TSTP Solution File: SWV779-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV779-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:18:29 EDT 2023
% Result : Unsatisfiable 8.57s 2.95s
% Output : Refutation 9.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 537
% Syntax : Number of formulae : 973 ( 383 unt; 102 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 : 205 ( 205 >; 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_type,type,
c_Event_Oknows: $i > $i > $i ).
thf(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i > $i ).
thf(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_List_Orev_type,type,
c_List_Orev: $i > $i ).
thf(c_Fun_Oinj__on_type,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_List_Oset_type,type,
c_List_Oset: $i > $i > $i ).
thf(c_List_Odistinct_type,type,
c_List_Odistinct: $i > $i > $o ).
thf(c_List_Omap_type,type,
c_List_Omap: $i > $i > $i > $i > $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_List_Oremove1_type,type,
c_List_Oremove1: $i > $i > $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(tc_bool_type,type,
tc_bool: $i ).
thf(c_List_Otake_type,type,
c_List_Otake: $i > $i > $i > $i ).
thf(c_List_Oappend_type,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_Nat_Osize__class_Osize_type,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_List_Olist__update_type,type,
c_List_Olist__update: $i > $i > $i > $i > $i ).
thf(c_List_Odrop_type,type,
c_List_Odrop: $i > $i > $i > $i ).
thf(c_List_Orotate_type,type,
c_List_Orotate: $i > $i > $i > $i ).
thf(c_List_Ofilter_type,type,
c_List_Ofilter: $i > $i > $i > $i ).
thf(c_List_Otl_type,type,
c_List_Otl: $i > $i > $i ).
thf(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_List_Olinorder__class_Osorted_type,type,
c_List_Olinorder__class_Osorted: $i > $i > $o ).
thf(c_Message_Oagent_OFriend_type,type,
c_Message_Oagent_OFriend: $i > $i ).
thf(c_Message_Oagent_OServer_type,type,
c_Message_Oagent_OServer: $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_List_OdropWhile_type,type,
c_List_OdropWhile: $i > $i > $i > $i ).
thf(c_List_Olist__all2_type,type,
c_List_Olist__all2: $i > $i > $i > $i > $i > $o ).
thf(c_Event_Oevent_OGets_type,type,
c_Event_Oevent_OGets: $i > $i > $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(c_List_Orotate1_type,type,
c_List_Orotate1: $i > $i > $i ).
thf(c_List_Oremdups_type,type,
c_List_Oremdups: $i > $i > $i ).
thf(c_List_Onull_type,type,
c_List_Onull: $i > $i > $o ).
thf(c_fequal_type,type,
c_fequal: $i > $i ).
thf(c_Map_Omap__upds_type,type,
c_Map_Omap__upds: $i > $i > $i > $i > $i > $i ).
thf(class_HOL_Oord_type,type,
class_HOL_Oord: $i > $o ).
thf(class_Divides_Osemiring__div_type,type,
class_Divides_Osemiring__div: $i > $o ).
thf(c_Divides_Odiv__class_Omod_type,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(c_List_Ofoldr_type,type,
c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).
thf(c_Event_Oevent_OSays_type,type,
c_Event_Oevent_OSays: $i > $i > $i > $i ).
thf(c_List_Olistsp_type,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(c_List_Osublist_type,type,
c_List_Osublist: $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_Divides_Oring__div_type,type,
class_Divides_Oring__div: $i > $o ).
thf(c_List_Olist__all_type,type,
c_List_Olist__all: $i > $i > $i > $o ).
thf(c_Message_Oagent_Oagent__case_type,type,
c_Message_Oagent_Oagent__case: $i > $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(c_Message_Osko__Message__Xagent__Xcase__cong__1__1_type,type,
c_Message_Osko__Message__Xagent__Xcase__cong__1__1: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Osetsum_type,type,
c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).
thf(c_List_Olistsum_type,type,
c_List_Olistsum: $i > $i > $i ).
thf(c_List_Oreplicate_type,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(c_List_Obutlast_type,type,
c_List_Obutlast: $i > $i > $i ).
thf(c_List_Ohd_type,type,
c_List_Ohd: $i > $i > $i ).
thf(c_Message_Oagent_Oagent__rec_type,type,
c_Message_Oagent_Oagent__rec: $i > $i > $i > $i > $i > $i ).
thf(c_List_Olist__ex_type,type,
c_List_Olist__ex: $i > $i > $i > $o ).
thf(c_List_Ofoldl_type,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(v_sko__List__XdropWhile__Xinduct__2_type,type,
v_sko__List__XdropWhile__Xinduct__2: $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(v_sko__List__Xlist__Xinduct__2_type,type,
v_sko__List__Xlist__Xinduct__2: $i > $i ).
thf(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
thf(v_sko__List__Xlist__Xinduct__1_type,type,
v_sko__List__Xlist__Xinduct__1: $i > $i ).
thf(c_List_Olist_Olist__rec_type,type,
c_List_Olist_Olist__rec: $i > $i > $i > $i > $i > $i ).
thf(v_sko__List__Xlist__update__Xinduct__2_type,type,
v_sko__List__Xlist__update__Xinduct__2: $i > $i ).
thf(c_List_Olist_Olist__case_type,type,
c_List_Olist_Olist__case: $i > $i > $i > $i > $i > $i ).
thf(v_sko__Message__Xagent__Xsplit__asm__1_type,type,
v_sko__Message__Xagent__Xsplit__asm__1: $i > $i > $i > $i ).
thf(c_List_Olast_type,type,
c_List_Olast: $i > $i > $i ).
thf(t_b_type,type,
t_b: $i ).
thf(v_sko__List__Xzip__Xinduct__1_type,type,
v_sko__List__Xzip__Xinduct__1: $i > $i ).
thf(v_sko__List__Xzip__Xinduct__2_type,type,
v_sko__List__Xzip__Xinduct__2: $i > $i ).
thf(v_sko__Message__Xagent__Xsplit__1_type,type,
v_sko__Message__Xagent__Xsplit__1: $i > $i > $i > $i ).
thf(v_sko__List__Xremove1__Xinduct__1_type,type,
v_sko__List__Xremove1__Xinduct__1: $i > $i ).
thf(v_sko__List__Xremove1__Xinduct__2_type,type,
v_sko__List__Xremove1__Xinduct__2: $i > $i ).
thf(c_List_Olistrelp_type,type,
c_List_Olistrelp: $i > $i > $i > $i > $o ).
thf(v_sko__List__Xlistset__Xinduct__2_type,type,
v_sko__List__Xlistset__Xinduct__2: $i > $i ).
thf(c_List_Ofiltermap_type,type,
c_List_Ofiltermap: $i > $i > $i > $i > $i ).
thf(v_sko__List__Xconcat__Xinduct__2_type,type,
v_sko__List__Xconcat__Xinduct__2: $i > $i ).
thf(v_sko__List__Xtake__Xinduct__2_type,type,
v_sko__List__Xtake__Xinduct__2: $i > $i ).
thf(v_sko__List__XremoveAll__Xinduct__1_type,type,
v_sko__List__XremoveAll__Xinduct__1: $i > $i ).
thf(v_sko__List__XremoveAll__Xinduct__2_type,type,
v_sko__List__XremoveAll__Xinduct__2: $i > $i ).
thf(v_sko__List__Xlast__Xinduct__1_type,type,
v_sko__List__Xlast__Xinduct__1: $i > $i ).
thf(v_sko__List__Xlast__Xinduct__2_type,type,
v_sko__List__Xlast__Xinduct__2: $i > $i ).
thf(v_sko__List__Xlistsum__Xinduct__2_type,type,
v_sko__List__Xlistsum__Xinduct__2: $i > $i ).
thf(c_NS__Shared__Mirabelle_Ons__sharedp_type,type,
c_NS__Shared__Mirabelle_Ons__sharedp: $i > $o ).
thf(c_List_Olist__inter_type,type,
c_List_Olist__inter: $i > $i > $i > $i ).
thf(c_Event_OinitState_type,type,
c_Event_OinitState: $i > $i ).
thf(v_sko__List__Xlist__update__Xinduct__1_type,type,
v_sko__List__Xlist__update__Xinduct__1: $i > $i ).
thf(v_sko__List__Xlistset__Xinduct__1_type,type,
v_sko__List__Xlistset__Xinduct__1: $i > $i ).
thf(v_sko__List__Xlistsum__Xinduct__1_type,type,
v_sko__List__Xlistsum__Xinduct__1: $i > $i ).
thf(v_sko__List__Xmap__Xinduct__2_type,type,
v_sko__List__Xmap__Xinduct__2: $i > $i ).
thf(v_sko__List__Xdistinct__Xinduct__2_type,type,
v_sko__List__Xdistinct__Xinduct__2: $i > $i ).
thf(v_sko__List__XtakeWhile__Xinduct__1_type,type,
v_sko__List__XtakeWhile__Xinduct__1: $i > $i ).
thf(v_sko__List__XtakeWhile__Xinduct__2_type,type,
v_sko__List__XtakeWhile__Xinduct__2: $i > $i ).
thf(v_sko__List__Xfoldl__Xinduct__2_type,type,
v_sko__List__Xfoldl__Xinduct__2: $i > $i ).
thf(v_sko__List__XdropWhile__Xinduct__1_type,type,
v_sko__List__XdropWhile__Xinduct__1: $i > $i ).
thf(v_sko__List__Xdistinct__Xinduct__1_type,type,
v_sko__List__Xdistinct__Xinduct__1: $i > $i ).
thf(393,axiom,
! [B: $i,A: $i] :
~ ( c_List_Olist__ex @ A @ ( c_List_Olist_ONil @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I1_J_0) ).
thf(1322,plain,
! [B: $i,A: $i] :
~ ( c_List_Olist__ex @ A @ ( c_List_Olist_ONil @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(400,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Says_0) ).
thf(1337,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ C @ D @ E ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(334,axiom,
c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_ONil @ tc_Event_Oevent ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ns__sharedp_ONil_0) ).
thf(1190,plain,
c_NS__Shared__Mirabelle_Ons__sharedp @ ( c_List_Olist_ONil @ tc_Event_Oevent ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(143,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Otake @ B @ C @ D ) @ ( c_List_Otake @ B @ E @ F ) @ D @ F )
| ~ ( c_List_Olist__all2 @ A @ C @ E @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__takeI_0) ).
thf(760,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Otake @ B @ C @ D ) @ ( c_List_Otake @ B @ E @ F ) @ D @ F )
| ~ ( c_List_Olist__all2 @ A @ C @ E @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(295,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__eq__ConsD_2) ).
thf(1105,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(183,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ B @ C @ D @ E )
| ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ F @ B @ D ) @ ( c_List_Olist_OCons @ G @ C @ E ) @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons_1) ).
thf(846,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ B @ C @ D @ E )
| ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ F @ B @ D ) @ ( c_List_Olist_OCons @ G @ C @ E ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(390,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ D @ E )
= ( c_Message_Oagent_Oagent__case @ F @ G @ H @ D @ E ) )
| ( D = c_Message_Oagent_OSpy )
| ( D
= ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ D @ B @ G @ E ) ) )
| ( D = c_Message_Oagent_OServer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_0) ).
thf(1315,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ D @ E )
= ( c_Message_Oagent_Oagent__case @ F @ G @ H @ D @ E ) )
| ( D = c_Message_Oagent_OSpy )
| ( D
= ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ D @ B @ G @ E ) ) )
| ( D = c_Message_Oagent_OServer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Gets_0) ).
thf(1179,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Event_Oknows @ c_Message_Oagent_OSpy @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(150,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ F @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
thf(777,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ F @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(382,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Map_Omap__upds @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upds__Nil1_0) ).
thf(1295,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Map_Omap__upds @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(297,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__XremoveAll__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_removeAll_Oinduct_0) ).
thf(1110,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__XremoveAll__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(92,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(645,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(204,axiom,
! [B: $i,A: $i] :
( ( c_List_Ofilter @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I1_J_0) ).
thf(892,plain,
! [B: $i,A: $i] :
( ( c_List_Ofilter @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(213,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ ( c_Message_Oagent_OFriend @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_1) ).
thf(909,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ ( c_Message_Oagent_OFriend @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(85,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OGets @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I4_J_0) ).
thf(628,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OGets @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(263,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ A ) @ A ) )
= ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).
thf(1031,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ A ) @ A ) )
= ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(240,axiom,
! [B: $i,A: $i] :
( ( c_List_Odistinct @ ( hAPP @ ( c_List_Orev @ A ) @ B ) @ A )
| ~ ( c_List_Odistinct @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rev_1) ).
thf(977,plain,
! [B: $i,A: $i] :
( ( c_List_Odistinct @ ( hAPP @ ( c_List_Orev @ A ) @ B ) @ A )
| ~ ( c_List_Odistinct @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(342,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).
thf(1211,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(144,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ E @ D )
= ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ E @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__length_0) ).
thf(762,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ E @ D )
= ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ E @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(429,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ( E = c_Message_Oagent_OSpy )
| ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_9) ).
thf(1401,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ( E = c_Message_Oagent_OSpy )
| ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(340,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(1205,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(655,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(191,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ A @ B @ C )
= B )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__all_0) ).
thf(861,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ A @ B @ C )
= B )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(309,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xzip__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zip_Oinduct_0) ).
thf(1137,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xzip__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_List_Olist__all2 @ ( c_fequal @ C ) @ A @ B @ C @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__eq_1) ).
thf(533,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_List_Olist__all2 @ ( c_fequal @ C ) @ A @ B @ C @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_OCons @ C @ D @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_0) ).
thf(550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_OCons @ C @ D @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(159,axiom,
! [B: $i,A: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remdups_0) ).
thf(797,plain,
! [B: $i,A: $i] : ( c_List_Odistinct @ ( c_List_Oremdups @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(472,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(353,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) )
!= ( hAPP @ C @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
| ( B = c_Message_Oagent_OServer )
| ( ( c_Message_Oagent_Oagent__case @ E @ A @ F @ B @ D )
= ( c_Message_Oagent_Oagent__case @ G @ C @ H @ B @ D ) )
| ( B = c_Message_Oagent_OSpy ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_2) ).
thf(1233,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) )
!= ( hAPP @ C @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
| ( B = c_Message_Oagent_OServer )
| ( ( c_Message_Oagent_Oagent__case @ E @ A @ F @ B @ D )
= ( c_Message_Oagent_Oagent__case @ G @ C @ H @ B @ D ) )
| ( B = c_Message_Oagent_OSpy ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rotate_0) ).
thf(814,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(403,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlast__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Oinduct_0) ).
thf(1342,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlast__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(277,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(1063,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(408,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Ofilter @ D @ E @ C ) )
| ( hBOOL @ ( hAPP @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__filterD_2) ).
thf(1354,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Ofilter @ D @ E @ C ) )
| ( hBOOL @ ( hAPP @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(101,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ E @ B @ C ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(670,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ E @ B @ C ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Odrop @ B @ C @ A ) )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ A ) ) @ B @ tc_nat ) @ ( hAPP @ ( c_List_Orev @ A ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__drop_0) ).
thf(1095,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Odrop @ B @ C @ A ) )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ A ) ) @ B @ tc_nat ) @ ( hAPP @ ( c_List_Orev @ A ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(207,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlist__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinduct_0) ).
thf(898,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlist__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(250,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ A ) @ ( v_sko__List__Xremove1__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Oinduct_1) ).
thf(1001,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xremove1__Xinduct__1 @ A ) @ ( v_sko__List__Xremove1__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(425,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olast @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_1) ).
thf(1391,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olast @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(410,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistrelp @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ D ) @ D )
| ~ ( c_List_Olistrelp @ A @ C @ F @ D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listrelp_OCons_0) ).
thf(1359,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistrelp @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ D ) @ D )
| ~ ( c_List_Olistrelp @ A @ C @ F @ D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(422,axiom,
! [B: $i,A: $i] :
( ( c_List_Orotate @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_1) ).
thf(1386,plain,
! [B: $i,A: $i] :
( ( c_List_Orotate @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(57,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Oappend @ B @ C @ D ) @ E @ D @ F )
= ( c_List_Ofoldr @ A @ B @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr__append_0) ).
thf(565,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Oappend @ B @ C @ D ) @ E @ D @ F )
= ( c_List_Ofoldr @ A @ B @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(1,negated_conjecture,
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_ONil @ tc_Event_Oevent ) )
!= ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( hAPP @ ( c_List_Orev @ tc_Event_Oevent ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(436,plain,
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_ONil @ tc_Event_Oevent ) )
!= ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( hAPP @ ( c_List_Orev @ tc_Event_Oevent ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(1265,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(238,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osplit_0) ).
thf(973,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_ONil @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(201,axiom,
! [B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(885,plain,
! [B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(270,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(1046,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(274,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__XremoveAll__Xinduct__1 @ A ) @ ( v_sko__List__XremoveAll__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_removeAll_Oinduct_1) ).
thf(1055,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__XremoveAll__Xinduct__1 @ A ) @ ( v_sko__List__XremoveAll__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(216,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlist__update__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update_Oinduct_0) ).
thf(917,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlist__update__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(335,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ B @ A @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(1191,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ B @ A @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(66,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
| ( c_List_Olist__all2 @ E @ ( c_List_Oappend @ A @ F @ B ) @ ( c_List_Oappend @ C @ G @ D ) @ B @ D )
| ~ ( c_List_Olist__all2 @ E @ F @ G @ B @ D )
| ~ ( c_List_Olist__all2 @ E @ A @ C @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append_2) ).
thf(587,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
| ( c_List_Olist__all2 @ E @ ( c_List_Oappend @ A @ F @ B ) @ ( c_List_Oappend @ C @ G @ D ) @ B @ D )
| ~ ( c_List_Olist__all2 @ E @ F @ G @ B @ D )
| ~ ( c_List_Olist__all2 @ E @ A @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
| ~ ( c_List_Olist__all @ A @ C @ D )
| ~ ( c_List_Olist__all @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__append_2) ).
thf(619,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
| ~ ( c_List_Olist__all @ A @ C @ D )
| ~ ( c_List_Olist__all @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(542,plain,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__drop_0) ).
thf(460,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(419,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Oappend @ B @ C @ A ) )
= ( c_List_Oappend @ ( hAPP @ ( c_List_Orev @ A ) @ C ) @ ( hAPP @ ( c_List_Orev @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__append_0) ).
thf(1379,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Oappend @ B @ C @ A ) )
= ( c_List_Oappend @ ( hAPP @ ( c_List_Orev @ A ) @ C ) @ ( hAPP @ ( c_List_Orev @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(287,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__ex @ A @ B @ C )
| ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( c_List_Olist__ex @ A @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_0) ).
thf(1087,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__ex @ A @ B @ C )
| ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( c_List_Olist__ex @ A @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(314,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(1147,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1247,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(194,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(870,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(147,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ A @ C ) @ B @ C )
= E )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_3) ).
thf(770,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ A @ C ) @ B @ C )
= E )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(199,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ B @ C )
| ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
thf(881,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ B @ C )
| ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(293,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__ex @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_1) ).
thf(1100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__ex @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(385,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ A ) @ ( v_sko__List__Xlistset__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listset_Oinduct_1) ).
thf(1302,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistset__Xinduct__1 @ A ) @ ( v_sko__List__Xlistset__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ A @ B @ C ) @ ( c_List_Odrop @ A @ B @ C ) @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).
thf(789,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ A @ B @ C ) @ ( c_List_Odrop @ A @ B @ C ) @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(267,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ c_Message_Oagent_OSpy @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_2) ).
thf(1040,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ c_Message_Oagent_OSpy @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(646,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(177,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ A @ B @ C @ D ) ) )
| ( A = c_Message_Oagent_OServer )
| ( ( c_Message_Oagent_Oagent__case @ E @ B @ F @ A @ D )
= ( c_Message_Oagent_Oagent__case @ G @ C @ F @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_1) ).
thf(834,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ A @ B @ C @ D ) ) )
| ( A = c_Message_Oagent_OServer )
| ( ( c_Message_Oagent_Oagent__case @ E @ B @ F @ A @ D )
= ( c_Message_Oagent_Oagent__case @ G @ C @ F @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_List_Onull @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps_I2_J_0) ).
thf(514,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_List_Onull @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(316,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ B @ C )
| ~ ( c_List_Olist__all @ A @ ( hAPP @ ( c_List_Orev @ C ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__rev_0) ).
thf(1151,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ B @ C )
| ~ ( c_List_Olist__all @ A @ ( hAPP @ ( c_List_Orev @ C ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(164,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_1) ).
thf(806,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Otake @ B @ C @ A ) )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ A ) ) @ B @ tc_nat ) @ ( hAPP @ ( c_List_Orev @ A ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__take_0) ).
thf(966,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Otake @ B @ C @ A ) )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ A ) ) @ B @ tc_nat ) @ ( hAPP @ ( c_List_Orev @ A ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(376,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( hAPP @ ( c_List_Orev @ A ) @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
thf(1283,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( hAPP @ ( c_List_Orev @ A ) @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) )
| ( ( c_List_Oappend @ A @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ B )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_2) ).
thf(475,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) )
| ( ( c_List_Oappend @ A @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_OdropWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ C @ D ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_1) ).
thf(924,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_OdropWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ C @ D ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(435,axiom,
! [A: $i] : ( c_List_Odistinct @ ( c_List_Olist_ONil @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).
thf(1418,plain,
! [A: $i] : ( c_List_Odistinct @ ( c_List_Olist_ONil @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Otake @ B @ C @ D ) @ D )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ ( c_List_Odrop @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__take_0) ).
thf(623,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Otake @ B @ C @ D ) @ D )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ ( c_List_Odrop @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(272,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons1_3) ).
thf(1051,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(170,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(821,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(211,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_Olist__rec @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( hAPP @ ( hAPP @ ( hAPP @ B @ C ) @ D ) @ ( c_List_Olist_Olist__rec @ A @ B @ D @ F @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Orecs_I2_J_0) ).
thf(905,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_Olist__rec @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( hAPP @ ( hAPP @ ( hAPP @ B @ C ) @ D ) @ ( c_List_Olist_Olist__rec @ A @ B @ D @ F @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(344,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Event_OinitState @ A ) @ ( c_Event_Oknows @ A @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_initState__subset__knows_0) ).
thf(1215,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Event_OinitState @ A ) @ ( c_Event_Oknows @ A @ B ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ( ( c_Message_Oagent_OFriend @ A )
!= ( c_Message_Oagent_OFriend @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Oinject_0) ).
thf(877,plain,
! [B: $i,A: $i] :
( ( ( c_Message_Oagent_OFriend @ A )
!= ( c_Message_Oagent_OFriend @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(231,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Oagent_Oagent__rec @ A @ B @ C @ ( c_Message_Oagent_OFriend @ D ) @ E )
= ( hAPP @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Orecs_I2_J_0) ).
thf(956,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Oagent_Oagent__rec @ A @ B @ C @ ( c_Message_Oagent_OFriend @ D ) @ E )
= ( hAPP @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(281,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Oagent_Oagent__rec @ A @ B @ C @ c_Message_Oagent_OSpy @ D )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Orecs_I3_J_0) ).
thf(1072,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Oagent_Oagent__rec @ A @ B @ C @ c_Message_Oagent_OSpy @ D )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(301,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
thf(1119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(426,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ A ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Oinduct_1) ).
thf(1394,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__XdropWhile__Xinduct__1 @ A ) @ ( v_sko__List__XdropWhile__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ A @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(1351,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ A @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(249,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ( E
= ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) )
| ( E = c_Message_Oagent_OServer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_4) ).
thf(998,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ( E
= ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) )
| ( E = c_Message_Oagent_OServer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(245,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_Olist__rec @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Orecs_I1_J_0) ).
thf(988,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_Olist__rec @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
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(1242,plain,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
thf(527,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
thf(602,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(146,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(766,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(324,axiom,
! [B: $i,A: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Olast @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_0) ).
thf(1169,plain,
! [B: $i,A: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Olast @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(109,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
thf(687,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) )
= ( c_List_Oappend @ ( hAPP @ ( c_List_Orev @ A ) @ C ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
thf(1074,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) )
= ( c_List_Oappend @ ( hAPP @ ( c_List_Orev @ A ) @ C ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofilter @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Ofilter @ A @ B @ D ) @ ( c_List_Ofilter @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__append_0) ).
thf(452,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofilter @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Ofilter @ A @ B @ D ) @ ( c_List_Ofilter @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(105,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ B @ E @ D )
= ( c_List_Olist__update @ A @ B @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).
thf(678,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ B @ E @ D )
= ( c_List_Olist__update @ A @ B @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C )
= ( c_List_Otl @ ( c_List_Odrop @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__tl_0) ).
thf(529,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C )
= ( c_List_Otl @ ( c_List_Odrop @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_OdropWhile @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__dropWhile_0) ).
thf(661,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_OdropWhile @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(387,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Orotate1 @ A @ B )
!= ( c_List_Olist_ONil @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).
thf(1306,plain,
! [B: $i,A: $i] :
( ( ( c_List_Orotate1 @ A @ B )
!= ( c_List_Olist_ONil @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(1199,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(317,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
| ~ ( c_List_Olist__all @ A @ C @ D )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_2) ).
thf(1153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
| ~ ( c_List_Olist__all @ A @ C @ D )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_List_Oappend @ A @ C @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_0) ).
thf(810,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_List_Oappend @ A @ C @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(401,axiom,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
thf(1338,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) @ C )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).
thf(1067,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Oreplicate @ D @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Oreplicate @ D @ B @ C ) @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
thf(714,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Oreplicate @ D @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Oreplicate @ D @ B @ C ) @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Oremove1 @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remove1_0) ).
thf(512,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Oremove1 @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(226,axiom,
! [B: $i,A: $i] :
( A
= ( hAPP @ ( c_List_Orev @ B ) @ ( hAPP @ ( c_List_Orev @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_0) ).
thf(942,plain,
! [B: $i,A: $i] :
( A
= ( hAPP @ ( c_List_Orev @ B ) @ ( hAPP @ ( c_List_Orev @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_List_Oset @ B @ C ) @ C @ D )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ A @ B @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__map_1) ).
thf(439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_List_Oset @ B @ C ) @ C @ D )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ A @ B @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ ( c_List_Oappend @ B @ A @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_1) ).
thf(546,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ ( c_List_Oappend @ B @ A @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(157,axiom,
! [B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate1 @ A @ B ) @ B )
| ~ ( c_List_Odistinct @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct1__rotate_1) ).
thf(793,plain,
! [B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate1 @ A @ B ) @ B )
| ~ ( c_List_Odistinct @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(160,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(798,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(275,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(1057,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(372,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ c_Message_Oagent_OSpy @ D )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I10_J_0) ).
thf(1274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ c_Message_Oagent_OSpy @ D )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(205,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ E @ D @ F )
= ( hAPP @ ( hAPP @ A @ B ) @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
thf(894,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ E @ D @ F )
= ( hAPP @ ( hAPP @ A @ B ) @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(259,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
= ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).
thf(1021,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
= ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(268,axiom,
! [A: $i] :
( ( c_List_Oremdups @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_1) ).
thf(1042,plain,
! [A: $i] :
( ( c_List_Oremdups @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(363,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(1255,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(326,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlistsum__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_Oinduct_0) ).
thf(1174,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlistsum__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Ofilter @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__filter_0) ).
thf(561,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Ofilter @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(112,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
thf(693,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(729,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ ( hAPP @ ( c_List_Orev @ B ) @ C ) @ B )
| ~ ( c_List_Olist__all @ A @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__rev_1) ).
thf(1238,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ ( hAPP @ ( c_List_Orev @ B ) @ C ) @ B )
| ~ ( c_List_Olist__all @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(137,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_List_Oset @ B @ A )
!= ( c_List_Oset @ C @ A ) )
| ~ ( c_List_Odistinct @ C @ A )
| ~ ( c_List_Olinorder__class_Osorted @ C @ A )
| ~ ( c_List_Odistinct @ B @ A )
| ~ ( c_List_Olinorder__class_Osorted @ B @ A )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__distinct__set__unique_0) ).
thf(746,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_List_Oset @ B @ A )
!= ( c_List_Oset @ C @ A ) )
| ~ ( c_List_Odistinct @ C @ A )
| ~ ( c_List_Olinorder__class_Osorted @ C @ A )
| ~ ( c_List_Odistinct @ B @ A )
| ~ ( c_List_Olinorder__class_Osorted @ B @ A )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(289,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
= ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).
thf(1091,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
= ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(154,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(788,plain,
class_HOL_Oord @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(415,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( hAPP @ ( c_List_Orev @ A ) @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_1) ).
thf(1370,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( hAPP @ ( c_List_Orev @ A ) @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Orotate @ C @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rotate_0) ).
thf(467,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Orotate @ C @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(484,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(413,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xfoldl__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl_Oinduct_0) ).
thf(1365,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xfoldl__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(82,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(625,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(186,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Obutlast @ B @ C ) @ C )
= ( c_List_Obutlast @ ( c_List_Odrop @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__butlast_0) ).
thf(852,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Obutlast @ B @ C ) @ C )
= ( c_List_Obutlast @ ( c_List_Odrop @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(320,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( C
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(1159,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( C
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(284,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_List_Olist_ONil @ B ) )
| ~ ( c_List_Onull @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__null_1) ).
thf(1079,plain,
! [B: $i,A: $i] :
( ( A
= ( c_List_Olist_ONil @ B ) )
| ~ ( c_List_Onull @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(142,axiom,
! [A: $i] :
( c_Message_Oagent_OServer
!= ( c_Message_Oagent_OFriend @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I2_J_0) ).
thf(757,plain,
! [A: $i] :
( c_Message_Oagent_OServer
!= ( c_Message_Oagent_OFriend @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
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(1128,plain,
c_Message_Oagent_OSpy != c_Message_Oagent_OServer,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(375,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_Olist__case @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( hAPP @ ( hAPP @ B @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I5_J_0) ).
thf(1281,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_Olist__case @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( hAPP @ ( hAPP @ B @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Osublist @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__sublistI_0) ).
thf(583,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Osublist @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B )
!= A )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ( ( c_List_Oappend @ C @ D @ B )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ D @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_4) ).
thf(522,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B )
!= A )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ( ( c_List_Oappend @ C @ D @ B )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ D @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(682,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(431,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) )
!= ( hAPP @ C @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
| ( B = c_Message_Oagent_OServer )
| ( ( c_Message_Oagent_Oagent__case @ E @ A @ F @ B @ D )
= ( c_Message_Oagent_Oagent__case @ G @ C @ F @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_3) ).
thf(1407,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) )
!= ( hAPP @ C @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
| ( B = c_Message_Oagent_OServer )
| ( ( c_Message_Oagent_Oagent__case @ E @ A @ F @ B @ D )
= ( c_Message_Oagent_Oagent__case @ G @ C @ F @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(380,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( c_List_Orev @ A ) @ B ) @ ( tc_List_Olist @ A ) )
= ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rev_0) ).
thf(1291,plain,
! [B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( c_List_Orev @ A ) @ B ) @ ( tc_List_Olist @ A ) )
= ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(118,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Odrop @ B @ C @ D ) @ ( c_List_Odrop @ B @ E @ F ) @ D @ F )
| ~ ( c_List_Olist__all2 @ A @ C @ E @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__dropI_0) ).
thf(710,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Odrop @ B @ C @ D ) @ ( c_List_Odrop @ B @ E @ F ) @ D @ F )
| ~ ( c_List_Olist__all2 @ A @ C @ E @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Odrop @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__drop_0) ).
thf(456,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Odrop @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(181,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).
thf(842,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ D @ ( c_List_Olist_OCons @ B @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).
thf(742,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ D @ ( c_List_Olist_OCons @ B @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(370,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( hAPP @ ( c_List_Orev @ B ) @ C ) @ D @ B @ E )
| ~ ( c_List_Olist__all2 @ A @ C @ ( hAPP @ ( c_List_Orev @ E ) @ D ) @ B @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__rev1_1) ).
thf(1270,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( hAPP @ ( c_List_Orev @ B ) @ C ) @ D @ B @ E )
| ~ ( c_List_Olist__all2 @ A @ C @ ( hAPP @ ( c_List_Orev @ E ) @ D ) @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(77,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Otake @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
= ( c_List_Omap @ B @ ( c_List_Otake @ A @ C @ D ) @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__map_0) ).
thf(615,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Otake @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
= ( c_List_Omap @ B @ ( c_List_Otake @ A @ C @ D ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(302,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) )
| ( A = c_Message_Oagent_OSpy ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Gets_0) ).
thf(1121,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ A @ B ) @ C @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ B @ ( c_Event_Oknows @ A @ C ) @ tc_Message_Omsg ) )
| ( A = c_Message_Oagent_OSpy ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(350,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1227,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(126,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
| ( c_List_Olist__all2 @ E @ F @ G @ B @ D )
| ~ ( c_List_Olist__all2 @ E @ ( c_List_Oappend @ A @ F @ B ) @ ( c_List_Oappend @ C @ G @ D ) @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append_1) ).
thf(725,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
| ( c_List_Olist__all2 @ E @ F @ G @ B @ D )
| ~ ( c_List_Olist__all2 @ E @ ( c_List_Oappend @ A @ F @ B ) @ ( c_List_Oappend @ C @ G @ D ) @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
thf(593,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ B @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_0) ).
thf(610,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ B @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Ofilter @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__filter__le_0) ).
thf(783,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Ofilter @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(188,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ B @ C )
| ~ ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_1) ).
thf(857,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ B @ C )
| ~ ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(697,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Oappend @ ( hAPP @ ( c_List_Orev @ A ) @ B ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ A ) @ A ) @ A ) )
= ( c_List_Olist_OCons @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
thf(1089,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Oappend @ ( hAPP @ ( c_List_Orev @ A ) @ B ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ A ) @ A ) @ A ) )
= ( c_List_Olist_OCons @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(196,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Oappend @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( c_List_Ofoldl @ A @ B @ C @ F @ E ) @ D @ F @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__append_0) ).
thf(874,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Oappend @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( c_List_Ofoldl @ A @ B @ C @ F @ E ) @ D @ F @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orotate @ A @ ( hAPP @ ( c_List_Orev @ B ) @ C ) @ B )
= ( hAPP @ ( c_List_Orev @ B ) @ ( c_List_Orotate @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ ( c_Divides_Odiv__class_Omod @ A @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ tc_nat ) @ tc_nat ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__rev_0) ).
thf(1143,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orotate @ A @ ( hAPP @ ( c_List_Orev @ B ) @ C ) @ B )
= ( hAPP @ ( c_List_Orev @ B ) @ ( c_List_Orotate @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ ( c_Divides_Odiv__class_Omod @ A @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ tc_nat ) @ tc_nat ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(396,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Omap @ B @ C @ D @ A ) )
= ( c_List_Omap @ B @ ( hAPP @ ( c_List_Orev @ D ) @ C ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__map_0) ).
thf(1329,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Omap @ B @ C @ D @ A ) )
= ( c_List_Omap @ B @ ( hAPP @ ( c_List_Orev @ D ) @ C ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(285,axiom,
! [A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Olist_ONil @ A ) )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).
thf(1082,plain,
! [A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Olist_ONil @ A ) )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(24,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
| ( c_List_Olist__all2 @ E @ A @ C @ B @ D )
| ~ ( c_List_Olist__all2 @ E @ ( c_List_Oappend @ A @ F @ B ) @ ( c_List_Oappend @ C @ G @ D ) @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append_0) ).
thf(488,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
| ( c_List_Olist__all2 @ E @ A @ C @ B @ D )
| ~ ( c_List_Olist__all2 @ E @ ( c_List_Oappend @ A @ F @ B ) @ ( c_List_Oappend @ C @ G @ D ) @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(411,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= ( c_List_Olist_ONil @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__iff_0) ).
thf(1361,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= ( c_List_Olist_ONil @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
!= ( hAPP @ ( c_List_Orev @ B ) @ C ) )
| ( C
= ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
thf(933,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
!= ( hAPP @ ( c_List_Orev @ B ) @ C ) )
| ( C
= ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd_Osimps_0) ).
thf(753,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(330,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_10) ).
thf(1182,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(209,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ A ) @ ( v_sko__List__Xlist__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinduct_1) ).
thf(901,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__Xinduct__1 @ A ) @ ( v_sko__List__Xlist__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(91,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
| ( ( c_Map_Omap__upds @ E @ A @ ( c_List_Oappend @ C @ F @ D ) @ B @ D )
= ( c_Map_Omap__upds @ E @ A @ C @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upds__append2__drop_0) ).
thf(642,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
| ( ( c_Map_Omap__upds @ E @ A @ ( c_List_Oappend @ C @ F @ D ) @ B @ D )
= ( c_Map_Omap__upds @ E @ A @ C @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
thf(637,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(318,axiom,
! [B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).
thf(1155,plain,
! [B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
= ( c_List_Olist_OCons @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(1016,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
= ( c_List_Olist_OCons @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(67,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( B
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ D @ C ) @ E @ C ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_1) ).
thf(590,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( B
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ D @ C ) @ E @ C ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(178,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps_I2_J_0) ).
thf(837,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ ( c_List_Oset @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ A @ D ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Says_0) ).
thf(1263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ A @ D ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(243,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ ( c_Message_Oagent_OFriend @ D ) @ E )
= ( hAPP @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I9_J_0) ).
thf(985,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ ( c_Message_Oagent_OFriend @ D ) @ E )
= ( hAPP @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(383,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ( E = c_Message_Oagent_OSpy )
| ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_9) ).
thf(1297,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ( E = c_Message_Oagent_OSpy )
| ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(738,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(352,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist__update @ B @ C @ D @ E ) @ E @ F )
= ( c_List_Olist__update @ ( c_List_Omap @ A @ B @ E @ F ) @ C @ ( hAPP @ A @ D ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__update_0) ).
thf(1231,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist__update @ B @ C @ D @ E ) @ E @ F )
= ( c_List_Olist__update @ ( c_List_Omap @ A @ B @ E @ F ) @ C @ ( hAPP @ A @ D ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(306,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).
thf(1131,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(276,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Odrop @ A @ B @ C )
= ( c_List_Olist_ONil @ C ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__all_0) ).
thf(1060,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Odrop @ A @ B @ C )
= ( c_List_Olist_ONil @ C ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(214,axiom,
! [A: $i] :
( c_Message_Oagent_OSpy
!= ( c_Message_Oagent_OFriend @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I7_J_0) ).
thf(911,plain,
! [A: $i] :
( c_Message_Oagent_OSpy
!= ( c_Message_Oagent_OFriend @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ A @ D @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(569,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ A @ D @ C ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(394,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( hAPP @ ( c_List_Orev @ B ) @ C ) @ ( hAPP @ ( c_List_Orev @ D ) @ E ) @ B @ D )
| ~ ( c_List_Olist__all2 @ A @ C @ E @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__rev_1) ).
thf(1324,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( hAPP @ ( c_List_Orev @ B ) @ C ) @ ( hAPP @ ( c_List_Orev @ D ) @ E ) @ B @ D )
| ~ ( c_List_Olist__all2 @ A @ C @ E @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(299,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ( E = c_Message_Oagent_OSpy )
| ( E
= ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) )
| ( E = c_Message_Oagent_OServer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_3) ).
thf(1114,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ( E = c_Message_Oagent_OSpy )
| ( E
= ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) )
| ( E = c_Message_Oagent_OServer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ A @ B ) @ ( tc_List_Olist @ B ) )
= ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rotate1_0) ).
thf(503,plain,
! [B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ A @ B ) @ ( tc_List_Olist @ B ) )
= ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= A )
| ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
= ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__remdups__eq_1) ).
thf(605,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= A )
| ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
= ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(398,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E )
= ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).
thf(1333,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E )
= ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(391,axiom,
! [B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Nil_0) ).
thf(1318,plain,
! [B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(339,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( c_List_Orev @ A ) @ B )
!= ( c_List_Olist_ONil @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).
thf(1202,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( c_List_Orev @ A ) @ B )
!= ( c_List_Olist_ONil @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
= ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__list__update_0) ).
thf(633,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
= ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oremdups @ ( c_List_Ofilter @ A @ B @ C ) @ C )
= ( c_List_Ofilter @ A @ ( c_List_Oremdups @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__filter_0) ).
thf(508,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oremdups @ ( c_List_Ofilter @ A @ B @ C ) @ C )
= ( c_List_Ofilter @ A @ ( c_List_Oremdups @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
thf(558,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(230,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Olist_ONil @ B ) )
| ~ ( c_List_Olist__all2 @ C @ A @ ( c_List_Olist_ONil @ D ) @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Nil2_0) ).
thf(953,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Olist_ONil @ B ) )
| ~ ( c_List_Olist__all2 @ C @ A @ ( c_List_Olist_ONil @ D ) @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(773,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(718,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(378,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Olast @ ( hAPP @ ( c_List_Orev @ A ) @ B ) @ A )
= ( c_List_Ohd @ B @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__rev_0) ).
thf(1286,plain,
! [B: $i,A: $i] :
( ( ( c_List_Olast @ ( hAPP @ ( c_List_Orev @ A ) @ B ) @ A )
= ( c_List_Ohd @ B @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(265,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Olast @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_1) ).
thf(1035,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Olast @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_List_Orev @ A ) @ B )
!= ( hAPP @ ( c_List_Orev @ A ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
thf(1187,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_List_Orev @ A ) @ B )
!= ( hAPP @ ( c_List_Orev @ A ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orotate @ A @ B @ C )
= ( c_List_Orotate @ ( c_Divides_Odiv__class_Omod @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__conv__mod_0) ).
thf(674,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orotate @ A @ B @ C )
= ( c_List_Orotate @ ( c_Divides_Odiv__class_Omod @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(261,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ( E
= ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_8) ).
thf(1026,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ( E
= ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(323,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D @ F @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(1167,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D @ F @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(374,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) )
!= ( hAPP @ C @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
| ( ( c_Message_Oagent_Oagent__case @ E @ A @ F @ B @ D )
= ( c_Message_Oagent_Oagent__case @ E @ C @ F @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_7) ).
thf(1278,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) )
!= ( hAPP @ C @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
| ( ( c_Message_Oagent_Oagent__case @ E @ A @ F @ B @ D )
= ( c_Message_Oagent_Oagent__case @ E @ C @ F @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(308,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(1135,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
thf(750,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(172,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
= ( c_List_Omap @ B @ ( c_List_Odrop @ A @ C @ D ) @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__map_0) ).
thf(824,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
= ( c_List_Omap @ B @ ( c_List_Odrop @ A @ C @ D ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(60,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( C = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_2) ).
thf(573,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( C = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(111,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(689,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ A @ B @ C @ D )
= A )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__beyond_0) ).
thf(444,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ A @ B @ C @ D )
= A )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(417,axiom,
! [A: $i] :
( ( c_Event_Oknows @ A @ ( c_List_Olist_ONil @ tc_Event_Oevent ) )
= ( c_Event_OinitState @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Nil_0) ).
thf(1374,plain,
! [A: $i] :
( ( c_Event_Oknows @ A @ ( c_List_Olist_ONil @ tc_Event_Oevent ) )
= ( c_Event_OinitState @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__replicate_0) ).
thf(733,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__remove1_0) ).
thf(819,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Oremove1 @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ A ) @ ( v_sko__List__Xzip__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zip_Oinduct_1) ).
thf(975,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xzip__Xinduct__1 @ A ) @ ( v_sko__List__Xzip__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(253,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlistset__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listset_Oinduct_0) ).
thf(1007,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlistset__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(424,axiom,
! [A: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).
thf(1389,plain,
! [A: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) )
| ( ( c_List_Oappend @ A @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ D @ B ) @ B )
= ( c_List_Oappend @ C @ D @ B ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_5) ).
thf(843,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) )
| ( ( c_List_Oappend @ A @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ D @ B ) @ B )
= ( c_List_Oappend @ C @ D @ B ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(423,axiom,
! [B: $i,A: $i] : ( c_List_Olist__all @ A @ ( c_List_Olist_ONil @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I1_J_0) ).
thf(1388,plain,
! [B: $i,A: $i] : ( c_List_Olist__all @ A @ ( c_List_Olist_ONil @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ B @ C )
| ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
thf(579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ B @ C )
| ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(232,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Ohd @ ( hAPP @ ( c_List_Orev @ A ) @ B ) @ A )
= ( c_List_Olast @ B @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__rev_0) ).
thf(958,plain,
! [B: $i,A: $i] :
( ( ( c_List_Ohd @ ( hAPP @ ( c_List_Orev @ A ) @ B ) @ A )
= ( c_List_Olast @ B @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(303,axiom,
! [A: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_0) ).
thf(1124,plain,
! [A: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(826,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(577,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(364,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all_Osimps_I2_J_0) ).
thf(1256,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_List_Olist__all @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(349,axiom,
! [B: $i,A: $i] : ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(1226,plain,
! [B: $i,A: $i] : ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ C @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Cons_0) ).
thf(1139,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ C @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(224,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
= ( c_List_Oreplicate @ B @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__replicate_0) ).
thf(936,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
= ( c_List_Oreplicate @ B @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(389,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ( E = c_Message_Oagent_OSpy )
| ( E
= ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_7) ).
thf(1312,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ( E = c_Message_Oagent_OSpy )
| ( E
= ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(947,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(348,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(1224,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__take_0) ).
thf(672,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(217,axiom,
! [A: $i] :
( ( c_Message_Oagent_OFriend @ A )
!= c_Message_Oagent_OSpy ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I6_J_0) ).
thf(919,plain,
! [A: $i] :
( ( c_Message_Oagent_OFriend @ A )
!= c_Message_Oagent_OSpy ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Otake @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__take_0) ).
thf(804,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Otake @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(365,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oremdups @ B @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_0) ).
thf(1258,plain,
! [B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oremdups @ B @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(116,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( A
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ D @ C ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_0) ).
thf(704,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( A
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ D @ C ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Otl @ A @ C ) @ B @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl__append2_0) ).
thf(1194,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Otl @ A @ C ) @ B @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Gets_0) ).
thf(900,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ B @ C ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(175,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(831,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(255,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Orotate @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_0) ).
thf(1011,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Orotate @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ B @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__remdups_0) ).
thf(567,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Oremdups @ B @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(94,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ A @ B @ C @ D ) ) )
| ( ( c_Message_Oagent_Oagent__case @ E @ B @ F @ A @ D )
= ( c_Message_Oagent_Oagent__case @ E @ C @ F @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_5) ).
thf(649,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ A @ B @ C @ D ) ) )
| ( ( c_Message_Oagent_Oagent__case @ E @ B @ F @ A @ D )
= ( c_Message_Oagent_Oagent__case @ E @ C @ F @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ A @ C @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_0) ).
thf(764,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ A @ C @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(241,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oremove1 @ A @ ( c_List_Ofilter @ B @ C @ D ) @ D )
= ( c_List_Ofilter @ B @ C @ D ) )
| ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1__filter__not_0) ).
thf(979,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oremove1 @ A @ ( c_List_Ofilter @ B @ C @ D ) @ D )
= ( c_List_Ofilter @ B @ C @ D ) )
| ( hBOOL @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(153,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I1_J_0) ).
thf(784,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OSays @ A @ B @ C )
!= ( c_Event_Oevent_OSays @ D @ E @ F ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).
thf(1117,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(271,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) ) )
| ( E = c_Message_Oagent_OServer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_6) ).
thf(1048,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) ) )
| ( E = c_Message_Oagent_OServer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_impossible__Cons_0) ).
thf(736,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(246,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) )
!= ( hAPP @ C @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
| ( ( c_Message_Oagent_Oagent__case @ E @ A @ F @ B @ D )
= ( c_Message_Oagent_Oagent__case @ E @ C @ G @ B @ D ) )
| ( B = c_Message_Oagent_OSpy ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_6) ).
thf(990,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) )
!= ( hAPP @ C @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ B @ A @ C @ D ) ) )
| ( ( c_Message_Oagent_Oagent__case @ E @ A @ F @ B @ D )
= ( c_Message_Oagent_Oagent__case @ E @ C @ G @ B @ D ) )
| ( B = c_Message_Oagent_OSpy ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(248,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_OCons @ D @ E @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osplit__asm_1) ).
thf(996,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_OCons @ D @ E @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(599,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(418,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Olist_ONil @ B ) )
| ~ ( c_List_Olist__all2 @ C @ ( c_List_Olist_ONil @ D ) @ A @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Nil_0) ).
thf(1376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Olist_ONil @ B ) )
| ~ ( c_List_Olist__all2 @ C @ ( c_List_Olist_ONil @ D ) @ A @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(890,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(26,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ E @ F @ D )
= ( c_List_Olist__update @ ( c_List_Olist__update @ A @ E @ F @ D ) @ B @ C @ D ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__swap_0) ).
thf(494,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ E @ F @ D )
= ( c_List_Olist__update @ ( c_List_Olist__update @ A @ E @ F @ D ) @ B @ C @ D ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ c_Message_Oagent_OServer @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I8_J_0) ).
thf(631,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ c_Message_Oagent_OServer @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Odrop @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__drop__subset_0) ).
thf(552,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Odrop @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(168,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ A @ C )
= D )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_2) ).
thf(816,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ A @ C )
= D )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(321,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Ohd @ ( c_List_OdropWhile @ A @ B @ C ) @ C ) ) )
| ( ( c_List_OdropWhile @ A @ B @ C )
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__dropWhile_0) ).
thf(1162,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Ohd @ ( c_List_OdropWhile @ A @ B @ C ) @ C ) ) )
| ( ( c_List_OdropWhile @ A @ B @ C )
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Odrop @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__drop_0) ).
thf(621,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Odrop @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(262,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_OCons @ D @ E @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osplit_1) ).
thf(1029,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_Olist__case @ B @ C @ ( c_List_Olist_OCons @ D @ E @ t_b ) @ t_a @ t_b ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Olist__update @ A @ B @ C @ D ) @ D ) @ ( c_Set_Oinsert @ C @ ( c_List_Oset @ A @ D ) @ D ) @ ( tc_fun @ D @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__update__subset__insert_0) ).
thf(626,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Olist__update @ A @ B @ C @ D ) @ D ) @ ( c_Set_Oinsert @ C @ ( c_List_Oset @ A @ D ) @ D ) @ ( tc_fun @ D @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
thf(1344,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(381,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Map_Omap__upds @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upds__Nil2_0) ).
thf(1293,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Map_Omap__upds @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(420,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= A )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(1381,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= A )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(13,axiom,
! [A: $i] :
( ( c_Message_Oagent_OFriend @ A )
!= c_Message_Oagent_OServer ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osimps_I3_J_0) ).
thf(462,plain,
! [A: $i] :
( ( c_Message_Oagent_OFriend @ A )
!= c_Message_Oagent_OServer ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xremove1__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Oinduct_0) ).
thf(1112,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xremove1__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ B @ C )
| ~ ( c_List_Olist__all @ A @ ( c_List_Oappend @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__append_1) ).
thf(848,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ B @ C )
| ~ ( c_List_Olist__all @ A @ ( c_List_Oappend @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(115,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_0) ).
thf(700,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).
thf(520,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(315,axiom,
! [B: $i,A: $i] :
( ( c_List_Osublist @ ( c_List_Olist_ONil @ A ) @ B @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sublist__nil_0) ).
thf(1149,plain,
! [B: $i,A: $i] :
( ( c_List_Osublist @ ( c_List_Olist_ONil @ A ) @ B @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(234,axiom,
! [B: $i,A: $i] :
( ( c_List_OdropWhile @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I1_J_0) ).
thf(964,plain,
! [B: $i,A: $i] :
( ( c_List_OdropWhile @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(427,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_List_Olistsum @ ( hAPP @ ( c_List_Orev @ A ) @ B ) @ A )
= ( c_List_Olistsum @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum__rev_0) ).
thf(1396,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_List_Olistsum @ ( hAPP @ ( c_List_Orev @ A ) @ B ) @ A )
= ( c_List_Olistsum @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(343,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).
thf(1213,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(151,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(780,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(883,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ B @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).
thf(563,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ B @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(294,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ ( c_List_Ofilter @ A @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_0) ).
thf(1102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ ( c_List_Ofilter @ A @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(30,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
| ( ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ F @ ( tc_List_Olist @ D ) ) )
| ( c_List_Olist__all2 @ G @ ( c_List_Oappend @ F @ C @ D ) @ ( c_List_Oappend @ E @ A @ B ) @ D @ B )
| ~ ( c_List_Olist__all2 @ G @ C @ A @ D @ B )
| ~ ( c_List_Olist__all2 @ G @ F @ E @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append1_5) ).
thf(505,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
| ( ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ F @ ( tc_List_Olist @ D ) ) )
| ( c_List_Olist__all2 @ G @ ( c_List_Oappend @ F @ C @ D ) @ ( c_List_Oappend @ E @ A @ B ) @ D @ B )
| ~ ( c_List_Olist__all2 @ G @ C @ A @ D @ B )
| ~ ( c_List_Olist__all2 @ G @ F @ E @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(218,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ B @ C @ D @ E )
| ~ ( c_List_Olist__all2 @ A @ ( hAPP @ ( c_List_Orev @ D ) @ B ) @ ( hAPP @ ( c_List_Orev @ E ) @ C ) @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__rev_0) ).
thf(922,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ B @ C @ D @ E )
| ~ ( c_List_Olist__all2 @ A @ ( hAPP @ ( c_List_Orev @ D ) @ B ) @ ( hAPP @ ( c_List_Orev @ E ) @ C ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_List_Oset @ C @ D ) @ D @ A )
= ( c_List_Olistsum @ ( c_List_Omap @ B @ C @ D @ A ) @ A ) )
| ~ ( c_List_Odistinct @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__set__distinct__conv__listsum_0) ).
thf(658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_List_Oset @ C @ D ) @ D @ A )
= ( c_List_Olistsum @ ( c_List_Omap @ B @ C @ D @ A ) @ A ) )
| ~ ( c_List_Odistinct @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ D @ C ) @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
thf(685,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ D @ C ) @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(325,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ( E
= ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_8) ).
thf(1171,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ( E
= ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(269,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_10) ).
thf(1044,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(113,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(695,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(358,axiom,
! [B: $i,A: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_0) ).
thf(1245,plain,
! [B: $i,A: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(327,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Omap @ B @ C @ D @ A ) )
| ( C
= ( c_List_Olist_ONil @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).
thf(1176,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Omap @ B @ C @ D @ A ) )
| ( C
= ( c_List_Olist_ONil @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(608,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(412,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ B @ C @ D ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__subset__knows__Spy__Says_0) ).
thf(1364,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ B @ C @ D ) @ A @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(361,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__update__Xinduct__1 @ A ) @ ( v_sko__List__Xlist__update__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update_Oinduct_1) ).
thf(1250,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlist__update__Xinduct__1 @ A ) @ ( v_sko__List__Xlist__update__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(386,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Oreplicate @ B @ C @ A ) )
= ( c_List_Oreplicate @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__replicate_0) ).
thf(1304,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Oreplicate @ B @ C @ A ) )
= ( c_List_Oreplicate @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(341,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_List_Orev @ A ) @ B )
!= ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ A ) @ A ) )
| ( B
= ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).
thf(1208,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_List_Orev @ A ) @ B )
!= ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ A ) @ A ) )
| ( B
= ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(220,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ ( c_Message_Oagent_OFriend @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_1) ).
thf(927,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ ( c_Message_Oagent_OFriend @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(166,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(812,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(138,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(749,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(52,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Omap @ A @ E @ C @ D ) )
| ( ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) )
= ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__imp__length__eq_0) ).
thf(553,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Omap @ A @ E @ C @ D ) )
| ( ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) )
= ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(433,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ( E = c_Message_Oagent_OSpy )
| ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) ) )
| ( E = c_Message_Oagent_OServer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_5) ).
thf(1413,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ( E = c_Message_Oagent_OSpy )
| ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) ) )
| ( E = c_Message_Oagent_OServer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(283,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ( E = c_Message_Oagent_OSpy )
| ( E
= ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_7) ).
thf(1076,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ( E = c_Message_Oagent_OSpy )
| ( E
= ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rotate_1) ).
thf(531,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Orotate @ A @ B @ C ) @ C )
| ~ ( c_List_Odistinct @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
= ( c_List_Olist_ONil @ D ) )
| ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__replicate_1) ).
thf(944,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
= ( c_List_Olist_ONil @ D ) )
| ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ B @ C )
| ~ ( c_List_Olist__all @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all__append_0) ).
thf(795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all @ A @ B @ C )
| ~ ( c_List_Olist__all @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(106,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Oappend @ B @ C @ D ) @ ( c_List_Oappend @ E @ F @ G ) @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ B @ E @ D @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__appendI_0) ).
thf(680,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Oappend @ B @ C @ D ) @ ( c_List_Oappend @ E @ F @ G ) @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ B @ E @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(99,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oreplicate @ A @ B @ C )
!= ( c_List_Oreplicate @ D @ E @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
thf(663,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oreplicate @ A @ B @ C )
!= ( c_List_Oreplicate @ D @ E @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).
thf(548,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Orotate @ A @ B @ C ) @ C )
= ( c_List_Oset @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rotate_0) ).
thf(617,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Orotate @ A @ B @ C ) @ C )
= ( c_List_Oset @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ A @ B ) @ ( c_List_Oset @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__subset__Cons_0) ).
thf(516,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ A @ B ) @ ( c_List_Oset @ ( c_List_Olist_OCons @ C @ A @ B ) @ B ) @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(225,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Orotate1 @ A @ B )
= ( c_List_Oappend @ ( c_List_Otl @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ A @ B ) @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__hd__tl_0) ).
thf(939,plain,
! [B: $i,A: $i] :
( ( ( c_List_Orotate1 @ A @ B )
= ( c_List_Oappend @ ( c_List_Otl @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ A @ B ) @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(402,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xdistinct__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Oinduct_0) ).
thf(1340,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xdistinct__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(313,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Omap @ B @ ( c_List_Olist_ONil @ C ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
thf(1145,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Omap @ B @ ( c_List_Olist_ONil @ C ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(258,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_OdropWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_OdropWhile @ A @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Osimps_I2_J_0) ).
thf(1018,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_OdropWhile @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_OdropWhile @ A @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( hAPP @ ( c_List_Orev @ A ) @ B ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
thf(968,plain,
! [B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( hAPP @ ( c_List_Orev @ A ) @ B ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Odrop @ A @ B @ D ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) ) @ tc_nat ) @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__append_0) ).
thf(458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Odrop @ A @ B @ D ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) ) @ tc_nat ) @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(329,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__subset__knows__Gets_0) ).
thf(1181,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Event_Oknows @ A @ B ) @ ( c_Event_Oknows @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ C @ D ) @ B @ tc_Event_Oevent ) ) @ ( tc_fun @ tc_Message_Omsg @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
thf(525,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ C @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_1) ).
thf(872,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Oappend @ C @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(707,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Oappend @ A @ ( c_List_Obutlast @ B @ C ) @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_1) ).
thf(887,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Oappend @ A @ ( c_List_Obutlast @ B @ C ) @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A ) @ A )
= ( c_List_Ohd @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__append_0) ).
thf(971,plain,
! [B: $i,A: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A ) @ A )
= ( c_List_Ohd @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ A @ B @ C @ D )
!= ( c_List_Olist_ONil @ D ) )
| ( A
= ( c_List_Olist_ONil @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
thf(1252,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ A @ B @ C @ D )
!= ( c_List_Olist_ONil @ D ) )
| ( A
= ( c_List_Olist_ONil @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= B )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(993,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= B )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(119,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
| ~ ( c_List_Olistsp @ A @ C @ D )
| ~ ( c_List_Olistsp @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).
thf(712,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
| ~ ( c_List_Olistsp @ A @ C @ D )
| ~ ( c_List_Olistsp @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(251,axiom,
! [B: $i,A: $i] : ( c_List_Olistrelp @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listrelp_ONil_0) ).
thf(1003,plain,
! [B: $i,A: $i] : ( c_List_Olistrelp @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ B @ C ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__Gets__rev_0) ).
thf(1053,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OGets @ B @ C ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(384,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_knows__Spy__Says_0) ).
thf(1300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ A @ B @ C ) @ D @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ C @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ D ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Oagent_Oagent__rec @ A @ B @ C @ c_Message_Oagent_OServer @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Orecs_I1_J_0) ).
thf(791,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Message_Oagent_Oagent__rec @ A @ B @ C @ c_Message_Oagent_OServer @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(332,axiom,
! [A: $i] : ( c_List_Onull @ ( c_List_Olist_ONil @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__null_0) ).
thf(1186,plain,
! [A: $i] : ( c_List_Onull @ ( c_List_Olist_ONil @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Oremove1 @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__remove1__subset_0) ).
thf(441,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Oremove1 @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(180,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(840,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(266,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xtake__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take_Oinduct_0) ).
thf(1038,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xtake__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Orotate1 @ A @ B ) @ B )
= ( c_List_Oset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rotate1_0) ).
thf(585,plain,
! [B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Orotate1 @ A @ B ) @ B )
= ( c_List_Oset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(377,axiom,
! [C: $i,B: $i,A: $i] : ( c_List_Olist__all2 @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ C ) @ B @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Nil_1) ).
thf(1285,plain,
! [C: $i,B: $i,A: $i] : ( c_List_Olist__all2 @ A @ ( c_List_Olist_ONil @ B ) @ ( c_List_Olist_ONil @ C ) @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(346,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Odrop @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__eq__Nil_0) ).
thf(1218,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Odrop @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ C @ A @ B @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__map_0) ).
thf(544,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Omap @ C @ A @ B @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(212,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons2_3) ).
thf(907,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(430,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ D @ E )
= ( c_Message_Oagent_Oagent__case @ A @ F @ G @ D @ E ) )
| ( D = c_Message_Oagent_OSpy )
| ( D
= ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ D @ B @ F @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Ocase__cong_4) ).
thf(1404,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Message_Oagent_Oagent__case @ A @ B @ C @ D @ E )
= ( c_Message_Oagent_Oagent__case @ A @ F @ G @ D @ E ) )
| ( D = c_Message_Oagent_OSpy )
| ( D
= ( c_Message_Oagent_OFriend @ ( c_Message_Osko__Message__Xagent__Xcase__cong__1__1 @ D @ B @ F @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(136,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(744,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(260,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_OdropWhile @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile__eq__Cons__conv_1) ).
thf(1023,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_OdropWhile @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orotate1 @ ( c_List_Orotate @ A @ B @ C ) @ C )
= ( c_List_Orotate @ A @ ( c_List_Orotate1 @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate1__rotate__swap_0) ).
thf(613,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orotate1 @ ( c_List_Orotate @ A @ B @ C ) @ C )
= ( c_List_Orotate @ A @ ( c_List_Orotate1 @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(347,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
thf(864,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Obutlast @ B @ C ) @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).
thf(1140,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Obutlast @ B @ C ) @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(416,axiom,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(1372,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(189,axiom,
class_Divides_Osemiring__div @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
thf(859,plain,
class_Divides_Osemiring__div @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(356,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons_2) ).
thf(1240,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ E @ F @ G ) @ D @ G )
| ~ ( c_List_Olist__all2 @ A @ C @ F @ D @ G )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(371,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D @ E )
= ( c_List_Oreplicate @ B @ ( hAPP @ A @ C ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__replicate_0) ).
thf(1272,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D @ E )
= ( c_List_Oreplicate @ B @ ( hAPP @ A @ C ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(75,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(612,plain,
class_Orderings_Opreorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I2_J_1) ).
thf(497,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OGets @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Otake @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__take__subset_0) ).
thf(876,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Otake @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Omap @ A @ B @ C @ D ) @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_List_Oset @ B @ C ) @ C @ D )
| ~ ( c_List_Odistinct @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__map_2) ).
thf(465,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odistinct @ ( c_List_Omap @ A @ B @ C @ D ) @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_List_Oset @ B @ C ) @ C @ D )
| ~ ( c_List_Odistinct @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(84,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(627,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Orotate1 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct1__rotate_0) ).
thf(556,plain,
! [B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( c_List_Orotate1 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(319,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlast__Xinduct__1 @ A ) @ ( v_sko__List__Xlast__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Oinduct_1) ).
thf(1157,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlast__Xinduct__1 @ A ) @ ( v_sko__List__Xlast__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(63,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Oappend @ B @ C @ D ) @ D @ E )
= ( c_List_Oappend @ ( c_List_Omap @ A @ B @ D @ E ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__append_0) ).
thf(581,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Oappend @ B @ C @ D ) @ D @ E )
= ( c_List_Oappend @ ( c_List_Omap @ A @ B @ D @ E ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(345,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).
thf(1216,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(304,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ B @ C @ D ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ D @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_spies__Says__rev_0) ).
thf(1126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oknows @ c_Message_Oagent_OSpy @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ ( c_Event_Oevent_OSays @ B @ C @ D ) @ ( c_List_Olist_ONil @ tc_Event_Oevent ) @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= ( c_Set_Oinsert @ D @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ A ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(379,axiom,
! [B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Obutlast @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_0) ).
thf(1289,plain,
! [B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Obutlast @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__snoc_0) ).
thf(1108,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(7,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Orotate @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
= ( c_List_Omap @ B @ ( c_List_Orotate @ A @ C @ D ) @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__map_0) ).
thf(450,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Orotate @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E )
= ( c_List_Omap @ B @ ( c_List_Orotate @ A @ C @ D ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(286,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) ) )
| ( E = c_Message_Oagent_OServer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_6) ).
thf(1084,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) ) )
| ( E = c_Message_Oagent_OServer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).
thf(931,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(45,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
| ( ( c_Map_Omap__upds @ E @ ( c_List_Oappend @ A @ F @ B ) @ C @ B @ D )
= ( c_Map_Omap__upds @ E @ A @ C @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upds__append__drop_0) ).
thf(539,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
| ( ( c_Map_Omap__upds @ E @ ( c_List_Oappend @ A @ F @ B ) @ C @ B @ D )
= ( c_Map_Omap__upds @ E @ A @ C @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(110,axiom,
! [B: $i,A: $i] : ( c_List_Olist__all2 @ ( c_fequal @ A ) @ B @ B @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__eq_0) ).
thf(688,plain,
! [B: $i,A: $i] : ( c_List_Olist__all2 @ ( c_fequal @ A ) @ B @ B @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(210,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(903,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(373,axiom,
! [B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( hAPP @ ( c_List_Orev @ B ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rev_0) ).
thf(1276,plain,
! [B: $i,A: $i] :
( ( c_List_Odistinct @ A @ B )
| ~ ( c_List_Odistinct @ ( hAPP @ ( c_List_Orev @ B ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Ohd @ A @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__append_1) ).
thf(1326,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Ohd @ A @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(233,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Ofilter @ A @ C @ D ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter_Osimps_I2_J_1) ).
thf(961,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Ofilter @ A @ C @ D ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= A )
| ( c_List_Odistinct @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__id__iff__distinct_0) ).
thf(517,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
!= A )
| ( c_List_Odistinct @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(206,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__XdropWhile__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dropWhile_Oinduct_0) ).
thf(896,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__XdropWhile__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) )
| ( ( c_List_Oremdups @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__remdups__eq_0) ).
thf(652,plain,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) )
| ( ( c_List_Oremdups @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
= ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__map_0) ).
thf(731,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
= ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(215,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
!= ( c_List_Olist_OCons @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(914,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
!= ( c_List_Olist_OCons @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(510,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(100,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
= ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
| ~ ( c_List_Olist__all2 @ E @ A @ C @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__def_0) ).
thf(667,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
= ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
| ~ ( c_List_Olist__all2 @ E @ A @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(221,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_Olist__case @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I4_J_0) ).
thf(929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_Olist__case @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otl @ ( c_List_Odrop @ A @ B @ C ) @ C )
= ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl__drop_0) ).
thf(478,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otl @ ( c_List_Odrop @ A @ B @ C ) @ C )
= ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(176,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__ex @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
| ~ ( c_List_Olist__ex @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__ex_Osimps_I2_J_2) ).
thf(832,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__ex @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
| ~ ( c_List_Olist__ex @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(388,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Olist_ONil @ D ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).
thf(1309,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Olist_ONil @ D ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_OCons @ C @ D @ A ) @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_2) ).
thf(716,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_OCons @ C @ D @ A ) @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Ofilter @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filter__is__subset_0) ).
thf(800,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Ofilter @ A @ B @ C ) @ C ) @ ( c_List_Oset @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Ofilter @ B @ C @ A ) )
= ( c_List_Ofilter @ B @ ( hAPP @ ( c_List_Orev @ A ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__filter_0) ).
thf(1133,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_List_Orev @ A ) @ ( c_List_Ofilter @ B @ C @ A ) )
= ( c_List_Ofilter @ B @ ( hAPP @ ( c_List_Orev @ A ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(1348,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ A @ B ) @ D @ B ) @ B )
!= D )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B )
!= A )
| ( C
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ A @ B ) )
| ( ( c_List_Oappend @ C @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ A @ B ) @ D @ B ) @ B )
= ( c_List_Oappend @ A @ D @ B ) ) ),
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] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ A @ B ) @ D @ B ) @ B )
!= D )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B )
!= A )
| ( C
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ A @ B ) )
| ( ( c_List_Oappend @ C @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ A @ B ) @ D @ B ) @ B )
= ( c_List_Oappend @ A @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(351,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(187,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OSays @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_event_Osimps_I5_J_0) ).
thf(854,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Event_Oevent_OGets @ A @ B )
!= ( c_Event_Oevent_OSays @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__simps_1) ).
thf(1248,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(193,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ tc_nat )
= B )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
thf(867,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ tc_nat )
= B )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(131,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(735,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(229,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ( E = c_Message_Oagent_OSpy )
| ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) ) )
| ( E = c_Message_Oagent_OServer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_5) ).
thf(950,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ( E = c_Message_Oagent_OSpy )
| ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) ) )
| ( E = c_Message_Oagent_OServer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(292,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ( E
= ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) )
| ( E = c_Message_Oagent_OServer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit__asm_4) ).
thf(1097,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ( E
= ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__asm__1 @ A @ C @ E ) ) )
| ( E = c_Message_Oagent_OServer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(162,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
| ( ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ F @ ( tc_List_Olist @ D ) ) )
| ( c_List_Olist__all2 @ G @ ( c_List_Oappend @ E @ A @ B ) @ ( c_List_Oappend @ F @ C @ D ) @ B @ D )
| ~ ( c_List_Olist__all2 @ G @ A @ C @ B @ D )
| ~ ( c_List_Olist__all2 @ G @ E @ F @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__append2_5) ).
thf(801,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ D ) ) )
| ( ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ B ) )
!= ( c_Nat_Osize__class_Osize @ F @ ( tc_List_Olist @ D ) ) )
| ( c_List_Olist__all2 @ G @ ( c_List_Oappend @ E @ A @ B ) @ ( c_List_Oappend @ F @ C @ D ) @ B @ D )
| ~ ( c_List_Olist__all2 @ G @ A @ C @ B @ D )
| ~ ( c_List_Olist__all2 @ G @ E @ F @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(399,axiom,
! [B: $i,A: $i] :
( ( c_List_Oset @ ( hAPP @ ( c_List_Orev @ A ) @ B ) @ A )
= ( c_List_Oset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev_0) ).
thf(1335,plain,
! [B: $i,A: $i] :
( ( c_List_Oset @ ( hAPP @ ( c_List_Orev @ A ) @ B ) @ A )
= ( c_List_Oset @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__mod__geq_0) ).
thf(828,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(635,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(278,axiom,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oremdups @ ( c_List_Olist_ONil @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_1) ).
thf(1065,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oremdups @ ( c_List_Olist_ONil @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(405,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__XtakeWhile__Xinduct__1 @ A ) @ ( v_sko__List__XtakeWhile__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Oinduct_1) ).
thf(1346,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__XtakeWhile__Xinduct__1 @ A ) @ ( v_sko__List__XtakeWhile__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_OdropWhile @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__dropWhile__le_0) ).
thf(474,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_OdropWhile @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(432,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(1410,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(264,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ B @ ( hAPP @ ( c_List_Orev @ C ) @ D ) @ E @ C )
| ~ ( c_List_Olist__all2 @ A @ ( hAPP @ ( c_List_Orev @ E ) @ B ) @ D @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__rev1_0) ).
thf(1033,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__all2 @ A @ B @ ( hAPP @ ( c_List_Orev @ C ) @ D ) @ E @ C )
| ~ ( c_List_Olist__all2 @ A @ ( hAPP @ ( c_List_Orev @ E ) @ B ) @ D @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ( c_List_Olist__inter @ ( c_List_Olist_ONil @ A ) @ B @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__inter_Osimps_I1_J_0) ).
thf(1197,plain,
! [B: $i,A: $i] :
( ( c_List_Olist__inter @ ( c_List_Olist_ONil @ A ) @ B @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Osublist @ A @ B @ C ) @ C ) @ ( c_List_Oset @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__sublist__subset_0) ).
thf(720,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_List_Oset @ ( c_List_Osublist @ A @ B @ C ) @ C ) @ ( c_List_Oset @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(322,axiom,
! [B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(1165,plain,
! [B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(366,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ C @ F @ G ) @ E @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__all2__Cons_0) ).
thf(1261,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( c_List_Olist__all2 @ A @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ C @ F @ G ) @ E @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(369,axiom,
! [A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(1268,plain,
! [A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(190,axiom,
class_HOL_Oord @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(860,plain,
class_HOL_Oord @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(421,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ c_Message_Oagent_OServer @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_0) ).
thf(1384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ c_Message_Oagent_OServer @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
= A )
| ~ ( c_List_Odistinct @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__remdups__id_0) ).
thf(596,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oremdups @ A @ B )
= A )
| ~ ( c_List_Odistinct @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(409,axiom,
! [B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( hAPP @ ( c_List_Orev @ B ) @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
thf(1357,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( hAPP @ ( c_List_Orev @ B ) @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Odrop @ A @ B @ C ) @ C )
= ( c_List_Odrop @ A @ ( c_List_Obutlast @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__drop_0) ).
thf(723,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Odrop @ A @ B @ C ) @ C )
= ( c_List_Odrop @ A @ ( c_List_Obutlast @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_0) ).
thf(822,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ B @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_1) ).
thf(850,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ B @ A )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Otake @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Otake @ A @ B @ D ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) ) @ tc_nat ) @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__append_0) ).
thf(442,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Otake @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Otake @ A @ B @ D ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) ) @ tc_nat ) @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(428,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__XtakeWhile__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Oinduct_0) ).
thf(1399,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__XtakeWhile__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(501,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(290,axiom,
! [B: $i,A: $i] :
( ( c_List_Oremove1 @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I1_J_0) ).
thf(1093,plain,
! [B: $i,A: $i] :
( ( c_List_Oremove1 @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(179,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__remdups__leq_0) ).
thf(839,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Oremdups @ A @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(127,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(728,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_OdropWhile @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__dropWhile_0) ).
thf(740,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_List_Olinorder__class_Osorted @ ( c_List_OdropWhile @ B @ C @ A ) @ A )
| ~ ( c_List_Olinorder__class_Osorted @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(354,axiom,
! [A: $i] :
( ( c_List_Otl @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl_Osimps_I1_J_0) ).
thf(1236,plain,
! [A: $i] :
( ( c_List_Otl @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(244,axiom,
! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_List_Orev @ A ) @ B @ ( tc_List_Olist @ A ) @ ( tc_List_Olist @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__rev_0) ).
thf(987,plain,
! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_List_Orev @ A ) @ B @ ( tc_List_Olist @ A ) @ ( tc_List_Olist @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(242,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(982,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(252,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ( E = c_Message_Oagent_OSpy )
| ( E
= ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) )
| ( E = c_Message_Oagent_OServer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_agent_Osplit_3) ).
thf(1004,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Message_Oagent_Oagent__case @ B @ C @ D @ E @ t_a ) ) )
| ( E = c_Message_Oagent_OSpy )
| ( E
= ( c_Message_Oagent_OFriend @ ( v_sko__Message__Xagent__Xsplit__1 @ A @ C @ E ) ) )
| ( E = c_Message_Oagent_OServer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(397,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xmap__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Oinduct_0) ).
thf(1331,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xmap__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__commute_0) ).
thf(486,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(392,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsum__Xinduct__1 @ A ) @ ( v_sko__List__Xlistsum__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_Oinduct_1) ).
thf(1320,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xlistsum__Xinduct__1 @ A ) @ ( v_sko__List__Xlistsum__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ofiltermap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_filtermap_Osimps_I1_J_0) ).
thf(1009,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ofiltermap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(331,axiom,
! [B: $i,A: $i] :
( ( c_List_Otake @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).
thf(1184,plain,
! [B: $i,A: $i] :
( ( c_List_Otake @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orotate @ A @ B @ C )
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Divides_Odiv__class_Omod @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) @ B @ C ) @ ( c_List_Otake @ ( c_Divides_Odiv__class_Omod @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__drop__take_0) ).
thf(775,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orotate @ A @ B @ C )
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Divides_Odiv__class_Omod @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) @ B @ C ) @ ( c_List_Otake @ ( c_Divides_Odiv__class_Omod @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(434,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ A ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Oinduct_1) ).
thf(1416,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_OCons @ ( v_sko__List__Xdistinct__Xinduct__1 @ A ) @ ( v_sko__List__Xdistinct__Xinduct__2 @ A ) @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(90,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(639,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ ( c_List_Oremove1 @ A @ C @ D ) @ D ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).
thf(491,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oremove1 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ ( c_List_Oremove1 @ A @ C @ D ) @ D ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(256,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xconcat__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_concat_Oinduct_0) ).
thf(1014,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xconcat__Xinduct__2 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Olist_ONil @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(16,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(469,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(414,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oappend @ ( c_List_Obutlast @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ A @ B ) @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= A )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__butlast__last__id_0) ).
thf(1367,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oappend @ ( c_List_Obutlast @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ A @ B ) @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= A )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Oremdups @ A @ B ) @ B )
= ( c_List_Oset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__remdups_0) ).
thf(755,plain,
! [B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Oremdups @ A @ B ) @ B )
= ( c_List_Oset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__replicate_0) ).
thf(676,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tl_Osimps_I2_J_0) ).
thf(454,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(280,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_List_Orev @ A ) @ B )
!= ( c_List_Olist_OCons @ C @ D @ A ) )
| ( B
= ( c_List_Oappend @ ( hAPP @ ( c_List_Orev @ A ) @ D ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
thf(1069,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_List_Orev @ A ) @ B )
!= ( c_List_Olist_OCons @ C @ D @ A ) )
| ( B
= ( c_List_Oappend @ ( hAPP @ ( c_List_Orev @ A ) @ D ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ A ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(1419,plain,
$false,
inference(e,[status(thm)],[1322,1337,1190,760,1105,846,1315,1179,777,1295,1110,645,892,909,628,1031,977,1211,762,1401,1205,655,861,1137,533,550,797,472,1233,814,1342,1063,1354,670,1095,898,1001,1391,1359,1386,565,436,1265,973,885,1046,1055,917,1191,587,619,542,460,1379,1087,1147,1247,870,770,881,1100,1302,789,1040,646,834,514,1151,806,966,1283,475,924,1418,623,1051,821,905,480,1215,877,956,1072,1119,1394,1351,998,988,1242,527,602,766,1169,687,1074,452,678,529,661,1306,1199,1153,810,1338,1067,714,512,942,439,546,793,798,1057,1274,894,1021,1042,1255,1174,561,693,729,1238,746,1091,788,1370,467,484,1365,625,852,1159,1079,757,1128,1281,583,522,682,1407,1291,710,456,842,742,1270,615,1121,1227,725,593,610,783,857,697,1089,874,1143,1329,1082,488,1361,933,753,1182,901,642,637,1155,1016,590,837,1263,985,1297,738,1231,1131,1060,911,721,569,1324,1114,503,605,1333,1318,1202,633,508,558,953,773,718,1286,1035,1187,674,1026,1167,1278,1135,750,824,573,689,444,1374,733,819,975,1007,1389,843,1388,579,958,1124,826,577,1256,1226,1139,936,1312,947,1224,672,919,804,1258,704,1194,900,831,1011,567,649,764,979,784,1117,1048,736,990,996,599,1376,890,494,631,552,816,1162,621,1029,626,1344,1293,1381,462,1112,848,700,520,1149,964,1396,1213,780,883,563,1102,505,922,658,685,1171,1044,695,1245,1176,608,1364,1250,1304,1208,927,812,749,553,1413,1076,531,944,795,680,663,548,617,516,939,1340,1145,1018,968,458,1181,525,872,707,887,971,1252,993,712,1003,1053,1300,791,1186,441,840,1038,585,1285,1218,544,907,1404,744,1023,613,1221,864,1140,1372,859,1240,1272,612,497,876,465,627,556,1157,581,1216,1126,1289,1108,450,1084,931,539,688,903,1276,1326,961,517,896,652,731,914,510,667,929,478,832,1309,536,716,800,1133,1348,447,1229,854,1248,867,735,950,1097,801,1335,828,635,1065,1346,474,1410,1033,1197,720,1165,1261,1268,860,1384,596,1357,723,822,850,442,1399,501,1093,839,728,740,1236,987,982,1004,1331,486,1320,1009,1184,775,1416,639,491,1014,469,1367,755,676,454,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV779-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n008.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 19 02:34:55 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.93/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.62/1.12 % [INFO] Parsing done (217ms).
% 1.62/1.13 % [INFO] Running in sequential loop mode.
% 2.20/1.33 % [INFO] eprover registered as external prover.
% 2.20/1.33 % [INFO] cvc4 registered as external prover.
% 2.20/1.33 % [INFO] Scanning for conjecture ...
% 2.69/1.43 % [INFO] Found a conjecture and 442 axioms. Running axiom selection ...
% 3.09/1.54 % [INFO] Axiom selection finished. Selected 434 axioms (removed 8 axioms).
% 3.48/1.67 % [INFO] Problem is propositional (TPTP CNF).
% 3.62/1.69 % [INFO] Type checking passed.
% 3.62/1.69 % [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 ...
% 8.57/2.94 % External prover 'e' found a proof!
% 8.57/2.94 % [INFO] Killing All external provers ...
% 8.57/2.95 % Time passed: 2416ms (effective reasoning time: 1816ms)
% 8.57/2.95 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 8.57/2.95 % 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
% 8.57/2.95 % No. of inferences in proof: 871
% 8.57/2.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2416 ms resp. 1816 ms w/o parsing
% 9.34/3.10 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.34/3.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------