TSTP Solution File: SWV906-1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV906-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.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 12:19:15 EDT 2023
% Result : Unsatisfiable 9.19s 3.07s
% Output : Refutation 9.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 599
% Syntax : Number of formulae : 1114 ( 391 unt; 85 typ; 0 def)
% Number of atoms : 1969 ( 708 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 13344 ( 996 ~; 940 |; 0 &;11408 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 157 ( 157 >; 0 *; 0 +; 0 <<)
% Number of symbols : 87 ( 85 usr; 17 con; 0-9 aty)
% Number of variables : 3646 ( 0 ^;3646 !; 0 ?;3646 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Hoare__Mirabelle_Ostate__not__singleton_type,type,
c_Hoare__Mirabelle_Ostate__not__singleton: $o ).
thf(c_Com_OWT__bodies_type,type,
c_Com_OWT__bodies: $o ).
thf(c_Com_OWT_type,type,
c_Com_OWT: $i > $o ).
thf(v_c_type,type,
v_c: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Com_Obody_type,type,
c_Com_Obody: $i ).
thf(v_pn_type,type,
v_pn: $i ).
thf(c_Option_Ooption_OSome_type,type,
c_Option_Ooption_OSome: $i > $i > $i ).
thf(v_y_type,type,
v_y: $i ).
thf(tc_Com_Ocom_type,type,
tc_Com_Ocom: $i ).
thf(c_Hoare__Mirabelle_Ohoare__derivs_type,type,
c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(tc_Hoare__Mirabelle_Otriple_type,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
thf(tc_Com_Ostate_type,type,
tc_Com_Ostate: $i ).
thf(tc_bool_type,type,
tc_bool: $i ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(c_Hoare__Mirabelle_OMGT_type,type,
c_Hoare__Mirabelle_OMGT: $i ).
thf(c_Com_Ocom_OBODY_type,type,
c_Com_Ocom_OBODY: $i ).
thf(tc_Com_Opname_type,type,
tc_Com_Opname: $i ).
thf(c_Map_Odom_type,type,
c_Map_Odom: $i > $i > $i > $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(class_Lattices_Oupper__semilattice_type,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(c_Com_Ocom_OLocal_type,type,
c_Com_Ocom_OLocal: $i > $i > $i > $i ).
thf(c_Com_Ocom_OAss_type,type,
c_Com_Ocom_OAss: $i > $i > $i ).
thf(c_Com_Ocom_OCall_type,type,
c_Com_Ocom_OCall: $i > $i > $i > $i ).
thf(c_Com_Ocom_OWhile_type,type,
c_Com_Ocom_OWhile: $i > $i > $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Lattices_Oupper__semilattice__class_Osup_type,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(c_Finite__Set_Olinorder__class_OMax_type,type,
c_Finite__Set_Olinorder__class_OMax: $i > $i > $i ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_in_type,type,
c_in: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(c_Hoare__Mirabelle_Otriple_Otriple_type,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_Fun_Ofun__upd_type,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(c_Map_Orestrict__map_type,type,
c_Map_Orestrict__map: $i > $i > $i > $i > $i ).
thf(c_Option_Ooption_ONone_type,type,
c_Option_Ooption_ONone: $i > $i ).
thf(tc_Option_Ooption_type,type,
tc_Option_Ooption: $i > $i ).
thf(class_Complete__Lattice_Ocomplete__lattice_type,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(c_Complete__Lattice_OInf__class_OInf_type,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).
thf(c_Com_Ocom_OSKIP_type,type,
c_Com_Ocom_OSKIP: $i ).
thf(class_Lattices_Obounded__lattice_type,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(c_Com_Ocom_OSemi_type,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(c_Com_Ocom_OCond_type,type,
c_Com_Ocom_OCond: $i > $i > $i > $i ).
thf(class_Orderings_Otop_type,type,
class_Orderings_Otop: $i > $o ).
thf(c_Complete__Lattice_OSup__class_OSup_type,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
thf(c_Collect_type,type,
c_Collect: $i > $i > $i ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(class_Finite__Set_Ofinite_Ofinite_type,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
thf(class_HOL_Ominus_type,type,
class_HOL_Ominus: $i > $o ).
thf(c_Finite__Set_Ofold1_type,type,
c_Finite__Set_Ofold1: $i > $i > $i > $i ).
thf(c_The_type,type,
c_The: $i > $i > $i ).
thf(c_Finite__Set_Ofold1Set_type,type,
c_Finite__Set_Ofold1Set: $i > $i > $i > $i ).
thf(c_Finite__Set_Olinorder__class_OMin_type,type,
c_Finite__Set_Olinorder__class_OMin: $i > $i > $i ).
thf(class_HOL_Oord_type,type,
class_HOL_Oord: $i > $o ).
thf(c_Complete__Lattice_Ocomplete__lattice_type,type,
c_Complete__Lattice_Ocomplete__lattice: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_Nitpick_Osko__Nitpick__XEx1__def__1__3_type,type,
c_Nitpick_Osko__Nitpick__XEx1__def__1__3: $i > $i > $i ).
thf(c_Set_Ocontents_type,type,
c_Set_Ocontents: $i > $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(v_x_type,type,
v_x: $i ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR_type,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastAtMost_type,type,
c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_Natural_Oevalc_type,type,
c_Natural_Oevalc: $i > $i ).
thf(c_Option_Othe_type,type,
c_Option_Othe: $i > $i ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i > $i ).
thf(c_fequal_type,type,
c_fequal: $i > $i ).
thf(c_Option_Oset_type,type,
c_Option_Oset: $i > $i > $i ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xsingle__stateE__1_type,type,
v_sko__Hoare__Mirabelle__Xsingle__stateE__1: $i > $i ).
thf(c_Hoare__Mirabelle_Ohoare__valids_type,type,
c_Hoare__Mirabelle_Ohoare__valids: $i > $i > $i > $o ).
thf(c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1_type,type,
c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1: $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__XMGF__lemma1__1_type,type,
v_sko__Hoare__Mirabelle__XMGF__lemma1__1: $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xescape__1_type,type,
v_sko__Hoare__Mirabelle__Xescape__1: $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xescape__2_type,type,
v_sko__Hoare__Mirabelle__Xescape__2: $i > $i > $i > $i > $i ).
thf(c_Com_Osko__Com__XWTs__elim__cases__7__1_type,type,
c_Com_Osko__Com__XWTs__elim__cases__7__1: $i > $i ).
thf(415,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ D @ B @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).
thf(1501,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ D @ B @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(510,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1718,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(629,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Map_Odom @ ( c_COMBK @ ( c_Option_Ooption_OSome @ A @ B ) @ ( tc_Option_Ooption @ B ) @ C ) @ C @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__const_0) ).
thf(1024,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Map_Odom @ ( c_COMBK @ ( c_Option_Ooption_OSome @ A @ B ) @ ( tc_Option_Ooption @ B ) @ C ) @ C @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(356,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).
thf(1369,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(267,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ C @ F ) @ E ) )
| ~ ( hBOOL @ ( c_in @ F @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__I_0) ).
thf(1168,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ C @ F ) @ E ) )
| ~ ( hBOOL @ ( c_in @ F @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(394,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(1454,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(299,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ D @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_derivs__insertD_0) ).
thf(1237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ D @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(941,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold1 @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).
thf(1179,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold1 @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(439,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ D @ A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__insert_0) ).
thf(1554,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ D @ A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_0) ).
thf(645,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ( c_Set_Ocontents @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_contents__eq_0) ).
thf(892,plain,
! [B: $i,A: $i] :
( ( c_Set_Ocontents @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).
thf(1322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(487,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(1665,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(441,axiom,
! [B: $i,A: $i] :
( ( c_Option_Ooption_ONone @ A )
!= ( c_Option_Ooption_OSome @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_0) ).
thf(1559,plain,
! [B: $i,A: $i] :
( ( c_Option_Ooption_ONone @ A )
!= ( c_Option_Ooption_OSome @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(238,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(1105,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(331,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_asm_0) ).
thf(1315,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(2,negated_conjecture,
c_Com_OWT__bodies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(518,plain,
c_Com_OWT__bodies,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_2) ).
thf(1083,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(170,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( hAPP @ c_Com_Ocom_OBODY @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I54_J_0) ).
thf(962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( hAPP @ c_Com_Ocom_OBODY @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(190,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).
thf(1005,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(456,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__UNIV_0) ).
thf(1596,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(80,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I57_J_0) ).
thf(730,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(426,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ C @ ( c_Option_Ooption_OSome @ D @ A ) @ B @ ( tc_Option_Ooption @ A ) ) @ B @ A )
= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__eq__singleton__conv_1) ).
thf(1522,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ C @ ( c_Option_Ooption_OSome @ D @ A ) @ B @ ( tc_Option_Ooption @ A ) ) @ B @ A )
= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(389,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Option_Ooption_OSome @ A @ B )
!= ( c_Option_Ooption_OSome @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Oinject_0) ).
thf(1443,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Option_Ooption_OSome @ A @ B )
!= ( c_Option_Ooption_OSome @ C @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(466,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1618,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(371,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ ( c_Option_Ooption_ONone @ D ) @ C @ ( tc_Option_Ooption @ D ) )
= ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__None__restrict_0) ).
thf(1401,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ ( c_Option_Ooption_ONone @ D ) @ C @ ( tc_Option_Ooption @ D ) )
= ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(445,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__singleton_0) ).
thf(1569,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(223,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
thf(1073,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(435,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( hAPP @ c_Com_Ocom_OBODY @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I58_J_0) ).
thf(1544,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( hAPP @ c_Com_Ocom_OBODY @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(136,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ C @ I @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__UNIV_0) ).
thf(878,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ C @ I @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(430,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ A @ F @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
thf(1533,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ A @ F @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(386,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(1437,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(208,axiom,
! [B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ A @ B ) )
| ~ ( c_Com_OWT @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_While_0) ).
thf(1041,plain,
! [B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ A @ B ) )
| ~ ( c_Com_OWT @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(7,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(523,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(262,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(1158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(30,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I37_J_0) ).
thf(582,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(254,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1142,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(1269,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(269,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ~ ( hBOOL @ ( c_in @ E @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant_0) ).
thf(1173,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ~ ( hBOOL @ ( c_in @ E @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(408,axiom,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( hAPP @ c_Com_Ocom_OBODY @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).
thf(1486,plain,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( hAPP @ c_Com_Ocom_OBODY @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(483,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( c_COMBK @ C @ A @ D ) @ D @ A )
= C )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP__const_0) ).
thf(1655,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( c_COMBK @ C @ A @ D ) @ D @ A )
= C )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(329,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(1310,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)],[329]) ).
thf(19,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
| ( B = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).
thf(550,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I11_J_0) ).
thf(797,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(150,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ B @ E @ A ) @ A )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
thf(913,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ B @ E @ A ) @ A )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(477,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(1640,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(349,axiom,
! [A: $i] :
( ( c_Option_Oset @ ( c_Option_Ooption_ONone @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty__eq_1) ).
thf(1354,plain,
! [A: $i] :
( ( c_Option_Oset @ ( c_Option_Ooption_ONone @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(292,axiom,
! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
thf(1222,plain,
! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(670,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(413,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I3_J_0) ).
thf(1497,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(505,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).
thf(1705,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(226,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(1078,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(1426,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I29_J_0) ).
thf(829,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(280,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( A = D )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( A = D )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(188,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(1001,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)],[188]) ).
thf(72,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(709,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(211,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ ( c_Set_Oimage @ C @ D @ E @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__surj_0) ).
thf(1046,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ ( c_Set_Oimage @ C @ D @ E @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(464,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Option_Ooption_OSome @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Option_Oset @ A @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_elem__set_0) ).
thf(1613,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Option_Ooption_OSome @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Option_Oset @ A @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(458,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(1601,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(504,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(782,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(388,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).
thf(1441,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(481,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OCond @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I55_J_0) ).
thf(1650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OCond @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(479,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(1645,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(512,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(1724,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(404,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( c_Option_Ooption_OSome @ C @ D ) )
| ( hBOOL @ ( c_in @ B @ ( c_Map_Odom @ A @ E @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domI_0) ).
thf(1475,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( c_Option_Ooption_OSome @ C @ D ) )
| ( hBOOL @ ( c_in @ B @ ( c_Map_Odom @ A @ E @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(295,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(1228,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(468,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(1623,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(306,axiom,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
thf(1254,plain,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(470,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(1628,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(485,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).
thf(1660,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(310,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
= ( c_Set_Oinsert @ C @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ F @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).
thf(1264,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
= ( c_Set_Oinsert @ C @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ F @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(87,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OAss @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I33_J_0) ).
thf(751,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OAss @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(105,axiom,
class_HOL_Ominus @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).
thf(802,plain,
class_HOL_Ominus @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(448,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ ( c_COMBB @ A @ B @ C @ D @ E ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ D ) @ D )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__range__imageI_0) ).
thf(1577,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ ( c_COMBB @ A @ B @ C @ D @ E ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ D ) @ D )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(330,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ A @ B @ C ) )
| ~ ( c_Com_OWT @ C )
| ~ ( c_Com_OWT @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OIf_0) ).
thf(1313,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ A @ B @ C ) )
| ~ ( c_Com_OWT @ C )
| ~ ( c_Com_OWT @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(316,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ( hBOOL @ ( c_in @ A @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(1279,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ( hBOOL @ ( c_in @ A @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(934,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ A @ B @ C ) )
| ~ ( c_Com_OWT @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OLocal_0) ).
thf(1191,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ A @ B @ C ) )
| ~ ( c_Com_OWT @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(257,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(1147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(881,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(242,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Option_Othe @ A ) @ ( c_Option_Ooption_OSome @ B @ A ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the_Osimps_0) ).
thf(1115,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Option_Othe @ A ) @ ( c_Option_Ooption_OSome @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(412,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(1494,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(236,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ D @ C @ E ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ F @ A @ G @ H @ I @ J @ K @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).
thf(1100,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ D @ C @ E ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ F @ A @ G @ H @ I @ J @ K @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(1232,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
thf(638,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(125,axiom,
class_HOL_Oord @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(853,plain,
class_HOL_Oord @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(230,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ ( hAPP @ c_Com_Ocom_OBODY @ C ) @ D @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ E ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ E ) ) @ E )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) @ D @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ E ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ E ) ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_weak__Body_0) ).
thf(1087,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ ( hAPP @ c_Com_Ocom_OBODY @ C ) @ D @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ E ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ E ) ) @ E )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) @ D @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ E ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ E ) ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(423,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 ) )
| ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(1514,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 ) )
| ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(346,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).
thf(1347,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(446,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ( F = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).
thf(1572,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ( F = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(154,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(924,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(399,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(1465,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( hAPP @ c_Com_Ocom_OBODY @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I30_J_0) ).
thf(1109,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( hAPP @ c_Com_Ocom_OBODY @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(259,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(1151,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).
thf(574,plain,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(1283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(409,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(1489,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(376,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
thf(1415,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(495,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
| ~ ( hBOOL @ ( c_in @ F @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP1__I_0) ).
thf(1682,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
| ~ ( hBOOL @ ( c_in @ F @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(252,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(1136,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)],[252]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(834,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(178,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(981,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(687,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(692,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(390,axiom,
! [B: $i,A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(1447,plain,
! [B: $i,A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(244,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ C @ F ) @ E ) )
| ~ ( hBOOL @ ( c_in @ F @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__iff_2) ).
thf(1119,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ C @ F ) @ E ) )
| ~ ( hBOOL @ ( c_in @ F @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rangeI_0) ).
thf(1394,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(345,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(1345,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(384,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).
thf(1433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(282,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) )
!= ( c_COMBK @ ( c_Option_Ooption_ONone @ D ) @ ( tc_Option_Ooption @ D ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__nonempty_0) ).
thf(1201,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) )
!= ( c_COMBK @ ( c_Option_Ooption_ONone @ D ) @ ( tc_Option_Ooption @ D ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(501,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(1697,plain,
class_Orderings_Oorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(11,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OAss @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I23_J_0) ).
thf(527,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OAss @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(284,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1206,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(61,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(678,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)],[61]) ).
thf(327,axiom,
! [B: $i,A: $i] :
( ( c_Collect @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
thf(1306,plain,
! [B: $i,A: $i] :
( ( c_Collect @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(281,axiom,
! [A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( c_Set_Oinsert @ ( hAPP @ c_Hoare__Mirabelle_OMGT @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Com_OWT @ A )
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGF_0) ).
thf(1199,plain,
! [A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( c_Set_Oinsert @ ( hAPP @ c_Hoare__Mirabelle_OMGT @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Com_OWT @ A )
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( hAPP @ c_Com_Ocom_OBODY @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I63_J_0) ).
thf(1338,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( hAPP @ c_Com_Ocom_OBODY @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I28_J_0) ).
thf(534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I15_J_0) ).
thf(714,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(475,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBB @ A @ B @ C @ D @ E ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ D )
= ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ C ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_range__composition_0) ).
thf(1636,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBB @ A @ B @ C @ D @ E ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ D )
= ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ C ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(387,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(1438,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(55,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OWhile @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I38_J_0) ).
thf(661,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OWhile @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Finite__Set_Olinorder__class_OMax @ C @ A ) @ A )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__ge_0) ).
thf(546,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Finite__Set_Olinorder__class_OMax @ C @ A ) @ A )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(101,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B @ F @ D @ E )
= ( c_Fun_Ofun__upd @ A @ B @ F @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).
thf(793,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B @ F @ D @ E )
= ( c_Fun_Ofun__upd @ A @ B @ F @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__subset_0) ).
thf(1153,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(91,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OSemi @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I51_J_0) ).
thf(761,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OSemi @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(216,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(1057,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(265,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(1163,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(314,axiom,
! [B: $i,A: $i] :
( c_Hoare__Mirabelle_Ostate__not__singleton
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_state__not__singleton__def_1) ).
thf(1274,plain,
! [B: $i,A: $i] :
( c_Hoare__Mirabelle_Ostate__not__singleton
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(1091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(199,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(1021,plain,
class_Lattices_Obounded__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(425,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
thf(1519,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(289,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E )
!= A )
| ( ( hAPP @ A @ B )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
thf(1217,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E )
!= A )
| ( ( hAPP @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(110,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(815,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)],[110]) ).
thf(364,axiom,
! [A: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ A )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I19_J_0) ).
thf(1387,plain,
! [A: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ A )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(149,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ C @ I @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).
thf(910,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ C @ I @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(168,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ A @ B ) @ C )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ A @ E @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UN_0) ).
thf(957,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ A @ B ) @ C )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ A @ E @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(293,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).
thf(1223,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ominus @ A )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
thf(894,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ominus @ A )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(114,axiom,
! [A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_Option_Ooption @ A ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite) ).
thf(825,plain,
! [A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_Option_Ooption @ A ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(344,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__upper_0) ).
thf(1343,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(246,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( hAPP @ c_Com_Ocom_OBODY @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I40_J_0) ).
thf(1123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( hAPP @ c_Com_Ocom_OBODY @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(129,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
thf(862,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(380,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ( F = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).
thf(1423,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ( F = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(205,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( c_Option_Ooption_ONone @ C ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Map_Odom @ A @ D @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domIff_0) ).
thf(1032,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( c_Option_Ooption_ONone @ C ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Map_Odom @ A @ D @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(354,axiom,
! [A: $i] :
( ( hAPP @ c_Hoare__Mirabelle_OMGT @ A )
= ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_fequal @ tc_Com_Ostate ) @ A @ ( c_Natural_Oevalc @ A ) @ tc_Com_Ostate ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGT__def_0) ).
thf(1365,plain,
! [A: $i] :
( ( hAPP @ c_Hoare__Mirabelle_OMGT @ A )
= ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_fequal @ tc_Com_Ostate ) @ A @ ( c_Natural_Oevalc @ A ) @ tc_Com_Ostate ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(271,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1178,plain,
class_Orderings_Opreorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1296,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(1210,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(89,axiom,
! [B: $i,A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_0) ).
thf(757,plain,
! [B: $i,A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(373,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ c_Com_Obody @ A )
!= ( c_Option_Ooption_OSome @ B @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__bodiesD_0) ).
thf(1407,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ c_Com_Obody @ A )
!= ( c_Option_Ooption_OSome @ B @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(248,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1128,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(317,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(1281,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(73,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OLocal @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I39_J_0) ).
thf(710,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OLocal @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(121,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I42_J_0) ).
thf(842,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(174,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).
thf(974,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(194,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
thf(1012,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(123,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(847,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ B @ A ) @ C @ A )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
thf(566,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ B @ A ) @ C @ A )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(497,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oimage @ B @ C @ D @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(1687,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oimage @ B @ C @ D @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(395,axiom,
! [B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ c_Hoare__Mirabelle_OMGT @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Com_OWT @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ c_Hoare__Mirabelle_OMGT @ ( hAPP @ c_Com_Ocom_OBODY @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ A ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGF__lemma1_1) ).
thf(1457,plain,
! [B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ c_Hoare__Mirabelle_OMGT @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Com_OWT @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ c_Hoare__Mirabelle_OMGT @ ( hAPP @ c_Com_Ocom_OBODY @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ A ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(474,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_1) ).
thf(1634,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(366,axiom,
! [A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oimage @ ( c_COMBB @ c_Hoare__Mirabelle_OMGT @ c_Com_Ocom_OBODY @ tc_Com_Ocom @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_Com_Opname ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ A @ tc_Com_Ostate )
| ~ ( c_lessequals @ A @ ( c_Set_Oimage @ ( c_COMBB @ c_Hoare__Mirabelle_OMGT @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Ocom @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_Com_Opname ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) )
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGF__lemma2__simult_0) ).
thf(1392,plain,
! [A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oimage @ ( c_COMBB @ c_Hoare__Mirabelle_OMGT @ c_Com_Ocom_OBODY @ tc_Com_Ocom @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_Com_Opname ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ A @ tc_Com_Ostate )
| ~ ( c_lessequals @ A @ ( c_Set_Oimage @ ( c_COMBB @ c_Hoare__Mirabelle_OMGT @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Ocom @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_Com_Opname ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) )
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(308,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ ( hAPP @ c_Com_Ocom_OBODY @ C ) @ D @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ E ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ E ) ) @ E )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ ( hAPP @ c_Com_Ocom_OBODY @ C ) @ D @ E ) @ A @ ( tc_Hoare__Mirabelle_Otriple @ E ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) @ D @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ E ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ E ) ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_BodyN_0) ).
thf(1259,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ ( hAPP @ c_Com_Ocom_OBODY @ C ) @ D @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ E ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ E ) ) @ E )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ ( hAPP @ c_Com_Ocom_OBODY @ C ) @ D @ E ) @ A @ ( tc_Hoare__Mirabelle_Otriple @ E ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) @ D @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ E ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ E ) ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(164,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(948,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).
thf(1017,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(39,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OAss @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I27_J_0) ).
thf(615,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OAss @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(338,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(1328,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(245,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
| ~ ( hBOOL @ ( c_in @ F @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).
thf(1121,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
| ~ ( hBOOL @ ( c_in @ F @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(219,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(1064,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Map_Orestrict__map @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a @ B ) @ v_x )
= ( c_Option_Ooption_ONone @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__map__to__empty_0) ).
thf(1006,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Map_Orestrict__map @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a @ B ) @ v_x )
= ( c_Option_Ooption_ONone @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(132,axiom,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
thf(869,plain,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ominus @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
thf(989,plain,
! [B: $i,A: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ominus @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(3,negated_conjecture,
c_Com_OWT @ v_c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(519,plain,
c_Com_OWT @ v_c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(84,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OCond @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I53_J_0) ).
thf(742,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OCond @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(697,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(231,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(1089,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ( c_Option_Ooption_ONone @ A )
!= ( c_Option_Ooption_OSome @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).
thf(1234,plain,
! [B: $i,A: $i] :
( ( c_Option_Ooption_ONone @ A )
!= ( c_Option_Ooption_OSome @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(434,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).
thf(1541,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(177,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(980,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(453,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Collect @ A @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
thf(1587,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Collect @ A @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(234,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) )
!= ( c_Fun_Ofun__upd @ F @ B @ ( c_Option_Ooption_OSome @ G @ D ) @ E @ ( tc_Option_Ooption @ D ) ) )
| ( C = G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__eqD1_0) ).
thf(1096,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) )
!= ( c_Fun_Ofun__upd @ F @ B @ ( c_Option_Ooption_OSome @ G @ D ) @ E @ ( tc_Option_Ooption @ D ) ) )
| ( C = G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(490,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(1672,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(857,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(369,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ D @ A @ C ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(1397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ D @ A @ C ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(444,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(1567,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(411,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(1493,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(263,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(1160,plain,
class_Lattices_Olattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).
thf(1028,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(352,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( c_Option_Ooption_OSome @ C @ D ) )
| ( B = E )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ E @ ( c_Option_Ooption_OSome @ F @ D ) @ G @ ( tc_Option_Ooption @ D ) ) @ B )
= ( c_Option_Ooption_OSome @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_4) ).
thf(1361,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( c_Option_Ooption_OSome @ C @ D ) )
| ( B = E )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ E @ ( c_Option_Ooption_OSome @ F @ D ) @ G @ ( tc_Option_Ooption @ D ) ) @ B )
= ( c_Option_Ooption_OSome @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(321,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1292,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(537,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(526,plain,
class_Lattices_Olattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(288,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__empty_0) ).
thf(1214,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(261,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Map_Orestrict__map @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ F @ D @ E )
= ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ F @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) )
| ~ ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__fun__upd_0) ).
thf(1155,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Map_Orestrict__map @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ F @ D @ E )
= ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ F @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) )
| ~ ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(71,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I36_J_0) ).
thf(706,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(378,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1419,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(146,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).
thf(901,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(224,axiom,
! [B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_1) ).
thf(1075,plain,
! [B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(837,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(336,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(1324,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_weaken_0) ).
thf(997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(392,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ A @ B ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ A ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSemi_0) ).
thf(1451,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ A @ B ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ A ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(250,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(1131,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(382,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= B )
| ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(1429,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= B )
| ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(509,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(1715,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(96,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I56_J_0) ).
thf(779,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(235,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).
thf(1099,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).
thf(985,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(5,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBB @ c_Hoare__Mirabelle_OMGT @ c_Com_Ocom_OBODY @ tc_Com_Ocom @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_Com_Opname ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(515,plain,
c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBB @ c_Hoare__Mirabelle_OMGT @ c_Com_Ocom_OBODY @ tc_Com_Ocom @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_Com_Opname ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(405,axiom,
! [B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ A @ B ) )
| ~ ( c_Com_OWT @ B )
| ~ ( c_Com_OWT @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OSemi_0) ).
thf(1478,plain,
! [B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ A @ B ) )
| ~ ( c_Com_OWT @ B )
| ~ ( c_Com_OWT @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(429,axiom,
! [A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
thf(1530,plain,
! [A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(362,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ D @ E )
= ( c_Set_Oinsert @ B @ ( c_Map_Odom @ A @ D @ E ) @ D ) )
| ( C
= ( c_Option_Ooption_ONone @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__fun__upd_1) ).
thf(1382,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ D @ E )
= ( c_Set_Oinsert @ B @ ( c_Map_Odom @ A @ D @ E ) @ D ) )
| ( C
= ( c_Option_Ooption_ONone @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(217,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(1060,plain,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(213,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(1050,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(457,axiom,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
thf(1599,plain,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(303,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 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(1246,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 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(340,axiom,
! [A: $i] :
( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ A ) )
| ( ( hAPP @ c_Com_Obody @ A )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OBody_0) ).
thf(1333,plain,
! [A: $i] :
( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ A ) )
| ( ( hAPP @ c_Com_Obody @ A )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(333,axiom,
! [A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(1318,plain,
! [A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(301,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(1241,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)],[301]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I10_J_0) ).
thf(805,plain,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(500,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ D @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ D @ E @ A ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_0) ).
thf(1695,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ D @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ D @ E @ A ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(153,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
= ( c_Set_Oimage @ A @ F @ D @ E ) )
| ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).
thf(921,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
= ( c_Set_Oimage @ A @ F @ D @ E ) )
| ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(657,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(215,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) )
= ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) ) )
| ~ ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__restrict__conv_0) ).
thf(1054,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) )
= ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) ) )
| ~ ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(268,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).
thf(1170,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(276,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(1187,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(202,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(1026,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(465,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(1616,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(12,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_1) ).
thf(530,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(140,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
thf(888,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCall @ A @ B @ C ) )
| ~ ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OCall_0) ).
thf(926,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCall @ A @ B @ C ) )
| ~ ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(319,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
thf(1286,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= B )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(1035,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= B )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(400,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ A ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCall @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I8_J_0) ).
thf(1466,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ A ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCall @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_1) ).
thf(1071,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(166,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(953,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(275,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Collect @ A @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectD_0) ).
thf(1185,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Collect @ A @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(480,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ D ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
thf(1648,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ D ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(256,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(1146,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(494,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1680,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(502,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__singleton_0) ).
thf(1698,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(407,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( c_Option_Ooption_OSome @ C @ D ) )
| ( ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__triv_0) ).
thf(1483,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( c_Option_Ooption_OSome @ C @ D ) )
| ( ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(437,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(1548,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(85,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OCall @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I50_J_0) ).
thf(745,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OCall @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(1301,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(65,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Map_Orestrict__map @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ F @ D @ E )
= ( c_Map_Orestrict__map @ A @ F @ D @ E ) )
| ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__fun__upd_1) ).
thf(689,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Map_Orestrict__map @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ F @ D @ E )
= ( c_Map_Orestrict__map @ A @ F @ D @ E ) )
| ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(358,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ D @ C )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ A @ D @ C ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__fun__upd_0) ).
thf(1374,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ D @ C )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ A @ D @ C ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OCall @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I62_J_0) ).
thf(965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OCall @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(514,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 ) )
| ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(1727,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 ) )
| ( hBOOL @ ( c_in @ B @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(421,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ A ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_2) ).
thf(1510,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ A ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(305,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Map_Odom @ A @ B @ C )
!= ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A
= ( c_Fun_Ofun__upd @ ( c_COMBK @ ( c_Option_Ooption_ONone @ C ) @ ( tc_Option_Ooption @ C ) @ B ) @ D @ ( c_Option_Ooption_OSome @ ( c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1 @ A @ D @ B @ C ) @ C ) @ B @ ( tc_Option_Ooption @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__eq__singleton__conv_0) ).
thf(1251,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Map_Odom @ A @ B @ C )
!= ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A
= ( c_Fun_Ofun__upd @ ( c_COMBK @ ( c_Option_Ooption_ONone @ C ) @ ( tc_Option_Ooption @ C ) @ B ) @ D @ ( c_Option_Ooption_OSome @ ( c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1 @ A @ D @ B @ C ) @ C ) @ B @ ( tc_Option_Ooption @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I46_J_0) ).
thf(618,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(473,axiom,
! [B: $i,A: $i] :
( ( c_Option_Ooption_OSome @ A @ B )
!= ( c_Option_Ooption_ONone @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__None__eq_1) ).
thf(1631,plain,
! [B: $i,A: $i] :
( ( c_Option_Ooption_OSome @ A @ B )
!= ( c_Option_Ooption_ONone @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(733,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ( c_Option_Ooption_OSome @ A @ B )
!= ( c_Option_Ooption_ONone @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I3_J_0) ).
thf(904,plain,
! [B: $i,A: $i] :
( ( c_Option_Ooption_OSome @ A @ B )
!= ( c_Option_Ooption_ONone @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(694,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
thf(772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(467,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).
thf(1620,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(577,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
thf(579,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(431,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ( hBOOL @ ( c_in @ A @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(1535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ( hBOOL @ ( c_in @ A @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(503,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(1701,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(307,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) ) @ F )
!= ( c_Option_Ooption_OSome @ G @ D ) )
| ( ( hAPP @ A @ F )
= ( c_Option_Ooption_OSome @ G @ D ) )
| ( C = G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_2) ).
thf(1256,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) ) @ F )
!= ( c_Option_Ooption_OSome @ G @ D ) )
| ( ( hAPP @ A @ F )
= ( c_Option_Ooption_OSome @ G @ D ) )
| ( C = G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(294,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(1226,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(936,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(506,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Map_Odom @ B @ C @ D ) @ C ) )
| ( ( hAPP @ B @ A )
= ( c_Option_Ooption_ONone @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domIff_1) ).
thf(1707,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Map_Odom @ B @ C @ D ) @ C ) )
| ( ( hAPP @ B @ A )
= ( c_Option_Ooption_ONone @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(74,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(713,plain,
class_Orderings_Obot @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(239,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
thf(1107,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(300,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ D @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ D @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(476,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ B ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ B ) ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ B ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OWhileTrue_0) ).
thf(1638,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ B ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ B ) ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ B ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__valids @ A @ B @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__sound_0) ).
thf(1356,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__valids @ A @ B @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(492,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( c_Option_Ooption_OSome @ C @ D ) )
| ( ( c_Set_Oinsert @ B @ ( c_Map_Odom @ A @ E @ D ) @ E )
= ( c_Map_Odom @ A @ E @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__dom_0) ).
thf(1675,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( c_Option_Ooption_OSome @ C @ D ) )
| ( ( c_Set_Oinsert @ B @ ( c_Map_Odom @ A @ E @ D ) @ E )
= ( c_Map_Odom @ A @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(59,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) )
| ( C = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_2) ).
thf(672,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) )
| ( C = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(253,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
thf(1139,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_1) ).
thf(1503,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(38,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).
thf(611,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I14_J_0) ).
thf(787,plain,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(681,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(427,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(1524,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(347,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
thf(1349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(459,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
thf(1603,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I6_J_0) ).
thf(1144,plain,
! [B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(498,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( hAPP @ c_Com_Ocom_OBODY @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).
thf(1690,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( hAPP @ c_Com_Ocom_OBODY @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(359,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(1376,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)],[359]) ).
thf(92,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_0) ).
thf(764,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(604,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(98,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ G @ D @ E )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ F @ G @ D @ E ) @ B @ C @ D @ E ) )
| ( B = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).
thf(784,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ G @ D @ E )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ F @ G @ D @ E ) @ B @ C @ D @ E ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(243,axiom,
! [B: $i,A: $i] :
( ( c_Option_Oset @ ( c_Option_Ooption_OSome @ A @ B ) @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Option_Oset_Osimps_I2_J_0) ).
thf(1117,plain,
! [B: $i,A: $i] :
( ( c_Option_Oset @ ( c_Option_Ooption_OSome @ A @ B ) @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(212,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(1048,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I9_J_0) ).
thf(736,plain,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(51,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_1) ).
thf(649,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(1043,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(402,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
thf(1471,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(472,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1630,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
thf(726,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OAss @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I8_J_0) ).
thf(621,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OAss @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(258,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(1149,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(241,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( c_Option_Ooption_ONone @ C ) )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ A @ D @ C ) @ ( c_Set_Oinsert @ B @ E @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ A @ D @ C ) @ E @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__minus_0) ).
thf(1112,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( c_Option_Ooption_ONone @ C ) )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ A @ D @ C ) @ ( c_Set_Oinsert @ B @ E @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ A @ D @ C ) @ E @ ( tc_fun @ D @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(890,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(488,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= C )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(1667,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= C )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(69,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OCall @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I60_J_0) ).
thf(700,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OCall @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(4,negated_conjecture,
( ( hAPP @ c_Com_Obody @ v_pn )
= ( c_Option_Ooption_OSome @ v_y @ tc_Com_Ocom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(520,plain,
( ( hAPP @ c_Com_Obody @ v_pn )
= ( c_Option_Ooption_OSome @ v_y @ tc_Com_Ocom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(43,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OLocal @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I35_J_0) ).
thf(626,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OLocal @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(151,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ C @ D @ ( c_Option_Ooption_OSome @ A @ E ) @ F @ ( tc_Option_Ooption @ E ) ) @ D )
!= ( c_Option_Ooption_OSome @ B @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_1) ).
thf(915,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ C @ D @ ( c_Option_Ooption_OSome @ A @ E ) @ F @ ( tc_Option_Ooption @ E ) ) @ D )
!= ( c_Option_Ooption_OSome @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(440,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ A )
!= ( hAPP @ c_Com_Ocom_OBODY @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
thf(1556,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ A )
!= ( hAPP @ c_Com_Ocom_OBODY @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(397,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
thf(1460,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(943,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(200,axiom,
( ( hAPP @ c_Hoare__Mirabelle_OMGT @ v_c )
= ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_fequal @ tc_Com_Ostate ) @ v_c @ ( c_Natural_Oevalc @ v_c ) @ tc_Com_Ostate ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGT__def__raw_0) ).
thf(1022,plain,
( ( hAPP @ c_Hoare__Mirabelle_OMGT @ v_c )
= ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_fequal @ tc_Com_Ostate ) @ v_c @ ( c_Natural_Oevalc @ v_c ) @ tc_Com_Ostate ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(983,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(169,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ D ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__WHILE__case_0) ).
thf(959,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ D ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(210,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(1044,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OSemi @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I49_J_0) ).
thf(1066,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OSemi @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).
thf(883,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_0) ).
thf(1015,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(270,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(1176,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(23,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ ( c_Option_Ooption_ONone @ D ) @ C @ ( tc_Option_Ooption @ D ) )
= ( c_Map_Orestrict__map @ A @ B @ C @ D ) )
| ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__None__restrict_1) ).
thf(563,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ ( c_Option_Ooption_ONone @ D ) @ C @ ( tc_Option_Ooption @ D ) )
= ( c_Map_Orestrict__map @ A @ B @ C @ D ) )
| ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(385,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(1435,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(237,axiom,
! [A: $i] :
( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ A )
!= A )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__stateE_0) ).
thf(1102,plain,
! [A: $i] :
( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ A )
!= A )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I1_J_1) ).
thf(653,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(442,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ B @ A )
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).
thf(1562,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ B @ A )
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(93,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_0) ).
thf(768,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(115,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(827,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(513,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
thf(1726,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(353,axiom,
class_HOL_Ominus @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
thf(1364,plain,
class_HOL_Ominus @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(375,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(1413,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(469,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ E @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).
thf(1626,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ E @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(451,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(1583,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)],[451]) ).
thf(486,axiom,
! [A: $i] :
( ( ( hAPP @ c_Com_Obody @ A )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ A ) @ tc_Com_Ocom ) )
| ~ ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I7_J_0) ).
thf(1662,plain,
! [A: $i] :
( ( ( hAPP @ c_Com_Obody @ A )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ A ) @ tc_Com_Ocom ) )
| ~ ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ A ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ A ) ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OBody_0) ).
thf(1304,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ A ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ A ) ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(266,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1166,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(102,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(795,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)],[102]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(548,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(496,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Collect @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).
thf(1684,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Collect @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(315,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(1277,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_lessequals @ D @ A @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_thin_0) ).
thf(1081,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_lessequals @ D @ A @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(1,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(516,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(160,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).
thf(939,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(88,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I24_J_0) ).
thf(754,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(438,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
thf(1551,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(285,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ tc_Com_Ostate ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ tc_Com_Ostate ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( c_Set_Oinsert @ ( hAPP @ c_Hoare__Mirabelle_OMGT @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGF__complete_0) ).
thf(1208,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ tc_Com_Ostate ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ tc_Com_Ostate ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( c_Set_Oinsert @ ( hAPP @ c_Hoare__Mirabelle_OMGT @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(32,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OSemi @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I34_J_0) ).
thf(589,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OSemi @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(109,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OLocal @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I22_J_0) ).
thf(812,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OLocal @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(420,axiom,
! [B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty_0) ).
thf(1509,plain,
! [B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(172,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(968,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(273,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( ( hAPP @ B @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ E @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).
thf(1181,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( ( hAPP @ B @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ E @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(9,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(525,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(424,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OWhile @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I59_J_0) ).
thf(1516,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OWhile @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(48,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OWhile @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I52_J_0) ).
thf(640,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OWhile @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ( c_The @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OThe__psimp_0) ).
thf(872,plain,
! [B: $i,A: $i] :
( ( c_The @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(463,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ A @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_escape_0) ).
thf(1611,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ A @ B @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(173,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E )
= ( hAPP @ A @ E ) )
| ~ ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__in_0) ).
thf(971,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E )
= ( hAPP @ A @ E ) )
| ~ ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(83,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(739,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)],[83]) ).
thf(311,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(1267,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(296,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) )
= ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__restrict_0) ).
thf(1230,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) )
= ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(993,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(436,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(1547,plain,
class_HOL_Oord @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(95,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OCond @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I44_J_0) ).
thf(776,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OCond @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(21,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I43_J_0) ).
thf(557,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(189,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(1003,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)],[189]) ).
thf(414,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ A @ C @ E ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_1) ).
thf(1499,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ A @ C @ E ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(383,axiom,
class_Orderings_Otop @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
thf(1432,plain,
class_Orderings_Otop @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCall @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I20_J_0) ).
thf(717,plain,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCall @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) @ C @ A )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__le_0) ).
thf(840,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) @ C @ A )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(332,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(1317,plain,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(290,axiom,
c_Finite__Set_Ofinite @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) @ tc_Com_Opname,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__dom__body_0) ).
thf(1220,plain,
c_Finite__Set_Ofinite @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) @ tc_Com_Opname,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(148,axiom,
! [A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
thf(907,plain,
! [A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(207,axiom,
! [B: $i,A: $i] :
( ( ( c_Option_Oset @ A @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( A
= ( c_Option_Ooption_ONone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty__eq_0) ).
thf(1038,plain,
! [B: $i,A: $i] :
( ( ( c_Option_Oset @ A @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( A
= ( c_Option_Ooption_ONone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(31,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_0) ).
thf(585,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OLocal @ A @ B @ C )
!= ( c_Com_Ocom_OLocal @ D @ E @ F ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(229,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(1085,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(484,axiom,
! [B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ c_Hoare__Mirabelle_OMGT @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Com_OWT @ B )
| ( hBOOL @ ( c_in @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ A ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) @ tc_Com_Opname ) )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGF__lemma1_0) ).
thf(1658,plain,
! [B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ c_Hoare__Mirabelle_OMGT @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Com_OWT @ B )
| ( hBOOL @ ( c_in @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ A ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) @ tc_Com_Opname ) )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(433,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ B @ A ) @ ( c_Finite__Set_Olinorder__class_OMax @ C @ A ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__mono_0) ).
thf(1538,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ B @ A ) @ ( c_Finite__Set_Olinorder__class_OMax @ C @ A ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(951,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(108,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_1) ).
thf(808,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(249,axiom,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(1130,plain,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(449,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
thf(1579,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(341,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(1336,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( c_Collect @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
thf(643,plain,
! [B: $i,A: $i] :
( ( c_Collect @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(291,axiom,
! [B: $i,A: $i] : ( c_Com_OWT @ ( c_Com_Ocom_OAss @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OAssign_0) ).
thf(1221,plain,
! [B: $i,A: $i] : ( c_Com_OWT @ ( c_Com_Ocom_OAss @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(35,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) )
| ( C = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_2) ).
thf(600,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) )
| ( C = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(1052,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(417,axiom,
c_Com_OWT @ c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OSkip_0) ).
thf(1504,plain,
c_Com_OWT @ c_Com_Ocom_OSKIP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(489,axiom,
! [B: $i,A: $i] :
( ( c_Map_Odom @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__empty_0) ).
thf(1670,plain,
! [B: $i,A: $i] :
( ( c_Map_Odom @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(192,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__Un_0) ).
thf(1008,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ A ) @ B @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
thf(571,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ A ) @ B @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(357,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
thf(1372,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(313,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(1272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(135,axiom,
! [A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UNIV_0) ).
thf(876,plain,
! [A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
thf(991,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
thf(1404,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(351,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(1358,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)],[351]) ).
thf(452,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
thf(1585,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(176,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(978,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(845,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(379,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ A @ B @ C ) ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ B ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OIfTrue_0) ).
thf(1421,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ A @ B @ C ) ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ B ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(396,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(1459,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(175,axiom,
! [B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ c_Hoare__Mirabelle_OMGT @ ( hAPP @ c_Com_Ocom_OBODY @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ c_Hoare__Mirabelle_OMGT @ ( hAPP @ c_Com_Ocom_OBODY @ B ) ) @ A @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( c_Set_Oinsert @ ( hAPP @ c_Hoare__Mirabelle_OMGT @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ B ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGT__BodyN_0) ).
thf(976,plain,
! [B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ c_Hoare__Mirabelle_OMGT @ ( hAPP @ c_Com_Ocom_OBODY @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ c_Hoare__Mirabelle_OMGT @ ( hAPP @ c_Com_Ocom_OBODY @ B ) ) @ A @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( c_Set_Oinsert @ ( hAPP @ c_Hoare__Mirabelle_OMGT @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ B ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(8,axiom,
class_Lattices_Oupper__semilattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(524,plain,
class_Lattices_Oupper__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(759,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(247,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ ( c_Com_Ocom_OSemi @ C @ D ) @ E @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ F ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ F ) ) @ F )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ D @ E @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ F ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ F ) ) @ F )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ G @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ F ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ F ) ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comp_0) ).
thf(1126,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ ( c_Com_Ocom_OSemi @ C @ D ) @ E @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ F ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ F ) ) @ F )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ D @ E @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ F ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ F ) ) @ F )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ G @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ F ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ F ) ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ B ) ) @ C ) @ C ) )
| ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OWhileFalse_0) ).
thf(1189,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ A @ B ) ) @ C ) @ C ) )
| ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(157,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
= B )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ J @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
thf(931,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
= B )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ J @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_1) ).
thf(539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(193,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(1010,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(365,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1390,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(447,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(1575,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(320,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(393,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Option_Oset @ ( c_Option_Ooption_OSome @ A @ B ) @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_elem__set_1) ).
thf(1453,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Option_Oset @ ( c_Option_Ooption_OSome @ A @ B ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(454,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ D ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com__det_0) ).
thf(1590,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ D ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oimage @ ( c_COMBB @ c_Hoare__Mirabelle_OMGT @ c_Com_Ocom_OBODY @ tc_Com_Ocom @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_Com_Opname ) @ B @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Finite__Set_Ofinite @ B @ tc_Com_Opname )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oimage @ ( c_COMBB @ c_Hoare__Mirabelle_OMGT @ c_Com_Ocom_OBODY @ tc_Com_Ocom @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_Com_Opname ) @ B @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBB @ c_Hoare__Mirabelle_OMGT @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Ocom @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_Com_Opname ) @ B @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGT__Body_0) ).
thf(1326,plain,
! [B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oimage @ ( c_COMBB @ c_Hoare__Mirabelle_OMGT @ c_Com_Ocom_OBODY @ tc_Com_Ocom @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_Com_Opname ) @ B @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Finite__Set_Ofinite @ B @ tc_Com_Opname )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oimage @ ( c_COMBB @ c_Hoare__Mirabelle_OMGT @ c_Com_Ocom_OBODY @ tc_Com_Ocom @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_Com_Opname ) @ B @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBB @ c_Hoare__Mirabelle_OMGT @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Ocom @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_Com_Opname ) @ B @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(6,negated_conjecture,
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( c_Set_Oinsert @ ( hAPP @ c_Hoare__Mirabelle_OMGT @ ( hAPP @ c_Com_Ocom_OBODY @ v_pn ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(517,plain,
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( c_Set_Oinsert @ ( hAPP @ c_Hoare__Mirabelle_OMGT @ ( hAPP @ c_Com_Ocom_OBODY @ v_pn ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(163,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(946,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(471,axiom,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(1629,plain,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(632,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(302,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
thf(1244,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(995,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(363,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
thf(1385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(511,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OAss @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I31_J_0) ).
thf(1721,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OAss @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(343,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Map_Orestrict__map @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ t_a ) @ B @ t_a @ A ) @ v_x )
= ( c_Option_Ooption_ONone @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__map__empty_0) ).
thf(1341,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Map_Orestrict__map @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ t_a ) @ B @ t_a @ A ) @ v_x )
= ( c_Option_Ooption_ONone @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(86,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OCond @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I26_J_0) ).
thf(748,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OCond @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(218,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_COMBC @ A @ B @ C @ D @ E @ F )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
thf(1062,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_COMBC @ A @ B @ C @ D @ E @ F )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(419,axiom,
! [C: $i,B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ c_Com_Ocom_OSKIP @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).
thf(1508,plain,
! [C: $i,B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ c_Com_Ocom_OSKIP @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I16_J_0) ).
thf(568,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
thf(1308,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
thf(1193,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(225,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(1077,plain,
class_Orderings_Obot @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
thf(1212,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(461,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).
thf(1607,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(145,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(899,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)],[145]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_0) ).
thf(1030,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(410,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(1491,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)],[410]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(667,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(322,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(1294,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold1 @ A @ B @ C )
= ( c_The @ ( c_Finite__Set_Ofold1Set @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__def_0) ).
thf(832,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold1 @ A @ B @ C )
= ( c_The @ ( c_Finite__Set_Ofold1Set @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I25_J_0) ).
thf(684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(264,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(1161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(800,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ C @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_0) ).
thf(1133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ C @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
thf(999,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(478,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) ) @ F )
!= ( c_Option_Ooption_OSome @ G @ D ) )
| ( ( hAPP @ A @ F )
= ( c_Option_Ooption_OSome @ G @ D ) )
| ( F = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_0) ).
thf(1642,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) ) @ F )
!= ( c_Option_Ooption_OSome @ G @ D ) )
| ( ( hAPP @ A @ F )
= ( c_Option_Ooption_OSome @ G @ D ) )
| ( F = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(422,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(1512,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(493,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
thf(1678,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(368,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ C @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ D )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ C @ D )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ D ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).
thf(1395,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ C @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ D )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ C @ D )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ D ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(111,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(818,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)],[111]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I21_J_0) ).
thf(854,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(131,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(867,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)],[131]) ).
thf(455,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) @ ( c_Finite__Set_Olinorder__class_OMin @ C @ A ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__antimono_0) ).
thf(1593,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) @ ( c_Finite__Set_Olinorder__class_OMin @ C @ A ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(361,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cut_0) ).
thf(1380,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(428,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(1527,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(491,axiom,
! [B: $i,A: $i] :
( ( c_The @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the__sym__eq__trivial_0) ).
thf(1673,plain,
! [B: $i,A: $i] :
( ( c_The @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(304,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) @ B @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__in_0) ).
thf(1248,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) @ B @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
thf(790,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(865,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).
thf(1480,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(152,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
| ( ( hAPP @ C @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ E @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
thf(918,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
| ( ( hAPP @ C @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ E @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(499,axiom,
! [B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_0) ).
thf(1693,plain,
! [B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(56,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OSemi @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I45_J_0) ).
thf(664,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OSemi @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(507,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OLocal @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I41_J_0) ).
thf(1710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OLocal @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(720,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(167,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ A @ B @ C ) ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ D ) @ E ) )
| ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OIfFalse_0) ).
thf(955,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ A @ B @ C ) ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ D ) @ E ) )
| ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(462,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(1610,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)],[462]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(897,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(374,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Map_Odom @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( A
= ( c_COMBK @ ( c_Option_Ooption_ONone @ C ) @ ( tc_Option_Ooption @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__eq__empty__conv_0) ).
thf(1410,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Map_Odom @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( A
= ( c_COMBK @ ( c_Option_Ooption_ONone @ C ) @ ( tc_Option_Ooption @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(46,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OCall @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I32_J_0) ).
thf(635,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OCall @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(403,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ D ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
thf(1473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ D ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(886,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(928,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(181,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
thf(987,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(348,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(1352,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)],[348]) ).
thf(309,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__UNIV_0) ).
thf(1261,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(128,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ C @ A @ G @ H @ I @ J @ K @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).
thf(860,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ C @ A @ G @ H @ I @ J @ K @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(432,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top1I_0) ).
thf(1537,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(723,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I17_J_0) ).
thf(822,plain,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(324,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
= ( c_Set_Oimage @ ( c_COMBB @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__image_0) ).
thf(1299,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
= ( c_Set_Oimage @ ( c_COMBB @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(37,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
| ( C = G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).
thf(607,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
| ( C = G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(233,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMax @ B @ A ) @ B @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__in_0) ).
thf(1093,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMax @ B @ A ) @ B @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( c_lessequals @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__greatest_0) ).
thf(624,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( c_lessequals @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I1_J_0) ).
thf(596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OAss @ A @ B )
!= ( c_Com_Ocom_OAss @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(360,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(1378,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)],[360]) ).
thf(450,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(1582,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(198,axiom,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__fold1SetE_0) ).
thf(1019,plain,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I47_J_0) ).
thf(850,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(508,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Collect @ B @ C ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectI_0) ).
thf(1713,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Collect @ B @ C ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(418,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
= B )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ J @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
thf(1505,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
= B )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ J @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(370,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
= ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(1399,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
= ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(803,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(334,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Map_Orestrict__map @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
= ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ C @ D @ E ) @ B @ ( hAPP @ A @ B ) @ D @ ( tc_Option_Ooption @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__map__insert_0) ).
thf(1320,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Map_Orestrict__map @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
= ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ C @ D @ E ) @ B @ ( hAPP @ A @ B ) @ D @ ( tc_Option_Ooption @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(1184,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(16,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OWhile @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I61_J_0) ).
thf(543,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OWhile @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(22,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(560,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)],[22]) ).
thf(377,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(1416,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(221,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) ) @ B )
= ( c_Option_Ooption_OSome @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_3) ).
thf(1069,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_OSome @ C @ D ) @ E @ ( tc_Option_Ooption @ D ) ) @ B )
= ( c_Option_Ooption_OSome @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(195,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
thf(1014,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(339,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(1331,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(460,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(1606,plain,
class_Lattices_Oupper__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(482,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(1653,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)],[482]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ A ) ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ A ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I6_J_0) ).
thf(1367,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ A ) ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ A ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(398,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(1463,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(54,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(659,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(443,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).
thf(1565,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(1204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(391,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(1449,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(33,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) )
| ( C = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_2) ).
thf(592,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCall @ A @ B @ C )
!= ( c_Com_Ocom_OCall @ D @ E @ F ) )
| ( C = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(401,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E )
= ( c_Option_Ooption_ONone @ D ) )
| ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__out_0) ).
thf(1468,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E )
= ( c_Option_Ooption_ONone @ D ) )
| ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(1729,plain,
$false,
inference(e,[status(thm)],[1501,1718,629,1024,1369,1168,1454,1237,941,1179,1554,645,892,1322,1665,1559,1105,1315,518,1083,962,1005,1596,730,1522,1443,1618,1401,1569,1073,1544,878,1533,1437,1041,523,1158,582,1142,1269,1173,1486,1655,1310,550,797,913,1640,1354,1222,670,1497,1705,1078,1426,829,1196,1001,709,1046,1613,1601,1703,782,1441,1650,1645,1724,1475,1228,1623,1254,1628,1660,1264,751,802,1577,1313,1279,934,1191,1147,881,1115,1494,1100,1232,638,853,1087,1514,1347,1572,924,1465,1109,1151,574,1283,1489,1415,1682,1136,834,981,687,692,1447,1119,1394,1345,1433,1201,1697,527,1206,678,1306,1199,1338,534,714,1636,1438,661,546,793,1153,761,1057,1163,1274,1091,1021,1519,1217,820,815,1387,910,957,1223,894,825,1343,1123,862,1423,1032,1365,1178,1296,1210,757,1407,1128,1281,710,842,974,1012,847,566,1687,1457,1634,1392,874,1259,948,1017,615,1328,1121,1064,1006,869,989,519,742,697,1089,1234,1541,980,1587,1096,1672,857,1397,1567,1493,1160,1028,1361,1292,554,537,526,1214,1155,706,1419,901,1075,837,1324,997,1451,1131,1429,1715,779,1099,985,515,1478,1530,1382,1060,1050,1599,1246,1333,1318,1241,805,1695,921,657,1054,1170,1187,1026,1616,530,888,926,1286,1035,1466,1071,953,1185,1648,1146,1680,1698,1483,1548,745,1301,689,1374,965,1727,1510,1251,618,1631,733,904,694,772,1620,577,579,1535,1701,1256,1226,936,1707,713,1107,1239,1638,1356,1675,672,1139,1503,611,787,681,1524,1349,1603,1144,1690,1376,764,604,784,1117,1048,736,649,1043,1471,1630,726,621,1149,1112,890,1667,700,520,626,915,1556,1460,943,1022,983,959,1044,1066,883,1015,1176,563,1435,1102,653,1562,768,827,1726,1364,1413,1626,1583,1662,1304,1166,795,548,1684,1277,1081,516,939,754,1551,1208,589,812,1509,968,1181,525,1516,640,872,1611,971,739,1267,1230,993,1547,776,557,1003,1499,1432,717,840,1317,1220,907,1038,585,1085,1658,1538,951,808,1130,1579,1336,643,703,1221,600,1052,1504,1670,1008,571,1372,1272,876,991,1404,1358,1585,978,845,1421,1459,976,524,759,1126,1189,931,539,1010,1390,1575,1289,1453,1590,1326,517,946,1629,632,1244,995,1385,1721,1341,748,1062,1508,568,1308,1193,1077,1212,1607,899,1030,1491,667,1294,832,684,1161,800,1133,999,1642,1512,1678,1395,818,854,867,1593,1380,1527,1673,1248,790,865,1480,918,1693,664,1710,720,955,1610,897,1410,635,1473,886,928,987,1352,1261,860,1537,723,822,1299,607,1093,624,596,1378,1582,1019,850,1713,1505,1399,803,1320,1184,543,560,1416,676,1069,1014,1331,1606,1653,1367,1463,659,1565,1204,1449,592,1468]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV906-1 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n007.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 02:30:09 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.97/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.67/1.12 % [INFO] Parsing done (232ms).
% 1.67/1.12 % [INFO] Running in sequential loop mode.
% 2.22/1.32 % [INFO] eprover registered as external prover.
% 2.22/1.32 % [INFO] cvc4 registered as external prover.
% 2.39/1.33 % [INFO] Scanning for conjecture ...
% 2.54/1.43 % [INFO] Found a conjecture and 508 axioms. Running axiom selection ...
% 3.28/1.55 % [INFO] Axiom selection finished. Selected 508 axioms (removed 0 axioms).
% 3.75/1.69 % [INFO] Problem is propositional (TPTP CNF).
% 3.75/1.70 % [INFO] Type checking passed.
% 3.75/1.71 % [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 ...
% 9.19/3.06 % External prover 'e' found a proof!
% 9.19/3.06 % [INFO] Killing All external provers ...
% 9.19/3.06 % Time passed: 2547ms (effective reasoning time: 1937ms)
% 9.19/3.06 % 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)>
% 9.19/3.07 % Axioms used in derivation (508): cls_top__fun__eq_0, cls_com_Osimps_I55_J_0, cls_option_Oinject_0, cls_atLeastatMost__subset__iff_2, cls_the__sym__eq__trivial_0, cls_map__upd__eqD1_0, cls_com_Osimps_I18_J_0, cls_Diff__iff_2, cls_restrict__map__to__empty_0, cls_set__empty__eq_1, cls_bot__fun__eq_0, cls_WTs__elim__cases_I6_J_0, clsarity_nat__HOL_Oord, cls_com_Osimps_I1_J_0, cls_Diff__cancel_0, cls_INT__extend__simps_I4_J_0, cls_asm_0, cls_subset__insert_1, cls_sup__ge1_0, cls_insertE_0, cls_Un__Diff_0, cls_com_Osimps_I3_J_0, cls_Un__subset__iff_0, cls_com_Osimps_I32_J_0, cls_equalityI_0, cls_sup__top__left_0, cls_image__constant_0, clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite, cls_order__eq__iff_0, cls_com_Osimps_I5_J_0, cls_subset__empty_1, cls_subset__image__iff_2, cls_finite__insert_0, cls_empty__is__image_1, cls_com_Osimps_I44_J_0, cls_com_Osimps_I14_J_0, cls_image__mono_0, cls_Un__empty__left_0, cls_fun__upd__apply_1, cls_map__upd__Some__unfold_4, cls_le__funD_0, cls_fun__upd__image_1, cls_weak__Body_0, cls_sup__bot__right_0, cls_insert__code_1, cls_WT_OSemi_0, cls_map__upd__Some__unfold_3, cls_le__SUPI_0, cls_WTs__elim__cases_I4_J_1, cls_complete__lattice_OSup__singleton_0, cls_Un__upper1_0, cls_fold1Set__sing_1, cls_Un__commute_0, cls_COMBK__def_0, cls_UnCI_1, cls_inf__sup__aci_I6_J_0, cls_restrict__fun__upd_0, cls_Option_Oset_Osimps_I2_J_0, clsarity_fun__Orderings_Oorder, cls_finite__Un_2, cls_triple_Oinject_1, cls_evalc_OSemi_0, clsarity_bool__HOL_Ominus, cls_Diff__subset__conv_0, cls_option_Osimps_I2_J_0, cls_mem__def_1, cls_fun__upd__image_0, clsarity_nat__Orderings_Olinorder, cls_com_Osimps_I56_J_0, cls_WT_OSkip_0, cls_Inf__lower_0, cls_insert__absorb_0, cls_WTs__elim__cases_I7_J_0, cls_empty__iff_0, cls_Min__le_0, cls_com_Osimps_I31_J_0, cls_restrict__map__insert_0, cls_derivs__insertD_1, cls_com_Osimps_I7_J_1, cls_com_Osimps_I5_J_1, cls_evalc__WHILE__case_0, cls_insert__subset_0, cls_fun__upd__None__restrict_0, clsarity_fun__Lattices_Oupper__semilattice, cls_com_Osimps_I4_J_2, cls_le__sup__iff_0, cls_dom__fun__upd_0, cls_com_Osimps_I43_J_0, cls_insert__iff_1, cls_Diff__insert_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_COMBB__def_0, cls_CollectI_0, cls_com_Osimps_I47_J_0, cls_subset__insert__iff_2, cls_WTs__elim__cases_I5_J_0, clsarity_fun__Orderings_Otop, cls_com_Osimps_I54_J_0, cls_evalc__elim__cases_I1_J_0, cls_hoare__derivs_OSkip_0, cls_finite__insert_1, cls_contents__eq_0, cls_Min__singleton_0, cls_Comp_0, cls_Un__left__commute_0, clsarity_bool__Finite__Set_Ofinite_Ofinite, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_BodyN_0, cls_fold1__def_0, cls_com_Osimps_I45_J_0, cls_Collect__empty__eq_0, cls_Inf__singleton_0, cls_UN__extend__simps_I1_J_0, cls_Un__subset__iff_1, cls_CollectD_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_evalc__elim__cases_I6_J_0, cls_le__supI_0, cls_empty__is__image_0, cls_SUP__const_0, cls_rangeI_0, cls_rev__image__eqI_0, cls_finite__range__imageI_0, cls_Diff__UNIV_0, cls_map__upd__Some__unfold_0, cls_triple_Oinject_2, cls_UN__extend__simps_I3_J_0, cls_order__eq__refl_0, cls_range__composition_0, cls_SUP1__I_0, cls_UN__absorb_0, clsarity_fun__Orderings_Obot, cls_le__supE_1, cls_fun__upd__other_0, cls_com_Osimps_I26_J_0, cls_UN__iff_2, cls_le__iff__sup_0, cls_WTs__elim__cases_I4_J_0, cls_Sup__UNIV_0, cls_image__constant__conv_1, cls_MGF__lemma1_1, cls_Un__UNIV__right_0, cls_dom__const_0, cls_Un__absorb2_0, cls_atLeastatMost__subset__iff_3, cls_inf__sup__aci_I8_J_0, cls_Un__empty__right_0, cls_insert__ident_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_com_Osimps_I61_J_0, cls_WT__bodiesD_0, cls_sup__eq__bot__eq2_0, cls_com_Osimps_I37_J_0, cls_com_Osimps_I10_J_0, cls_Un__upper2_0, cls_UN__Un_0, cls_Max__mono_0, cls_com_Osimps_I38_J_0, cls_Sup__singleton_0, cls_not__None__eq_1, cls_com_Osimps_I48_J_0, cls_MGF__complete_0, cls_com_Osimps_I60_J_0, cls_evalc_OWhileFalse_0, cls_com_Osimps_I6_J_0, cls_UnCI_0, cls_com_Osimps_I23_J_0, cls_MGF_0, cls_escape_0, cls_ATP__Linkup_OCOMBC__def_0, cls_com_Osimps_I20_J_0, cls_subset__iff_0, cls_insert__code_2, cls_com_Osimps_I58_J_0, clsarity_fun__HOL_Oord, cls_evalc_OSkip_0, cls_Diff__idemp_0, cls_subset__empty_0, cls_com_Osimps_I40_J_0, cls_rev__predicate1D_0, cls_com_Osimps_I21_J_0, cls_elem__set_1, cls_complete__lattice_OInf__UNIV_0, cls_WTs__elim__cases_I8_J_0, cls_singleton__iff_1, cls_atLeastatMost__empty__iff_1, cls_finite_0, cls_complete__lattice_OInf__empty_0, cls_insert__Diff__single_0, cls_com_Osimps_I57_J_0, cls_image__insert_0, cls_finite__Diff_0, cls_SUP1__iff_2, cls_atLeastatMost__empty__iff2_0, clsarity_bool__Lattices_Oupper__semilattice, cls_UNIV__not__empty_0, cls_WT_OCall_0, cls_com_Osimps_I7_J_0, cls_Sup__binary_0, cls_the_Osimps_0, cls_Un__insert__left_0, cls_evalc__elim__cases_I5_J_0, cls_UN__subset__iff_0, cls_diff__single__insert_0, clsarity_fun__Finite__Set_Ofinite_Ofinite, cls_com_Osimps_I51_J_0, cls_doubleton__eq__iff_2, cls_map__upd__nonempty_0, cls_com_Osimps_I59_J_0, cls_subset__insert__iff_3, cls_fun__upd__triv_0, clsarity_nat__Orderings_Obot, cls_com__det_0, cls_finite__surj_0, cls_finite__UnI_0, cls_set__eq__subset_2, cls_Un__mono_0, cls_dom__eq__empty__conv_0, cls_insert__subset_1, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_com_Osimps_I50_J_0, cls_ex__in__conv_0, cls_sup__commute_0, cls_evalc_OBody_0, cls_com_Osimps_I30_J_0, cls_fun__upd__restrict__conv_0, cls_linorder__linear_0, cls_Un__empty_0, cls_ATP__Linkup_OCOMBB__def_0, cls_Un__subset__iff_2, cls_complete__lattice_OSup__UNIV_0, clsarity_fun__Lattices_Olattice, cls_MGT__BodyN_0, cls_order__antisym_0, cls_com_Osimps_I2_J_0, cls_com_Osimps_I46_J_0, cls_insert__is__Un_0, cls_com_Osimps_I19_J_0, cls_order__trans_0, cls_image__empty_0, cls_finite__UNIV_0, cls_dom__eq__singleton__conv_0, cls_subset__trans_0, cls_atLeastAtMost__singleton_0, cls_double__diff_0, cls_com_Osimps_I3_J_1, cls_com_Osimps_I27_J_0, cls_com_Osimps_I8_J_0, cls_DiffI_0, cls_map__upd__triv_0, cls_state__not__singleton__def_1, cls_com_Osimps_I29_J_0, cls_map__upd__Some__unfold_1, cls_com_Osimps_I9_J_0, clsarity_bool__Orderings_Opreorder, cls_le__supE_0, cls_empty__not__insert_0, cls_sup__assoc_0, cls_insert__Diff1_0, cls_dom__empty_0, cls_MGT__def__raw_0, cls_image__constant__conv_0, cls_MGF__lemma1_0, cls_insertI1_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_Nitpick_OEx1__def_2, cls_hoare__derivs_Oinsert_0, cls_fun__upd__twist_0, cls_atLeastatMost__subset__iff_0, cls_doubleton__eq__iff_0, cls_Un__absorb1_0, cls_sup__top__right_0, cls_Diff__insert2_0, cls_MGT__def_0, cls_Un__UNIV__left_0, cls_Sup__upper_0, cls_sup__least_0, cls_com_Osimps_I17_J_0, cls_empty__subsetI_0, cls_top__greatest_0, cls_sup1E_0, cls_WTs__elim__cases_I3_J_0, cls_subset__refl_0, cls_Max__singleton_0, cls_WTs__elim__cases_I5_J_1, cls_singletonE_0, clsarity_nat__Orderings_Opreorder, cls_com_Osimps_I25_J_0, cls_Inf__UNIV_0, clsarity_nat__Lattices_Olattice, cls_elem__set_0, cls_image__iff_2, cls_finite__dom__body_0, cls_insertCI_0, cls_dom__eq__singleton__conv_1, cls_com_Osimps_I34_J_0, cls_Un__Diff__cancel_0, cls_complete__lattice_OInf__insert_0, cls_image__Un_0, cls_insert__Diff_0, cls_not__Some__eq_1, cls_image__diff__subset_0, cls_insert__dom_0, cls_UNIV__I_0, cls_DiffE_0, cls_sup1CI_1, cls_complete__lattice_OInf__binary_0, cls_fun__upd__apply_0, cls_complete__lattice_OSup__binary_0, cls_restrict__in_0, cls_top1I_0, cls_order__eq__iff_2, cls_bot1E_0, cls_weaken_0, cls_evalc_OWhileTrue_0, cls_WT_OBody_0, cls_insert__mono_0, cls_Un__assoc_0, cls_fold1__singleton_0, cls_Collect__def_0, cls_le__supI2_0, cls_domI_0, cls_Un__Diff__cancel2_0, cls_Max__ge_0, cls_empty__fold1SetE_0, cls_bex__empty_0, cls_doubleton__eq__iff_3, cls_inf__sup__ord_I4_J_0, cls_com_Osimps_I28_J_0, cls_domIff_0, cls_Diff__mono_0, cls_order__antisym__conv_0, cls_com_Osimps_I2_J_1, cls_UnE_0, cls_subset__insertI2_0, cls_atLeastatMost__empty__iff_0, cls_finite__Diff__insert_1, cls_finite__Diff2_1, cls_com_Osimps_I42_J_0, cls_com_Osimps_I13_J_0, cls_Un__absorb_0, clsarity_bool__Lattices_Olattice, cls_MGT__Body_0, cls_subset__insert__iff_4, cls_fun__upd__restrict_0, cls_com_Osimps_I49_J_0, clsarity_bool__Lattices_Obounded__lattice, cls_bot__empty__eq_0, cls_eq__eqI_0, cls_complete__lattice_OInf__lower_0, cls_com_Osimps_I36_J_0, cls_le__supI1_0, cls_le__eqI_0, cls_WT_OIf_0, cls_sup__left__idem_0, cls_complete__lattice_OSup__insert_0, cls_thin_0, cls_subsetD_0, cls_insert__not__empty_0, cls_finite__Un_0, cls_le__sup__iff_2, clsarity_fun__Lattices_Obounded__lattice, clsarity_fun__Complete__Lattice_Ocomplete__lattice, cls_com_Osimps_I12_J_0, cls_finite__subset_0, cls_insert__subset_2, cls_com_Osimps_I35_J_0, cls_restrict__out_0, cls_insert__absorb2_0, cls_sup__fun__eq_0, cls_UNION__empty__conv_I1_J_0, cls_fun__upd__idem_0, cls_finite__Diff__insert_0, cls_subset__singletonD_0, cls_com_Osimps_I52_J_0, cls_single__stateE_0, cls_UN__I_0, cls_doubleton__eq__iff_1, cls_UN__extend__simps_I2_J_0, cls_fun__upd__idem__iff_0, cls_fun__diff__def_0, cls_Sup__insert_0, cls_xt1_I6_J_0, cls_subset__insert__iff_0, cls_empty_0, cls_complete__lattice_OInf__singleton_0, cls_Sup__empty_0, cls_set__empty__eq_0, cls_Nitpick_OEx1__def_3, cls_dom__minus_0, cls_com_Osimps_I1_J_1, clsarity_bool__Complete__Lattice_Ocomplete__lattice, cls_Diff__empty_0, cls_Un__left__absorb_0, cls_empty__Collect__eq_0, cls_atLeastatMost__subset__iff_1, cls_evalc__elim__cases_I5_J_2, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_inf__sup__aci_I5_J_0, cls_singleton__inject_0, cls_map__upd__Some__unfold_2, cls_triple_Oinject_0, cls_Un__empty_1, cls_subset__insert_0, cls_sup__idem_0, cls_MGF__lemma2__simult_0, clsarity_nat__Lattices_Oupper__semilattice, cls_emptyE_0, cls_inf__sup__ord_I3_J_0, cls_fun__upd__same_0, cls_eq__eqI_1, cls_com_Osimps_I4_J_1, cls_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_sup__ge2_0, cls_UN__upper_0, cls_fun__upd__None__restrict_1, cls_Un__least_0, cls_option_Osimps_I3_J_0, cls_sup1CI_0, cls_restrict__fun__upd_1, clsarity_fun__Orderings_Opreorder, cls_atLeastatMost__empty__iff2_1, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_finite_OemptyI_0, cls_subset__UNIV_0, cls_image__subset__iff_0, cls_finite__imageI_0, cls_insertCI_1, cls_doubleton__eq__iff_4, cls_Max__in_0, cls_complete__lattice_OSup__upper_0, cls_com_Osimps_I22_J_0, cls_fold1Set__sing_0, cls_Inf__empty_0, cls_finite__UN_0, cls_com_Osimps_I41_J_0, cls_Nitpick_OThe__psimp_0, cls_image__eqI_0, cls_dom__fun__upd_1, cls_Diff__subset__conv_1, cls_insert__code_0, cls_le__eqI_1, cls_subset__insertI_0, cls_evalc_OIfFalse_0, cls_WT_OAssign_0, cls_domIff_1, cls_DiffE_1, cls_complete__lattice_OSup__empty_0, cls_Diff__partition_0, cls_UNION__empty__conv_I2_J_0, cls_sup__bot__left_0, cls_insert__image_0, cls_rev__finite__subset_0, cls_finite__Un_1, cls_fun__upd__upd_0, cls_hoare__sound_0, cls_com_Osimps_I15_J_0, cls_insert__commute_0, cls_insert__iff_2, cls_image__image_0, cls_Diff__insert__absorb_0, cls_evalc__elim__cases_I5_J_1, cls_com_Osimps_I16_J_0, clsarity_nat__Orderings_Oorder, cls_finite__Diff2_0, cls_restrict__map__empty_0, cls_image__is__empty_0, cls_Min__in_0, cls_Un__insert__right_0, cls_com_Osimps_I2_J_2, cls_equalityE_0, cls_com_Osimps_I24_J_0, cls_com_Osimps_I63_J_0, cls_com_Osimps_I11_J_0, cls_cut_0, clsarity_fun__HOL_Ominus, cls_sup__absorb1_0, cls_com_Osimps_I53_J_0, cls_com_Osimps_I39_J_0, cls_UN__insert_0, cls_com_Osimps_I33_J_0, cls_imageI_0, cls_WT_OLocal_0, cls_com_Osimps_I4_J_0, cls_evalc_OIfTrue_0, clsarity_bool__Orderings_Otop, cls_ball__empty_0, cls_singleton__conv2_0, cls_subset__insert__iff_1, cls_com_Osimps_I62_J_0, cls_Min__antimono_0, cls_While_0, cls_Diff__subset_0, cls_derivs__insertD_0, cls_predicate1D_0, cls_empty__Diff_0, cls_fun__upd__idem__iff_1, clsarity_nat__HOL_Ominus, cls_com_Osimps_I7_J_2
% 9.19/3.07 % No. of inferences in proof: 1029
% 9.19/3.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2547 ms resp. 1937 ms w/o parsing
% 9.99/3.23 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.99/3.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------