(842,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_List_Olist__ex ) ) )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(425,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_1) ).
thf(1402,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)],[425]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
thf(874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_1) ).
thf(1259,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)],[360]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(650,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)],[93]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( C @ ( B @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__Gets__rev_0) ).
thf(1064,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Event_Oevent @ ( tc_Event_Oevent @ ( tc_Event_Oevent @ c_List_Olist_ONil @ ( C @ ( B @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) )
= ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(725,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)],[122]) ).
thf(189,axiom,
tc_nat @ class_Divides_Osemiring__div,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
thf(869,plain,
tc_nat @ class_Divides_Osemiring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
= ( C @ ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Otake ) ) @ ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__drop__take_0) ).
thf(783,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
= ( C @ ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Otake ) ) @ ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(422,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Orotate ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_1) ).
thf(1397,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Orotate ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__id__iff__distinct_0) ).
thf(519,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(131,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(742,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(412,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( D @ ( C @ ( B @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Says_0) ).
thf(1375,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)],[412]) ).
thf(297,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__XremoveAll__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_removeAll_Oinduct_0) ).
thf(1121,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__XremoveAll__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(293,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_1) ).
thf(1111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(345,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).
thf(1227,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)],[345]) ).
thf(315,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osublist ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sublist__nil_0) ).
thf(1160,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Osublist ) ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(325,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( E
= ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__asm__1 ) ) @ c_Message_Oagent_OFriend ) )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_8) ).
thf(1182,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( E
= ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__asm__1 ) ) @ c_Message_Oagent_OFriend ) )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(901,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)],[203]) ).
thf(433,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = c_Message_Oagent_OServer )
| ~ ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__1 ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( E = c_Message_Oagent_OSpy )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_5) ).
thf(1424,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = c_Message_Oagent_OServer )
| ~ ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__1 ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( E = c_Message_Oagent_OSpy )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__list__update_0) ).
thf(637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(24,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append_0) ).
thf(489,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
= ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Orotate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__conv__mod_0) ).
thf(679,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
= ( C @ ( B @ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_List_Orotate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(115,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_0) ).
thf(706,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)],[115]) ).
thf(196,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= ( E @ ( F @ ( D @ ( E @ ( F @ ( C @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__append_0) ).
thf(884,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Oappend ) ) @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) )
= ( E @ ( F @ ( D @ ( E @ ( F @ ( C @ ( B @ ( A @ c_List_Ofoldl ) ) ) ) @ ( A @ c_List_Ofoldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(391,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Odrop ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Nil_0) ).
thf(1329,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Odrop ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(375,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
= ( D @ ( C @ ( B @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I5_J_0) ).
thf(1292,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( F @ ( E @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
= ( D @ ( C @ ( B @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(218,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( E @ c_List_Orev @ hAPP ) @ ( B @ ( D @ c_List_Orev @ hAPP ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__rev_0) ).
thf(933,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( E @ c_List_Orev @ hAPP ) @ ( B @ ( D @ c_List_Orev @ hAPP ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Oset ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__drop__subset_0) ).
thf(554,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Oset ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(137,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( B @ c_List_Odistinct ) )
| ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( C @ c_List_Odistinct ) )
| ( ( A @ ( B @ c_List_Oset ) )
!= ( A @ ( C @ c_List_Oset ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__distinct__set__unique_0) ).
thf(753,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( B @ c_List_Odistinct ) )
| ~ ( A @ ( C @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ ( C @ c_List_Odistinct ) )
| ( ( A @ ( B @ c_List_Oset ) )
!= ( A @ ( C @ c_List_Oset ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ c_List_Olist_ONil ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
!= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
thf(1263,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)],[362]) ).
thf(113,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(701,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)],[113]) ).
thf(378,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ ( B @ ( A @ c_List_Orev @ hAPP ) @ c_List_Olast ) )
= ( A @ ( B @ c_List_Ohd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__rev_0) ).
thf(1297,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ ( B @ ( A @ c_List_Orev @ hAPP ) @ c_List_Olast ) )
= ( A @ ( B @ c_List_Ohd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__map_0) ).
thf(738,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(363,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(1266,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(329,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( D @ ( C @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Gets_0) ).
thf(1192,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)],[329]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ ( C @ ( B @ ( D @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
thf(721,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)],[120]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(503,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)],[28]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( C @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Cons_0) ).
thf(1150,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)],[310]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_List_Olist__all ) ) )
| ( B @ ( C @ ( B @ c_List_Orev @ hAPP ) @ ( A @ c_List_Olist__all ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__rev_1) ).
thf(1249,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_List_Olist__all ) ) )
| ( B @ ( C @ ( B @ c_List_Orev @ hAPP ) @ ( A @ c_List_Olist__all ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(238,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ c_List_Olist_ONil @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osplit_0) ).
thf(984,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ c_List_Olist_ONil @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( A @ ( C @ ( B @ c_Event_Oevent_OGets ) @ c_List_Olist_OCons ) ) @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( A @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Gets_0) ).
thf(911,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)],[208]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( B @ c_List_Oremdups ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__remdups_0) ).
thf(569,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)],[58]) ).
thf(435,axiom,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).
thf(1429,plain,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(393,axiom,
! [B: $i,A: $i] :
~ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__ex ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I1_J_0) ).
thf(1333,plain,
! [B: $i,A: $i] :
~ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__ex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(220,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( E @ c_Message_Oagent_OFriend @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_1) ).
thf(938,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( E @ c_Message_Oagent_OFriend @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(45,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( C @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_Map_Omap__upds ) ) ) ) )
= ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upds__append__drop_0) ).
thf(541,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( C @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_Map_Omap__upds ) ) ) ) )
= ( D @ ( B @ ( C @ ( A @ ( E @ c_Map_Omap__upds ) ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(320,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(1170,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)],[320]) ).
thf(327,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( D @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).
thf(1187,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( D @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(146,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(773,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)],[146]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ c_List_Odistinct ) )
| ( ( A @ ( D @ ( D @ ( C @ c_List_Oset ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ ( A @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ c_List_Olistsum ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__set__distinct__conv__listsum_0) ).
thf(662,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ c_List_Odistinct ) )
| ( ( A @ ( D @ ( D @ ( C @ c_List_Oset ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ ( A @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ c_List_Olistsum ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(335,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( A
!= ( C @ ( A @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(1202,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)],[335]) ).
thf(153,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_0) ).
thf(792,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)],[153]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct1__rotate_0) ).
thf(558,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)],[53]) ).
thf(276,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_List_Odrop ) ) )
= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__all_0) ).
thf(1071,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_List_Odrop ) ) )
= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(226,axiom,
! [B: $i,A: $i] :
( A
= ( A @ ( B @ c_List_Orev @ hAPP ) @ ( B @ c_List_Orev @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_0) ).
thf(953,plain,
! [B: $i,A: $i] :
( A
= ( A @ ( B @ c_List_Orev @ hAPP ) @ ( B @ c_List_Orev @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(326,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xlistsum__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_Oinduct_0) ).
thf(1185,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xlistsum__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(303,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Orotate1 ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_0) ).
thf(1135,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)],[303]) ).
thf(356,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons_2) ).
thf(1251,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(308,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(1146,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( B @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(183,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( E @ ( C @ ( G @ c_List_Olist_OCons ) ) @ ( D @ ( B @ ( F @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons_1) ).
thf(856,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( E @ ( C @ ( G @ c_List_Olist_OCons ) ) @ ( D @ ( B @ ( F @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(745,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)],[133]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__beyond_0) ).
thf(444,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(341,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( A @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( A @ c_List_Orev @ hAPP ) )
!= ( A @ ( A @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).
thf(1219,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( A @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) )
| ( ( B @ ( A @ c_List_Orev @ hAPP ) )
!= ( A @ ( A @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rotate_0) ).
thf(824,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_Nat_Osize__class_Osize ) )
= ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ c_List_Orev @ hAPP ) @ ( A @ c_List_Orotate ) ) )
= ( B @ ( C @ ( tc_nat @ ( tc_nat @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Orotate ) ) @ ( B @ c_List_Orev @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__rev_0) ).
thf(1154,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ c_List_Orev @ hAPP ) @ ( A @ c_List_Orotate ) ) )
= ( B @ ( C @ ( tc_nat @ ( tc_nat @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ ( A @ c_Divides_Odiv__class_Omod ) ) @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Orotate ) ) @ ( B @ c_List_Orev @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(234,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_OdropWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I1_J_0) ).
thf(975,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)],[234]) ).
thf(126,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( G @ ( F @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append_1) ).
thf(732,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( G @ ( C @ c_List_Oappend ) ) @ ( B @ ( F @ ( A @ c_List_Oappend ) ) @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( G @ ( F @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
!= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(299,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = c_Message_Oagent_OServer )
| ( E
= ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__asm__1 ) ) @ c_Message_Oagent_OFriend ) )
| ( E = c_Message_Oagent_OSpy )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_3) ).
thf(1125,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = c_Message_Oagent_OServer )
| ( E
= ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__asm__1 ) ) @ c_Message_Oagent_OFriend ) )
| ( E = c_Message_Oagent_OSpy )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_impossible__Cons_0) ).
thf(743,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( A @ ( C @ ( B @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(958,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)],[228]) ).
thf(248,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osplit__asm_1) ).
thf(1007,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_b @ ( t_a @ ( t_b @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ c_List_Olist_Olist__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(111,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(694,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)],[111]) ).
thf(168,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( A @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_2) ).
thf(826,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( A @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
= D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(116,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( A
= ( C @ ( D @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_0) ).
thf(711,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( A
= ( C @ ( D @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(358,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olast ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_0) ).
thf(1256,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)],[358]) ).
thf(344,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( B @ ( A @ c_Event_Oknows ) @ ( A @ c_Event_OinitState @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__subset__knows_0) ).
thf(1226,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)],[344]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
thf(641,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(305,axiom,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I5_J_0) ).
thf(1139,plain,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( D @ ( C @ c_Event_Oevent_OGets ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_1) ).
thf(498,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)],[27]) ).
thf(284,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Onull ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__null_1) ).
thf(1090,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Onull ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) )
| ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__append_0) ).
thf(804,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) )
| ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1258,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(224,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( C @ ( B @ c_List_Oreplicate ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__replicate_0) ).
thf(947,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)],[224]) ).
thf(343,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__update ) ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).
thf(1224,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)],[343]) ).
thf(100,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__def_0) ).
thf(672,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ ( A @ ( E @ c_List_Olist__all2 ) ) ) ) )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) )
= ( D @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(170,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(831,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)],[170]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_Nat_Osize__class_Osize ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__replicate_0) ).
thf(681,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_Nat_Osize__class_Osize ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(736,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)],[128]) ).
thf(401,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ c_List_Olist_ONil @ ( A @ c_List_Orev @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
thf(1349,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ c_List_Olist_ONil @ ( A @ c_List_Orev @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(57,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( E @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofoldr ) ) ) ) )
= ( F @ ( D @ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ c_List_Ofoldr ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr__append_0) ).
thf(567,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( E @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Ofoldr ) ) ) ) )
= ( F @ ( D @ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Ofoldr ) ) ) ) @ ( B @ ( A @ c_List_Ofoldr ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ ( A @ c_List_Orev @ hAPP ) @ ( B @ c_List_Ofilter ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__filter_0) ).
thf(1144,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ ( C @ ( A @ c_List_Orev @ hAPP ) @ ( B @ c_List_Ofilter ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(75,axiom,
tc_bool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(616,plain,
tc_bool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(413,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xfoldl__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl_Oinduct_0) ).
thf(1376,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xfoldl__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(142,axiom,
! [A: $i] :
( c_Message_Oagent_OServer
!= ( A @ c_Message_Oagent_OFriend ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I2_J_0) ).
thf(764,plain,
! [A: $i] :
( c_Message_Oagent_OServer
!= ( A @ c_Message_Oagent_OFriend ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( B @ ( A @ c_List_Orev @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
thf(979,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( A @ c_List_Olist_ONil )
!= ( B @ ( A @ c_List_Orev @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(241,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_Oremove1 ) ) )
= ( D @ ( C @ ( B @ c_List_Ofilter ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1__filter__not_0) ).
thf(990,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)],[241]) ).
thf(243,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ c_Message_Oagent_OFriend @ ( C @ ( B @ ( A @ c_Message_Oagent_Oagent__case ) ) ) ) )
= ( D @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I9_J_0) ).
thf(996,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ c_Message_Oagent_OFriend @ ( C @ ( B @ ( A @ c_Message_Oagent_Oagent__case ) ) ) ) )
= ( D @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(194,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(880,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)],[194]) ).
thf(92,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(649,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(280,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( D @ ( A @ c_List_Orev @ hAPP ) @ c_List_Oappend ) ) ) )
| ( ( B @ ( A @ c_List_Orev @ hAPP ) )
!= ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
thf(1080,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( C @ c_List_Olist_OCons ) ) @ ( D @ ( A @ c_List_Orev @ hAPP ) @ c_List_Oappend ) ) ) )
| ( ( B @ ( A @ c_List_Orev @ hAPP ) )
!= ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(84,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(631,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( A @ ( C @ c_fequal @ c_List_Olist__all2 ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__eq_1) ).
thf(535,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( A @ ( C @ c_fequal @ c_List_Olist__all2 ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__remdups__eq_1) ).
thf(609,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(67,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( B
= ( C @ ( E @ ( C @ ( D @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_1) ).
thf(594,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ tc_List_Olist @ ( D @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( B
= ( C @ ( E @ ( C @ ( D @ ( C @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( E @ ( D @ c_List_Oappend ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(316,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ c_List_Orev @ hAPP ) @ ( A @ c_List_Olist__all ) ) )
| ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__rev_0) ).
thf(1162,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( C @ c_List_Orev @ hAPP ) @ ( A @ c_List_Olist__all ) ) )
| ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Oset ) )
= ( C @ ( B @ c_List_Oset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rotate_0) ).
thf(621,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Oset ) )
= ( C @ ( B @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(258,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OdropWhile ) ) )
= ( D @ ( C @ ( A @ c_List_OdropWhile ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_0) ).
thf(1029,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)],[258]) ).
thf(230,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Nil2_0) ).
thf(964,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist__all2 ) ) ) ) )
| ( A
= ( B @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(398,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) )
= ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).
thf(1344,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) )
= ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(144,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( D @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__length_0) ).
thf(769,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( D @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( D @ ( C @ ( E @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(255,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_0) ).
thf(1022,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Orotate ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(415,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Orev @ hAPP ) @ ( A @ c_List_Orev @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_1) ).
thf(1381,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Orev @ hAPP ) @ ( A @ c_List_Orev @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OServer ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I3_J_0) ).
thf(462,plain,
! [A: $i] :
( ( A @ c_Message_Oagent_OFriend )
!= c_Message_Oagent_OServer ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) )
| ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__append_1) ).
thf(858,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all ) ) )
| ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_0) ).
thf(552,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)],[50]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_List_Orev @ hAPP ) )
!= ( C @ ( A @ c_List_Orev @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
thf(1198,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_List_Orev @ hAPP ) )
!= ( C @ ( A @ c_List_Orev @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(339,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orev @ hAPP ) )
!= ( A @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).
thf(1213,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orev @ hAPP ) )
!= ( A @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(264,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( D @ ( B @ ( E @ c_List_Orev @ hAPP ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( C @ ( E @ ( D @ ( C @ c_List_Orev @ hAPP ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__rev1_0) ).
thf(1044,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( D @ ( B @ ( E @ c_List_Orev @ hAPP ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( C @ ( E @ ( D @ ( C @ c_List_Orev @ hAPP ) @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(274,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__XremoveAll__Xinduct__2 @ ( A @ v_sko__List__XremoveAll__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_removeAll_Oinduct_1) ).
thf(1066,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__XremoveAll__Xinduct__2 @ ( A @ v_sko__List__XremoveAll__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(252,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = c_Message_Oagent_OServer )
| ( E
= ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__1 ) ) @ c_Message_Oagent_OFriend ) )
| ( E = c_Message_Oagent_OSpy )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_3) ).
thf(1015,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = c_Message_Oagent_OServer )
| ( E
= ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__1 ) ) @ c_Message_Oagent_OFriend ) )
| ( E = c_Message_Oagent_OSpy )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(322,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(1176,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xzip__Xinduct__2 @ ( A @ v_sko__List__Xzip__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zip_Oinduct_1) ).
thf(986,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xzip__Xinduct__2 @ ( A @ v_sko__List__Xzip__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(289,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).
thf(1102,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orotate1 ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rotate1_0) ).
thf(505,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Orotate1 ) @ c_Nat_Osize__class_Osize ) )
= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(94,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( F @ ( B @ ( E @ c_Message_Oagent_Oagent__case ) ) ) ) )
= ( D @ ( A @ ( F @ ( C @ ( E @ c_Message_Oagent_Oagent__case ) ) ) ) ) )
| ( A
= ( D @ ( C @ ( B @ ( A @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ c_Message_Oagent_OFriend ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_5) ).
thf(653,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( F @ ( B @ ( E @ c_Message_Oagent_Oagent__case ) ) ) ) )
= ( D @ ( A @ ( F @ ( C @ ( E @ c_Message_Oagent_Oagent__case ) ) ) ) ) )
| ( A
= ( D @ ( C @ ( B @ ( A @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ c_Message_Oagent_OFriend ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(214,axiom,
! [A: $i] :
( c_Message_Oagent_OSpy
!= ( A @ c_Message_Oagent_OFriend ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I7_J_0) ).
thf(922,plain,
! [A: $i] :
( c_Message_Oagent_OSpy
!= ( A @ c_Message_Oagent_OFriend ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(209,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xlist__Xinduct__2 @ ( A @ v_sko__List__Xlist__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinduct_1) ).
thf(912,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xlist__Xinduct__2 @ ( A @ v_sko__List__Xlist__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(106,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( D @ ( E @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Oappend ) ) @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__appendI_0) ).
thf(685,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( D @ ( E @ ( B @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Oappend ) ) @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(294,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Ofilter ) ) @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_0) ).
thf(1113,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)],[294]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__filter_0) ).
thf(563,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)],[55]) ).
thf(278,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_1) ).
thf(1076,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)],[278]) ).
thf(260,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_OdropWhile ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_1) ).
thf(1034,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)],[260]) ).
thf(101,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( C @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(675,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( C @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(381,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upds__Nil2_0) ).
thf(1304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_Map_Omap__upds ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(318,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ c_List_Obutlast ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).
thf(1166,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)],[318]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( C @ ( C @ ( A @ ( B @ c_List_Oappend ) ) @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_1) ).
thf(548,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( C @ ( C @ ( A @ ( B @ c_List_Oappend ) ) @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__commute_0) ).
thf(487,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).
thf(749,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)],[135]) ).
thf(396,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ ( D @ ( C @ ( D @ c_List_Orev @ hAPP ) @ ( B @ c_List_Omap ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__map_0) ).
thf(1340,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ ( D @ ( C @ ( D @ c_List_Orev @ hAPP ) @ ( B @ c_List_Omap ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(253,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xlistset__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listset_Oinduct_0) ).
thf(1018,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xlistset__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) @ ( D @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__append_0) ).
thf(458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Odrop ) ) @ ( D @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(836,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(266,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xtake__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take_Oinduct_0) ).
thf(1049,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xtake__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Olist__inter ) ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__inter_Osimps_I1_J_0) ).
thf(1208,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)],[337]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_List_Orotate1 ) @ c_List_Oset ) )
= ( B @ ( A @ c_List_Oset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rotate1_0) ).
thf(589,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)],[65]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Otl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__tl_0) ).
thf(531,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Otl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(223,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 ) ) )
!= ( C @ ( B @ c_List_Orev @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
thf(944,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 ) ) )
!= ( C @ ( B @ c_List_Orev @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( B @ c_List_Orotate1 ) @ ( A @ c_List_Orotate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__rotate__swap_0) ).
thf(617,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Orotate ) ) @ c_List_Orotate1 ) )
= ( C @ ( C @ ( B @ c_List_Orotate1 ) @ ( A @ c_List_Orotate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onull ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps_I2_J_0) ).
thf(516,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Onull ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oreplicate ) ) @ c_List_Oappend ) ) @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
thf(690,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)],[108]) ).
thf(256,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xconcat__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_concat_Oinduct_0) ).
thf(1025,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xconcat__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(313,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Omap ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
thf(1156,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_List_Olist_ONil )
= ( A @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Omap ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(424,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Obutlast ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).
thf(1400,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)],[424]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Oagent_OFriend )
!= ( B @ c_Message_Oagent_OFriend ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Oinject_0) ).
thf(887,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Message_Oagent_OFriend )
!= ( B @ c_Message_Oagent_OFriend ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(409,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Orev @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
thf(1368,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) )
= ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist_OCons ) ) @ ( B @ c_List_Orev @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(364,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_0) ).
thf(1267,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(287,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) )
| ( D @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_List_Olist__ex ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_0) ).
thf(1098,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__ex ) ) )
| ( D @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_List_Olist__ex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(242,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(993,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)],[242]) ).
thf(268,axiom,
! [A: $i] :
( ( A @ ( A @ c_List_Olist_ONil @ c_List_Oremdups ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_1) ).
thf(1053,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)],[268]) ).
thf(379,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Obutlast ) )
= ( B @ ( A @ c_List_Obutlast ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_0) ).
thf(1300,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)],[379]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__filter__le_0) ).
thf(791,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( C @ ( B @ ( A @ c_List_Oremove1 ) ) @ c_List_Oset ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__remove1__subset_0) ).
thf(441,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)],[3]) ).
thf(63,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__append_0) ).
thf(585,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(118,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( D @ ( F @ ( E @ ( B @ c_List_Odrop ) ) @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__dropI_0) ).
thf(717,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( D @ ( F @ ( E @ ( B @ c_List_Odrop ) ) @ ( D @ ( C @ ( B @ c_List_Odrop ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(348,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
= ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ c_List_Olist_ONil @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(1235,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)],[348]) ).
thf(387,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).
thf(1317,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)],[387]) ).
thf(301,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofoldr ) ) ) ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
thf(1130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofoldr ) ) ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(372,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( c_Message_Oagent_OSpy @ ( C @ ( B @ ( A @ c_Message_Oagent_Oagent__case ) ) ) ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I10_J_0) ).
thf(1285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( c_Message_Oagent_OSpy @ ( C @ ( B @ ( A @ c_Message_Oagent_Oagent__case ) ) ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(90,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(643,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( A @ c_List_Orev @ hAPP ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
thf(1085,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ ( A @ ( A @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( A @ c_List_Orev @ hAPP ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(60,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( F @ ( E @ ( D @ c_Event_Oevent_OSays ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_2) ).
thf(576,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)],[60]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(544,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(206,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__XdropWhile__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Oinduct_0) ).
thf(907,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__XdropWhile__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(703,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)],[114]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_List_Oremdups ) )
= A )
| ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
!= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__remdups__eq_0) ).
thf(656,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_List_Oremdups ) )
= A )
| ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Oremdups ) @ c_Nat_Osize__class_Osize ) )
!= ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(187,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Event_Oevent_OGets ) )
!= ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I5_J_0) ).
thf(864,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)],[187]) ).
thf(434,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xdistinct__Xinduct__2 @ ( A @ v_sko__List__Xdistinct__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Oinduct_1) ).
thf(1427,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xdistinct__Xinduct__2 @ ( A @ v_sko__List__Xdistinct__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( C @ ( B @ ( A @ c_List_Osublist ) ) @ c_List_Oset ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__sublist__subset_0) ).
thf(727,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( C @ ( B @ ( A @ c_List_Osublist ) ) @ c_List_Oset ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( D @ ( A @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(571,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)],[59]) ).
thf(411,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
!= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_0) ).
thf(1372,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)],[411]) ).
thf(351,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1240,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)],[351]) ).
thf(403,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xlast__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Oinduct_0) ).
thf(1353,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xlast__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remdups__id_0) ).
thf(600,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_List_Odistinct ) )
| ( ( B @ ( A @ c_List_Oremdups ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(366,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( E @ ( G @ ( F @ ( C @ c_List_Olist_OCons ) ) @ ( E @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons_0) ).
thf(1272,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( E @ ( G @ ( F @ ( C @ c_List_Olist_OCons ) ) @ ( E @ ( D @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Olist_OCons ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(612,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)],[73]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__take_0) ).
thf(627,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( D @ ( C @ ( A @ c_List_Odrop ) ) @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(7,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Orotate ) ) )
= ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Orotate ) ) @ ( B @ c_List_Omap ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__map_0) ).
thf(450,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Orotate ) ) )
= ( E @ ( D @ ( D @ ( C @ ( A @ c_List_Orotate ) ) @ ( B @ c_List_Omap ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(324,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) @ c_List_Olast ) )
= ( B @ ( A @ c_List_Olast ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_0) ).
thf(1180,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)],[324]) ).
thf(204,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Ofilter ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I1_J_0) ).
thf(903,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)],[204]) ).
thf(340,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(1216,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)],[340]) ).
thf(419,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ ( B @ ( A @ c_List_Orev @ hAPP ) @ ( C @ ( A @ c_List_Orev @ hAPP ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__append_0) ).
thf(1390,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ ( B @ ( A @ c_List_Orev @ hAPP ) @ ( C @ ( A @ c_List_Orev @ hAPP ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( A @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_0) ).
thf(771,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)],[145]) ).
thf(292,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = c_Message_Oagent_OServer )
| ( E
= ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__asm__1 ) ) @ c_Message_Oagent_OFriend ) )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_4) ).
thf(1108,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = c_Message_Oagent_OServer )
| ( E
= ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__asm__1 ) ) @ c_Message_Oagent_OFriend ) )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(432,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oappend ) ) )
!= ( C @ ( C @ ( C @ c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(1421,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)],[432]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ~ ( D @ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__map_2) ).
thf(465,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ~ ( D @ ( C @ ( C @ ( B @ c_List_Oset ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( C @ c_List_Oappend ) ) )
= ( B @ ( B @ ( D @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_4) ).
thf(524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( C @ c_List_Oappend ) ) )
= ( B @ ( B @ ( D @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(581,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(26,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) )
= ( D @ ( C @ ( B @ ( D @ ( F @ ( E @ ( A @ c_List_Olist__update ) ) ) @ c_List_Olist__update ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__swap_0) ).
thf(495,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)],[26]) ).
thf(429,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__asm__1 ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( E = c_Message_Oagent_OSpy )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_9) ).
thf(1412,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__asm__1 ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( E = c_Message_Oagent_OSpy )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(374,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( F @ ( A @ ( E @ c_Message_Oagent_Oagent__case ) ) ) ) )
= ( D @ ( B @ ( F @ ( C @ ( E @ c_Message_Oagent_Oagent__case ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ ( B @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_7) ).
thf(1289,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( F @ ( A @ ( E @ c_Message_Oagent_Oagent__case ) ) ) ) )
= ( D @ ( B @ ( F @ ( C @ ( E @ c_Message_Oagent_Oagent__case ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ ( B @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(177,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( F @ ( B @ ( E @ c_Message_Oagent_Oagent__case ) ) ) ) )
= ( D @ ( A @ ( F @ ( C @ ( G @ c_Message_Oagent_Oagent__case ) ) ) ) ) )
| ( A = c_Message_Oagent_OServer )
| ( A
= ( D @ ( C @ ( B @ ( A @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ c_Message_Oagent_OFriend ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_1) ).
thf(844,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( F @ ( B @ ( E @ c_Message_Oagent_Oagent__case ) ) ) ) )
= ( D @ ( A @ ( F @ ( C @ ( G @ c_Message_Oagent_Oagent__case ) ) ) ) ) )
| ( A = c_Message_Oagent_OServer )
| ( A
= ( D @ ( C @ ( B @ ( A @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ c_Message_Oagent_OFriend ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(1276,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)],[368]) ).
thf(390,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = c_Message_Oagent_OServer )
| ( D
= ( E @ ( G @ ( B @ ( D @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ c_Message_Oagent_OFriend ) )
| ( D = c_Message_Oagent_OSpy )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Message_Oagent_Oagent__case ) ) ) ) )
= ( E @ ( D @ ( H @ ( G @ ( F @ c_Message_Oagent_Oagent__case ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_0) ).
thf(1326,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = c_Message_Oagent_OServer )
| ( D
= ( E @ ( G @ ( B @ ( D @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ c_Message_Oagent_OFriend ) )
| ( D = c_Message_Oagent_OSpy )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Message_Oagent_Oagent__case ) ) ) ) )
= ( E @ ( D @ ( H @ ( G @ ( F @ c_Message_Oagent_Oagent__case ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(201,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(896,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Oappend ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(272,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons1_3) ).
thf(1062,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(85,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Event_Oevent_OSays ) ) )
!= ( E @ ( D @ c_Event_Oevent_OGets ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I4_J_0) ).
thf(632,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)],[85]) ).
thf(353,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = c_Message_Oagent_OSpy )
| ( ( D @ ( B @ ( F @ ( A @ ( E @ c_Message_Oagent_Oagent__case ) ) ) ) )
= ( D @ ( B @ ( H @ ( C @ ( G @ c_Message_Oagent_Oagent__case ) ) ) ) ) )
| ( B = c_Message_Oagent_OServer )
| ( ( D @ ( C @ ( A @ ( B @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_2) ).
thf(1244,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = c_Message_Oagent_OSpy )
| ( ( D @ ( B @ ( F @ ( A @ ( E @ c_Message_Oagent_Oagent__case ) ) ) ) )
= ( D @ ( B @ ( H @ ( C @ ( G @ c_Message_Oagent_Oagent__case ) ) ) ) ) )
| ( B = c_Message_Oagent_OServer )
| ( ( D @ ( C @ ( A @ ( B @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( A @ ( B @ c_Message_Osko__Message__Xagent__Xcase__cong__1__1 ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(781,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)],[148]) ).
thf(357,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I4_J_0) ).
thf(1253,plain,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(112,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
thf(699,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(229,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = c_Message_Oagent_OServer )
| ~ ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__asm__1 ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( E = c_Message_Oagent_OSpy )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_5) ).
thf(961,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = c_Message_Oagent_OServer )
| ~ ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__asm__1 ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( E = c_Message_Oagent_OSpy )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__take_0) ).
thf(813,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_List_Odistinct ) )
| ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(417,axiom,
! [A: $i] :
( ( tc_Event_Oevent @ c_List_Olist_ONil @ ( A @ c_Event_Oknows ) )
= ( A @ c_Event_OinitState ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Nil_0) ).
thf(1385,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)],[417]) ).
thf(210,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(914,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)],[210]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Ofilter ) ) @ c_List_Oremdups ) )
= ( C @ ( C @ ( B @ c_List_Oremdups ) @ ( A @ c_List_Ofilter ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__filter_0) ).
thf(510,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)],[31]) ).
thf(383,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__1 ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( E = c_Message_Oagent_OSpy )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_9) ).
thf(1308,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__1 ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( E = c_Message_Oagent_OSpy )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(330,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__1 ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_10) ).
thf(1193,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__1 ) ) @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Otl ) )
= ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl__drop_0) ).
thf(478,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Odrop ) ) @ c_List_Otl ) )
= ( C @ ( C @ ( B @ c_List_Otl ) @ ( A @ c_List_Odrop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( A @ c_List_Oremove1 ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_0) ).
thf(832,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)],[171]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( c_Message_Oagent_OServer @ ( C @ ( B @ ( A @ c_Message_Oagent_Oagent__rec ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Orecs_I1_J_0) ).
thf(800,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( c_Message_Oagent_OServer @ ( C @ ( B @ ( A @ c_Message_Oagent_Oagent__rec ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(99,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Oreplicate ) ) )
!= ( C @ ( E @ ( D @ c_List_Oreplicate ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
thf(667,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)],[99]) ).
thf(376,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Orev @ hAPP ) @ ( A @ c_List_Orev @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
thf(1294,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Orev @ hAPP ) @ ( A @ c_List_Orev @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(295,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_List_Ofilter ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__eq__ConsD_2) ).
thf(1116,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)],[295]) ).
thf(400,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( tc_Message_Omsg @ tc_fun ) @ ( tc_Event_Oevent @ ( B @ ( E @ ( D @ ( C @ c_Event_Oevent_OSays ) ) @ c_List_Olist_OCons ) ) @ ( A @ c_Event_Oknows ) @ ( B @ ( A @ c_Event_Oknows ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Says_0) ).
thf(1348,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)],[400]) ).
thf(245,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Orecs_I1_J_0) ).
thf(999,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__rec ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( C @ c_List_Oappend ) ) )
= ( B @ ( D @ ( A @ c_List_Oappend ) ) ) )
| ( C
!= ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) )
| ( ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
!= A )
| ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) )
!= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_6) ).
thf(447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( C @ c_List_Oappend ) ) )
= ( B @ ( D @ ( A @ c_List_Oappend ) ) ) )
| ( C
!= ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) ) )
| ( ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Otake ) ) )
!= A )
| ( ( B @ ( B @ ( D @ ( B @ ( A @ ( B @ tc_List_Olist @ ( C @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) @ ( B @ ( C @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize__class_Osize ) @ c_List_Odrop ) ) @ c_List_Oappend ) ) )
!= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(231,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ c_Message_Oagent_OFriend @ ( C @ ( B @ ( A @ c_Message_Oagent_Oagent__rec ) ) ) ) )
= ( D @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Orecs_I2_J_0) ).
thf(967,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ c_Message_Oagent_OFriend @ ( C @ ( B @ ( A @ c_Message_Oagent_Oagent__rec ) ) ) ) )
= ( D @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(225,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( A @ c_List_Orotate1 ) )
= ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Ohd ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Otl ) @ c_List_Oappend ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__hd__tl_0) ).
thf(950,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)],[225]) ).
thf(346,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_List_Odrop ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__eq__Nil_0) ).
thf(1229,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_List_Odrop ) ) )
!= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(421,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( c_Message_Oagent_OServer @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_0) ).
thf(1395,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( c_Message_Oagent_OServer @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(309,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xzip__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zip_Oinduct_0) ).
thf(1148,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xzip__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(188,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) )
| ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_1) ).
thf(867,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all ) ) )
| ( C @ ( B @ ( A @ c_List_Olist__all ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(603,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(127,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(735,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(212,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons2_3) ).
thf(918,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( D @ ( F @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( G @ ( D @ ( G @ ( F @ ( E @ c_List_Olist_OCons ) ) @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(160,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(807,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)],[160]) ).
thf(394,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( E @ ( D @ c_List_Orev @ hAPP ) @ ( C @ ( B @ c_List_Orev @ hAPP ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__rev_1) ).
thf(1335,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( D @ ( B @ ( E @ ( D @ c_List_Orev @ hAPP ) @ ( C @ ( B @ c_List_Orev @ hAPP ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(332,axiom,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Onull ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__null_0) ).
thf(1197,plain,
! [A: $i] : ( A @ ( A @ c_List_Olist_ONil @ c_List_Onull ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( c_Message_Oagent_OServer @ ( C @ ( B @ ( A @ c_Message_Oagent_Oagent__case ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I8_J_0) ).
thf(635,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( c_Message_Oagent_OServer @ ( C @ ( B @ ( A @ c_Message_Oagent_Oagent__case ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__replicate_1) ).
thf(955,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)],[227]) ).
thf(399,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Orev @ hAPP ) @ c_List_Oset ) )
= ( A @ ( B @ c_List_Oset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev_0) ).
thf(1346,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_List_Orev @ hAPP ) @ c_List_Oset ) )
= ( A @ ( B @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__dropWhile__le_0) ).
thf(474,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_OdropWhile ) ) @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(428,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__XtakeWhile__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Oinduct_0) ).
thf(1410,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__XtakeWhile__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(143,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( D @ ( F @ ( E @ ( B @ c_List_Otake ) ) @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__takeI_0) ).
thf(767,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( E @ ( C @ ( A @ c_List_Olist__all2 ) ) ) ) )
| ( F @ ( D @ ( F @ ( E @ ( B @ c_List_Otake ) ) @ ( D @ ( C @ ( B @ c_List_Otake ) ) @ ( A @ c_List_Olist__all2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oset ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__take__subset_0) ).
thf(886,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ c_List_Oset ) @ ( C @ ( C @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oset ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(216,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xlist__update__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update_Oinduct_0) ).
thf(928,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ( A @ v_sko__List__Xlist__update__Xinduct__2 @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(285,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).
thf(1093,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ c_List_Orev @ hAPP ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(361,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xlist__update__Xinduct__2 @ ( A @ v_sko__List__Xlist__update__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update_Oinduct_1) ).
thf(1261,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xlist__update__Xinduct__2 @ ( A @ v_sko__List__Xlist__update__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ ( C @ c_List_Oappend ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( B @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_1) ).
thf(860,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)],[185]) ).
thf(414,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_List_Olist_ONil ) )
| ( ( B @ ( B @ ( B @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ c_List_Olist_OCons ) ) @ ( B @ ( A @ c_List_Obutlast ) @ c_List_Oappend ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__butlast__last__id_0) ).
thf(1378,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)],[414]) ).
thf(405,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__XtakeWhile__Xinduct__2 @ ( A @ v_sko__List__XtakeWhile__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Oinduct_1) ).
thf(1357,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__XtakeWhile__Xinduct__2 @ ( A @ v_sko__List__XtakeWhile__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ( A @ ( A @ ( A @ ( D @ ( C @ c_List_Olist_OCons ) ) @ ( B @ c_List_Olist_OCons ) ) @ c_List_Olinorder__class_Osorted ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_2) ).
thf(723,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)],[121]) ).
thf(166,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) )
= ( C @ ( C @ ( D @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(822,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)],[166]) ).
thf(180,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(850,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)],[180]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( D @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__append_0) ).
thf(442,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Otake ) ) )
= ( D @ ( D @ ( C @ ( tc_nat @ ( D @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Otake ) ) @ ( D @ ( B @ ( A @ c_List_Otake ) ) @ c_List_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(191,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_List_Otake ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__all_0) ).
thf(871,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize__class_Osize ) @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_List_Otake ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(423,axiom,
! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__all ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I1_J_0) ).
thf(1399,plain,
! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olist__all ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oappend ) ) @ ( A @ c_List_Oappend ) ) )
= ( D @ ( C @ ( D @ ( B @ ( A @ c_List_Oappend ) ) @ c_List_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(728,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)],[124]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Oreplicate ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__replicate_0) ).
thf(740,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Oreplicate ) ) @ ( A @ c_List_Odrop ) ) )
= ( D @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_List_Oreplicate ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_List_Olist_ONil @ c_List_Oappend ) ) @ c_List_Ohd ) )
= ( A @ ( B @ c_List_Ohd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__append_0) ).
thf(982,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)],[237]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ c_List_Olist_ONil ) )
| ( ( C @ ( B @ ( A @ c_List_Oappend ) ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(1004,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)],[247]) ).
thf(392,axiom,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xlistsum__Xinduct__2 @ ( A @ v_sko__List__Xlistsum__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_Oinduct_1) ).
thf(1331,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ c_List_Olist_ONil @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( A @ v_sko__List__Xlistsum__Xinduct__2 @ ( A @ v_sko__List__Xlistsum__Xinduct__1 @ c_List_Olist_OCons ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(388,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
!= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).
thf(1320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( C @ c_List_Olist_ONil ) )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
!= ( D @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(659,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(639,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Otl ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl_Osimps_I2_J_0) ).
thf(454,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)],[9]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_List_Oappend ) ) @ c_List_Odistinct ) )
| ( B @ ( A @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_1) ).
thf(882,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)],[195]) ).
thf(16,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(469,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(221,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I4_J_0) ).
thf(940,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olist_Olist__case ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_OdropWhile ) ) )
= ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_1) ).
thf(935,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)],[219]) ).
thf(249,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = c_Message_Oagent_OServer )
| ( E
= ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__1 ) ) @ c_Message_Oagent_OFriend ) )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_4) ).
thf(1009,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = c_Message_Oagent_OServer )
| ( E
= ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__1 ) ) @ c_Message_Oagent_OFriend ) )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(261,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( E
= ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__1 ) ) @ c_Message_Oagent_OFriend ) )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_8) ).
thf(1037,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ hAPP ) @ hBOOL )
| ( E
= ( E @ ( C @ ( A @ v_sko__Message__Xagent__Xsplit__1 ) ) @ c_Message_Oagent_OFriend ) )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( t_a @ ( E @ ( D @ ( C @ ( B @ c_Message_Oagent_Oagent__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
thf(560,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(251,axiom,
! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistrelp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listrelp_ONil_0) ).
thf(1014,plain,
! [B: $i,A: $i] : ( B @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ c_List_Olistrelp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(233,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ hAPP ) @ hBOOL )
| ( ( D @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( C @ ( A @ c_List_Ofilter ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_1) ).
thf(972,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)],[233]) ).
thf(1432,plain,
$false,
inference(e,[status(thm)],[892,809,1337,629,1190,1237,909,1083,555,1168,760,1315,518,977,683,730,1068,1205,597,1173,1158,762,1142,1269,614,677,1078,1137,533,550,472,538,1164,797,1342,747,1222,930,898,1001,841,1046,1359,565,436,829,1095,1055,1287,719,785,751,802,460,587,1323,619,838,1313,1279,1059,1132,853,1087,1247,870,1362,1100,1232,969,606,1415,475,492,591,1040,646,514,1151,806,1283,1051,1302,756,1418,623,485,834,1383,1020,905,480,687,1119,1351,998,988,1405,1201,507,527,877,692,1104,1242,849,1074,452,920,529,546,925,1306,810,1311,714,512,942,439,798,1057,1274,1387,894,778,1042,1355,820,815,1238,1123,862,693,630,788,1370,847,1032,1365,625,852,1178,1210,1027,757,1128,1281,1392,1012,1106,916,467,1296,665,583,522,1195,1407,456,842,1402,874,1259,650,1064,725,869,783,1397,519,742,1375,1121,1111,1227,1160,1182,901,1424,637,489,679,706,884,1329,1292,933,554,753,1263,701,1297,738,1266,1192,721,503,1150,1249,984,911,569,1429,1333,938,541,1170,1187,773,662,1202,792,558,1071,953,1185,1135,1251,1146,856,745,444,1219,824,1154,975,732,1125,743,958,1007,694,826,711,1256,1226,641,1139,498,1090,804,1258,947,1224,672,831,681,736,1349,567,1144,616,1376,764,979,990,996,880,649,1080,631,535,609,594,1162,621,1029,964,1344,769,1022,1381,462,858,552,1198,1213,1044,1066,1015,1176,986,1102,505,653,922,912,685,1113,563,1076,1034,675,1304,1166,548,487,749,1340,1018,458,836,1049,1208,589,531,944,617,516,690,1025,1156,1400,887,1368,1267,1098,993,1053,1300,791,441,585,717,1235,1317,1130,1285,643,1085,576,544,907,703,656,864,1427,727,571,1372,1240,1353,600,1272,612,627,450,1180,903,1216,1390,771,1108,1421,465,524,581,495,1412,1289,844,1276,1326,896,1062,632,1244,781,1253,699,961,813,1385,914,510,1308,1193,478,832,800,667,1294,1116,1348,999,447,967,950,1229,1395,1148,867,603,735,918,807,1335,1197,635,955,1346,474,1410,767,886,928,1093,1261,860,1378,1357,723,822,850,442,871,1399,728,740,982,1004,1331,1320,659,639,454,882,469,940,935,1009,1037,560,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV778-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.23/0.48 % Computer : n016.cluster.edu
% 0.23/0.48 % Model : x86_64 x86_64
% 0.23/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48 % Memory : 8046.5625MB
% 0.23/0.48 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Sat Sep 26 15:01:32 UTC 2026
% 0.23/0.49 % CPUTime :
% 0.23/0.49 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.36/1.33 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.77/1.82 % [INFO] Parsing done (488ms).
% 2.77/1.84 % [INFO] Running in sequential loop mode.
% 4.60/2.42 % [INFO] eprover registered as external prover.
% 4.60/2.43 % [INFO] Scanning for conjecture ...
% 5.22/2.66 % [INFO] Found a conjecture (or negated_conjecture) and 442 axioms. Running axiom selection ...
% 6.36/2.94 % [INFO] Axiom selection finished. Selected 434 axioms (removed 8 axioms).
% 7.71/3.29 % [INFO] Problem is propositional (TPTP CNF).
% 8.12/3.32 % [INFO] Type checking passed.
% 8.12/3.33 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 19.16/6.10 % External prover 'e' found a proof!
% 19.16/6.10 % [INFO] Killing All external provers ...
% 19.16/6.10 % Time passed: 5408ms (effective reasoning time: 4255ms)
% 19.16/6.11 % Axioms used in derivation (434): cls_set__subset__Cons_0, clsarity_nat__HOL_Oord, cls_butlast__snoc_0, cls_last_Osimps_0, cls_append__eq__append__conv__if_3, cls_length__filter__le_0, cls_rev__swap_1, cls_last_Osimps_1, cls_takeWhile_Oinduct_1, cls_distinct_Oinduct_0, cls_Nil__is__rev__conv_1, cls_Nil__is__map__conv_1, cls_list_Orecs_I1_J_0, cls_agent_Ocase__cong_3, cls_knows__Spy__Gets_0, cls_dropWhile_Osimps_I1_J_0, cls_agent_Osplit_10, cls_Cons__eq__append__conv_5, cls_equalityI_0, cls_remove1_Osimps_I2_J_0, cls_le__diff__iff_0, cls_listrelp_OCons_0, cls_list__all__append_1, cls_list__all2__Cons_2, cls_listsum_Oinduct_0, cls_eq__imp__le_0, cls_list__update__overwrite_0, cls_list__all_Osimps_I2_J_1, cls_Nat_Odiff__diff__eq_0, cls_list__all2__eq_1, cls_map__replicate_0, cls_append__self__conv_0, cls_butlast_Osimps_I1_J_0, cls_initState__subset__knows_0, cls_agent_Osplit__asm_10, cls_drop__append_0, cls_insert__code_1, cls_le__funD_0, cls_agent_Osplit__asm_3, cls_agent_Oinject_0, cls_list_Oinject_0, cls_eq__diff__iff_0, cls_filter__is__subset_0, cls_knows__Says_0, cls_Cons__eq__map__conv_3, cls_rotate__map_0, cls_agent_Ocase__cong_0, cls_agent_Osplit_3, cls_tl_Osimps_I1_J_0, cls_rev__singleton__conv_1, cls_agent_Osimps_I6_J_0, cls_distinct__filter_0, cls_not__Cons__self2_0, cls_remove1__filter__not_0, cls_rev__is__rev__conv_0, clsarity_nat__Orderings_Olinorder, cls_distinct__rev_1, cls_append__eq__append__conv__if_6, cls_listsp_ONil_0, cls_list__update__nonempty_1, cls_filter__eq__ConsD_2, cls_self__append__conv_0, cls_same__append__eq_0, cls_list_Osimps_I5_J_0, cls_knows__subset__knows__Cons_0, cls_remdups__filter_0, cls_append__eq__Cons__conv_4, cls_list__update_Oinduct_1, cls_eq__Nil__appendI_0, cls_list_Oinduct_1, cls_zip_Oinduct_0, cls_mod__diff__eq_0, cls_knows__subset__knows__Says_0, cls_list__all_Osimps_I2_J_0, cls_hd__append_0, cls_agent_Osimps_I5_J_0, clsarity_bool__HOL_Oord, cls_knows__Nil_0, cls_append__Cons_0, cls_listset_Oinduct_1, cls_butlast_Osimps_I2_J_1, cls_set__remove1__subset_0, cls_rotate__conv__mod_0, cls_agent_Ocase__cong_7, cls_Nil__is__map__conv_0, cls_drop__map_0, cls_length__map_0, cls_filter_Osimps_I2_J_0, cls_setsum__set__distinct__conv__listsum_0, cls_replicate__eq__replicate_0, cls_append__eq__append__conv__if_2, cls_foldr_Osimps_I1_J_0, cls_append__eq__append__conv2_4, cls_agent_Osplit_8, clsarity_nat__Divides_Osemiring__div, cls_diff__le__mono2_0, cls_sorted_Osimps_I3_J_1, cls_le__antisym_0, cls_list__all2__append2_5, cls_append1__eq__conv_1, cls_rev__drop_0, cls_rev__take_0, cls_diff__diff__cancel_0, cls_list__all__rev_0, cls_order__eq__refl_0, cls_list__all2__rev_1, cls_filter__append_0, cls_sorted__take_0, cls_distinct_Osimps_I2_J_1, cls_list__all2__rev_0, cls_list__all2__Cons_1, cls_distinct_Osimps_I1_J_0, cls_inj__on__insert_0, cls_agent_Osimps_I9_J_0, cls_last_Oinduct_1, cls_concat_Oinduct_0, cls_length__remdups__eq_0, cls_inj__on__rev_0, cls_replicate__append__same_0, cls_agent_Ocase__cong_4, cls_rev__map_0, cls_hd__append_1, cls_filter_Osimps_I1_J_0, cls_empty__null_0, cls_spies__Gets__rev_0, cls_list__update__beyond_0, cls_takeWhile_Oinduct_0, cls_listset_Oinduct_0, cls_rev_Osimps_I2_J_0, cls_distinct__remove1_0, cls_list_Osimps_I4_J_0, cls_removeAll_Oinduct_0, cls_rev__singleton__conv_0, cls_agent_Osplit_2, cls_listrelp_ONil_0, cls_rotate__rev_0, cls_append__self__conv2_0, cls_remdups__id__iff__distinct_0, cls_Nil__is__append__conv_0, cls_list__update__code_I1_J_0, cls_list__all__append_2, cls_dropWhile__eq__Cons__conv_1, cls_append__Nil2_0, cls_agent_Osplit__asm_7, cls_rotate__is__Nil__conv_0, cls_self__append__conv2_0, cls_distinct__map_0, cls_drop__tl_0, cls_insert__code_2, cls_agent_Osplit_1, cls_distinct__append_0, clsarity_fun__HOL_Oord, cls_remdups__eq__nil__iff_1, cls_map__eq__Cons__conv_3, cls_remove1_Oinduct_0, cls_self__append__conv2_1, cls_sorted__drop_0, cls_sorted_Osimps_I3_J_2, cls_append__eq__append__conv__if_4, cls_List_Oset_Osimps_I2_J_0, cls_rev__predicate1D_0, cls_map__update_0, cls_append__is__Nil__conv_2, cls_list_Osplit_0, cls_length__list__update_0, cls_append__Nil_0, cls_map__is__Nil__conv_0, cls_append__eq__append__conv2_5, cls_append__eq__Cons__conv_5, cls_le__mod__geq_0, cls_take__map_0, cls_append__in__listsp__conv_1, cls_append__in__listsp__conv_0, cls_last__append_1, cls_append__butlast__last__id_0, cls_singleton__rev__conv_0, cls_list__all__rev_1, cls_set__rotate1_0, cls_agent_Orecs_I3_J_0, cls_zip_Oinduct_1, cls_distinct__rev_0, cls_set__eq__subset_2, cls_knows__Gets_0, cls_agent_Osimps_I4_J_0, cls_filter__replicate_1, cls_rev__is__Nil__conv_0, cls_list__all2__Cons_0, cls_insert__subset_1, cls_map__upds__Nil2_0, cls_list__ex_Osimps_I1_J_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_length__remdups__eq_1, cls_foldl__Cons_0, cls_set__rev_0, cls_hd__dropWhile_0, cls_distinct__rotate_1, cls_linorder__linear_0, cls_replicate__app__Cons__same_0, cls_ns__sharedp_ONil_0, cls_filter__replicate_0, cls_agent_Osplit_9, cls_rotate__simps_0, cls_distinct__sublistI_0, cls_fun__upds__append2__drop_0, cls_map__eq__imp__length__eq_0, cls_rotate1__is__Nil__conv_0, cls_list__all2__appendI_0, cls_list__all2__Nil_1, cls_subset__trans_0, cls_agent_Osimps_I3_J_0, cls_sublist__nil_0, cls_self__append__conv_1, cls_take__append_0, cls_rev__filter_0, cls_set__rotate_0, cls_list__update_Osimps_I1_J_0, cls_order__trans_0, cls_append__eq__conv__conj_2, cls_butlast__append_0, cls_agent_Osplit__asm_6, cls_rotate1__rotate__swap_0, cls_length__remdups__leq_0, cls_not__Cons__self_0, cls_append__same__eq_0, cls_last__snoc_0, cls_length__dropWhile__le_0, cls_append__take__drop__id_0, clsarity_bool__Orderings_Opreorder, cls_fun__upds__append__drop_0, cls_butlast__drop_0, cls_agent_Osplit__asm_8, cls_agent_Osplit_5, cls_last__append_0, cls_list__all2__def_0, cls_list__update__swap_0, cls_length__rev_0, cls_append__eq__conv__conj_0, cls_list__all2__rev1_1, cls_rotate__drop__take_0, cls_knows__Spy__Says_0, cls_neq__Nil__conv_1, cls_Nil__is__append__conv_1, cls_list__update__length_0, cls_mod__diff__cong_0, cls_sorted__Cons_0, cls_list__inter_Osimps_I1_J_0, cls_distinct1__rotate_0, cls_drop__Nil_0, cls_event_Osimps_I2_J_1, cls_append__assoc_0, cls_append__eq__append__conv__if_1, cls_subset__refl_0, cls_butlast__append_1, cls_le__trans_0, cls_foldr_Osimps_I2_J_0, cls_agent_Ocase__cong_5, cls_set__update__subset__insert_0, cls_agent_Osplit__asm_5, cls_map__upds__Nil1_0, cls_list__all2__Nil2_0, cls_drop__butlast_0, cls_remove1_Oinduct_1, cls_agent_Osplit_0, cls_remove1_Osimps_I1_J_0, clsarity_nat__Orderings_Opreorder, cls_take_Oinduct_0, cls_last__rev_0, cls_append__in__listsp__conv_2, cls_list__all2__dropI_0, cls_take__eq__Nil_2, cls_distinct__append_1, cls_event_Osimps_I1_J_1, cls_map__append_0, cls_insert__mono_0, cls_mod__diff__right__eq_0, cls_subset__insertI2_0, cls_sorted__remdups_0, cls_distinct__remdups__id_0, cls_remdups__eq__nil__right__iff_1, cls_agent_Osplit_6, cls_mod__mod__trivial_0, cls_distinct__map_1, cls_tl__append2_0, cls_list__all2__Nil_0, cls_rev__replicate_0, cls_List_Onull_Osimps_I2_J_0, cls_foldr__append_0, cls_sorted_Osimps_I1_J_0, cls_sorted__remove1_0, cls_rotate__simps_1, cls_rev__eq__Cons__iff_1, cls_list_Osplit__asm_1, cls_set__remdups_0, cls_distinct__dropWhile_0, cls_rotate__is__Nil__conv_1, cls_map__is__Nil__conv_1, cls_list_Osimps_I3_J_0, cls_list_Orecs_I2_J_0, cls_sorted__distinct__set__unique_0, cls_sorted__append_0, cls_event_Osimps_I4_J_0, cls_drop__replicate_0, cls_event_Osimps_I2_J_0, cls_listsum__rev_0, cls_eq__eqI_0, cls_agent_Osplit__asm_1, cls_le__eqI_0, cls_length__rotate1_0, cls_agent_Osimps_I8_J_0, cls_append__eq__conv__conj_1, cls_map_Osimps_I2_J_0, cls_mod__less__eq__dividend_0, cls_list__ex_Osimps_I2_J_1, cls_rev__is__Nil__conv_1, cls_list__all2__Cons1_3, cls_agent_Ocase__cong_2, cls_rotate1__hd__tl_0, cls_insert__absorb2_0, cls_listsum_Oinduct_1, cls_length__rotate_0, cls_list__all2__append1_5, cls_distinct__rotate_0, cls_append__is__Nil__conv_1, cls_list__all2__append_0, cls_event_Osimps_I1_J_2, cls_list__all2__takeI_0, cls_dropWhile_Osimps_I2_J_1, cls_diff__le__self_0, cls_dropWhile_Oinduct_0, cls_nat__le__linear_0, cls_length__drop_0, cls_mod__diff__left__eq_0, cls_list__all2__append_2, cls_Cons__eq__appendI_0, cls_event_Osimps_I1_J_0, cls_agent_Ocase__cong_6, cls_agent_Osimps_I7_J_0, cls_Nil__is__rev__conv_0, cls_set__take__subset_0, cls_append__is__Nil__conv_0, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_distinct__take_0, cls_eq__eqI_1, cls_singleton__rev__conv_1, cls_list_Oinject_1, cls_subset__inj__on_0, cls_butlast_Osimps_I2_J_0, cls_append__eq__append__conv__if_0, cls_agent_Osplit_4, cls_Cons__eq__append__conv_4, cls_append__eq__appendI_0, cls_list__all_Osimps_I2_J_2, cls_distinct__map_2, cls_le__diff__iff_1, cls_list__all_Osimps_I1_J_0, cls_hd_Osimps_0, cls_rev__append_0, cls_agent_Osplit__asm_4, cls_drop__take_0, cls_foldl__append_0, cls_distinct__remdups_0, clsarity_fun__Orderings_Opreorder, cls_remove1_Osimps_I2_J_1, cls_list__update_Oinduct_0, cls_agent_Osplit__asm_9, cls_map_Oinduct_0, cls_take__all_0, cls_Nil__is__append__conv_2, cls_hd__rev_0, cls_set__sublist__subset_0, cls_list__all2__eq_0, cls_rev__swap_0, cls_tl__drop_0, cls_agent_Osimps_I10_J_0, cls_knows__Spy__subset__knows__Spy__Says_0, cls_append__replicate__commute_0, cls_append__eq__append__conv__if_5, cls_list_Osplit_1, cls_sorted_Osimps_I2_J_0, cls_filtermap_Osimps_I1_J_0, cls_knows__subset__knows__Gets_0, cls_tl_Osimps_I2_J_0, cls_foldl__Nil_0, cls_distinct__drop_0, cls_insert__code_0, cls_le__eqI_1, cls_subset__insertI_0, cls_diff__le__mono_0, cls_last_Oinduct_0, cls_list_Oinduct_0, cls_impossible__Cons_0, cls_length__replicate_0, cls_sorted__append_1, cls_rev__eq__Cons__iff_0, cls_list__ex_Osimps_I2_J_0, cls_diff__commute_0, cls_agent_Orecs_I1_J_0, cls_drop__all_0, cls_set__drop__subset_0, cls_drop__eq__Nil_0, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_agent_Osplit_7, cls_insert__commute_0, cls_agent_Orecs_I2_J_0, cls_list__ex_Osimps_I2_J_2, cls_agent_Osimps_I2_J_0, cls_remdups__eq__nil__iff_0, cls_filter_Osimps_I2_J_1, cls_equalityE_0, cls_rev__rev__ident_0, cls_distinct1__rotate_1, cls_event_Osimps_I5_J_0, cls_sorted_Osimps_I3_J_0, cls_list__all2__Cons2_3, cls_append1__eq__conv_0, cls_sorted__dropWhile_0, cls_dropWhile_Oinduct_1, cls_distinct_Oinduct_1, cls_Cons__eq__filterD_2, cls_list_Osimps_I2_J_0, cls_remdups__eq__nil__right__iff_0, cls_removeAll_Oinduct_1, cls_le__refl_0, cls_agent_Ocase__cong_1, cls_knows__Spy__subset__knows__Spy__Gets_0, cls_list__all2__append_1, cls_dropWhile_Osimps_I2_J_0, cls_list__all__append_0, cls_foldl_Oinduct_0, cls_predicate1D_0, cls_spies__Says__rev_0, cls_list__update__nonempty_0, cls_empty__null_1, cls_list__all2__rev1_0
% 19.16/6.11 % No. of inferences in proof: 871
% 19.16/6.11 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5408 ms resp. 4255 ms w/o parsing
% 21.04/6.58 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.04/6.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------