%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV834-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:00:43 AM UTC 2026
% Result : Unsatisfiable 61.35s 24.16s
% Output : Refutation 64.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 643
% Syntax : Number of formulae : 1287 ( 367 unt; 0 typ; 0 def)
% Number of atoms : 2821 ( 816 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 26438 (1470 ~;1534 |; 0 &;23434 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 108 ( 106 usr; 17 con; 0-9 aty)
% Number of variables : 4780 ( 0 ^;4780 !; 0 ?;4780 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Hoare__Mirabelle_Ohoare__derivs_decl,type,
c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).
thf(v_G_decl,type,
v_G: $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_Set_Oinsert_decl,type,
c_Set_Oinsert: $i > $i ).
thf(tc_Hoare__Mirabelle_Otriple_decl,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple_decl,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i > $i > $i > $i ).
thf(c_COMBK_decl,type,
c_COMBK: $i > $i > $i > $i ).
thf(c_False_decl,type,
c_False: $i ).
thf(tc_bool_decl,type,
tc_bool: $i ).
thf(tc_Com_Ostate_decl,type,
tc_Com_Ostate: $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(v_c_decl,type,
v_c: $i ).
thf(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i > $i ).
thf(c_COMBB_decl,type,
c_COMBB: $i > $i > $i > $i ).
thf(c_COMBS_decl,type,
c_COMBS: $i > $i > $i > $i ).
thf(c_and_decl,type,
c_and: $i ).
thf(v_P_decl,type,
v_P: $i ).
thf(c_Not_decl,type,
c_Not: $i ).
thf(v_b_decl,type,
v_b: $i ).
thf(c_Orderings_Obot__class_Obot_decl,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(c_Com_Ocom_OWhile_decl,type,
c_Com_Ocom_OWhile: $i > $i > $i ).
thf(class_Lattices_Oupper__semilattice_decl,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i ).
thf(c_Lattices_Oupper__semilattice__class_Osup_decl,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i ).
thf(class_Lattices_Olower__semilattice_decl,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(c_Finite__Set_Ofold1_decl,type,
c_Finite__Set_Ofold1: $i > $i > $i > $i ).
thf(c_Lattices_Olower__semilattice__class_Oinf_decl,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofinite_decl,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(c_Com_Ocom_OSKIP_decl,type,
c_Com_Ocom_OSKIP: $i ).
thf(c_Com_Ocom_OSemi_decl,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(c_Com_Ocom_OBODY_decl,type,
c_Com_Ocom_OBODY: $i > $i ).
thf(c_Com_Ocom_OCond_decl,type,
c_Com_Ocom_OCond: $i > $i > $i > $i ).
thf(c_Collect_decl,type,
c_Collect: $i > $i > $i ).
thf(c_Fun_Oinj__on_decl,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_Fun_Ocomp_decl,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i > $i ).
thf(class_Complete__Lattice_Ocomplete__lattice_decl,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR_decl,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i > $i > $i ).
thf(class_Finite__Set_Ofinite_Ofinite_decl,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
thf(class_Lattices_Olattice_decl,type,
class_Lattices_Olattice: $i > $o ).
thf(c_The_decl,type,
c_The: $i > $i > $i ).
thf(c_Finite__Set_Ofold1Set_decl,type,
c_Finite__Set_Ofold1Set: $i > $i > $i > $i ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OINFI_decl,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: $i > $i > $i > $i > $i ).
thf(c_Orderings_Otop__class_Otop_decl,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_HOL_Oord__class_Oless_decl,type,
c_HOL_Oord__class_Oless: $i > $i ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i ).
thf(class_Lattices_Obounded__lattice_decl,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Set_Ocontents_decl,type,
c_Set_Ocontents: $i > $i > $i ).
thf(c_fequal_decl,type,
c_fequal: $i > $i ).
thf(c_Complete__Lattice_Ocomplete__lattice_decl,type,
c_Complete__Lattice_Ocomplete__lattice: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(c_HOL_Otimes__class_Otimes_decl,type,
c_HOL_Otimes__class_Otimes: $i > $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(class_Orderings_Otop_decl,type,
class_Orderings_Otop: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_SetInterval_Oord__class_OatLeastAtMost_decl,type,
c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_Hoare__Mirabelle_Opeek__and_decl,type,
c_Hoare__Mirabelle_Opeek__and: $i > $i > $i > $i ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(c_Finite__Set_Osetsum_decl,type,
c_Finite__Set_Osetsum: $i > $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_decl,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3_decl,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3: $i > $i > $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2_decl,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2: $i > $i > $i > $i > $i ).
thf(class_HOL_Ominus_decl,type,
class_HOL_Ominus: $i > $o ).
thf(v_sko__Hoare__Mirabelle__Xconseq12__1_decl,type,
v_sko__Hoare__Mirabelle__Xconseq12__1: $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xconseq12__2_decl,type,
v_sko__Hoare__Mirabelle__Xconseq12__2: $i > $i > $i > $i > $i ).
thf(class_Orderings_Obot_decl,type,
class_Orderings_Obot: $i > $o ).
thf(v_sko__Hoare__Mirabelle__Xconseq2__1_decl,type,
v_sko__Hoare__Mirabelle__Xconseq2__1: $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xconseq2__2_decl,type,
v_sko__Hoare__Mirabelle__Xconseq2__2: $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__ring__strict_decl,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(c_Complete__Lattice_OSup__class_OSup_decl,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i ).
thf(class_Ring__and__Field_Osemiring__0_decl,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1_decl,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1: $i > $i > $i > $i > $i ).
thf(class_HOL_Oord_decl,type,
class_HOL_Oord: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_Lattices_Odistrib__lattice_decl,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(t_b_decl,type,
t_b: $i ).
thf(v_Q_decl,type,
v_Q: $i ).
thf(c_Complete__Lattice_OInf__class_OInf_decl,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i ).
thf(c_Finite__Set_Olinorder__class_OMax_decl,type,
c_Finite__Set_Olinorder__class_OMax: $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xconseq1__1_decl,type,
v_sko__Hoare__Mirabelle__Xconseq1__1: $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xconseq1__2_decl,type,
v_sko__Hoare__Mirabelle__Xconseq1__2: $i > $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__mult_decl,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(c_Option_Othe_decl,type,
c_Option_Othe: $i > $i > $i ).
thf(c_Com_Obody_decl,type,
c_Com_Obody: $i > $i ).
thf(tc_Com_Ocom_decl,type,
tc_Com_Ocom: $i ).
thf(c_Nitpick_Osko__Nitpick__XEx1__def__1__3_decl,type,
c_Nitpick_Osko__Nitpick__XEx1__def__1__3: $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xconseq12__3_decl,type,
v_sko__Hoare__Mirabelle__Xconseq12__3: $i > $i > $i > $i > $i ).
thf(c_List_Ofilter_decl,type,
c_List_Ofilter: $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xescape__1_decl,type,
v_sko__Hoare__Mirabelle__Xescape__1: $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xescape__2_decl,type,
v_sko__Hoare__Mirabelle__Xescape__2: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Olinorder__class_OMin_decl,type,
c_Finite__Set_Olinorder__class_OMin: $i > $i > $i ).
thf(c_Ex_decl,type,
c_Ex: $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_or_decl,type,
c_or: $i ).
thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3_decl,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3: $i > $i > $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2_decl,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2: $i > $i > $i > $i > $i ).
thf(c_List_Olistsp_decl,type,
c_List_Olistsp: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oring_decl,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(c_Wellfounded_OwfP_decl,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1_decl,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1: $i > $i > $i > $i > $i ).
thf(282,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1322,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
thf(1036,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(349,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1469,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(760,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(629,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( F @ ( C @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( E @ ( D @ c_in ) ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__subset__iff_0) ).
thf(2109,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( F @ ( C @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( E @ ( D @ c_in ) ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(423,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ ( c_or @ ( B @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( B @ ( A @ c_Collect ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__disjI_1) ).
thf(1633,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ ( c_or @ ( B @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( B @ ( A @ c_Collect ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(581,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(1995,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(189,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(1105,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( C @ ( B @ ( A @ ( t_a @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) )
= ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
thf(893,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( C @ ( B @ ( A @ ( t_a @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) )
= ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(519,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( F @ tc_fun ) @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( F @ tc_fun ) @ ( C @ ( A @ ( E @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I10_J_0) ).
thf(1850,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( F @ tc_fun ) @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( F @ tc_fun ) @ ( C @ ( A @ ( E @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(941,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(1179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(1549,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(446,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(1686,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(399,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(1586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(809,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(290,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__3 ) ) ) @ ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_2) ).
thf(1337,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__3 ) ) ) @ ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(459,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
thf(1718,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(304,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( F @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ ( B @ ( D @ ( A @ ( F @ c_Set_Oimage ) ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I10_J_0) ).
thf(1369,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( F @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ ( B @ ( D @ ( A @ ( F @ c_Set_Oimage ) ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(505,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
= ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(1823,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
= ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(224,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ ( C @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ ( C @ ( A @ ( A @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__right__distrib_0) ).
thf(1190,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ ( C @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ ( C @ ( A @ ( A @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(245,axiom,
tc_bool @ class_Orderings_Obot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(1237,plain,
tc_bool @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(77,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
thf(846,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(179,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(1083,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(962,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(234,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).
thf(1211,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(144,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(1005,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(173,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( B @ hAPP ) )
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I2_J_0) ).
thf(1068,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( B @ hAPP ) )
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(337,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1443,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(416,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( F @ ( E @ hAPP ) @ ( D @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
thf(1618,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( F @ ( E @ hAPP ) @ ( D @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(1401,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(328,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( F @ tc_fun ) @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= ( tc_bool @ ( F @ tc_fun ) @ ( C @ ( A @ ( E @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I10_J_0) ).
thf(1422,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( F @ tc_fun ) @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= ( tc_bool @ ( F @ tc_fun ) @ ( C @ ( A @ ( E @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(380,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(1544,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(464,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I3_J_0) ).
thf(1728,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(259,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I1_J_0) ).
thf(1269,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(335,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
thf(1437,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(356,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(1486,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(521,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(1855,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(616,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(2077,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(474,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(1750,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(133,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).
thf(977,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(405,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).
thf(1596,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(320,axiom,
tc_bool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1406,plain,
tc_bool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(627,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(2104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(32,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I53_J_0) ).
thf(730,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(533,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(1882,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(625,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_fequal @ hAPP ) @ c_Collect ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
thf(2099,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_fequal @ hAPP ) @ c_Collect ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(402,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(1591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(91,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( I @ ( C @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/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] :
( ~ ( B @ ( I @ ( C @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I16_J_0) ).
thf(655,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(570,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(1971,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(375,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
thf(1533,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(360,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I2_J_0) ).
thf(1497,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(440,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(1671,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(467,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( A @ c_in ) ) @ hBOOL )
| ~ ( F @ ( E @ ( C @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__iff_0) ).
thf(1735,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( A @ c_in ) ) @ hBOOL )
| ~ ( F @ ( E @ ( C @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(212,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(715,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(641,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_1) ).
thf(2141,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(1233,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(1260,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).
thf(945,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(601,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(2042,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(298,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1354,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(112,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
thf(930,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(670,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(177,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ ( tc_bool @ ( A @ ( A @ ( A @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ ( c_and @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conv__if_1) ).
thf(1078,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ ( tc_bool @ ( A @ ( A @ ( A @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ ( c_and @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(330,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(1426,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(478,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
| ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(1761,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
| ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(292,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(1342,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(170,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(1063,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(562,axiom,
tc_bool @ class_Lattices_Oupper__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(1954,plain,
tc_bool @ class_Lattices_Oupper__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_The ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OThe__psimp_0) ).
thf(898,plain,
! [B: $i,A: $i] :
( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_The ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(546,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ c_Collect ) )
!= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
thf(1914,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ c_Collect ) )
!= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) )
= ( A @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( B
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( C
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__Un_0) ).
thf(1243,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) )
= ( A @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( B
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( C
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(394,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__upper_0) ).
thf(1576,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Finite__Set_Ofold1 ) ) )
= ( C @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold1Set ) ) @ c_The ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__def_0) ).
thf(782,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Finite__Set_Ofold1 ) ) )
= ( C @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold1Set ) ) @ c_The ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(709,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(590,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( D @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(2020,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( D @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(414,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(1613,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(586,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
thf(2010,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(431,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( B @ ( D @ hAPP ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__insert_0) ).
thf(1650,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( B @ ( D @ hAPP ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(408,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(1601,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(303,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set__sing_0) ).
thf(1366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(568,axiom,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite_Ofinite )
| ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
thf(1967,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite_Ofinite )
| ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(535,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( C @ ( B @ ( A @ ( t_a @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) )
= ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
thf(1887,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( C @ ( B @ ( A @ ( t_a @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) )
= ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(651,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(69,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(829,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold1SetE_0) ).
thf(1095,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(973,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(885,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(639,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ c_Finite__Set_Olinorder__class_OMin ) @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__antimono_0) ).
thf(2136,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ c_Finite__Set_Olinorder__class_OMin ) @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(453,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty_0) ).
thf(1703,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(267,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(576,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(1985,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(528,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(1871,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(838,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(802,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(507,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(1826,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(263,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( F @ ( E @ hAPP ) @ ( F @ ( D @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).
thf(1279,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( F @ ( E @ hAPP ) @ ( F @ ( D @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(342,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( tc_bool @ ( A @ ( A @ ( A @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv_0) ).
thf(1455,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( tc_bool @ ( A @ ( A @ ( A @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(510,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1832,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(121,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( I @ ( G @ hAPP ) @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( H @ ( G @ ( F @ c_Fun_Ocomp ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
thf(949,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( I @ ( G @ hAPP ) @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( H @ ( G @ ( F @ c_Fun_Ocomp ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
thf(1055,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(322,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
thf(1409,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(491,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(1792,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(332,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(1430,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(523,axiom,
! [A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
thf(1860,plain,
! [A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(257,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ ( D @ c_Set_Oinsert @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eq__UN_0) ).
thf(1264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ ( D @ c_Set_Oinsert @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(345,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__2 ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_escape_0) ).
thf(1462,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__2 ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_0) ).
thf(1132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(902,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(537,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(1892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(536,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__Un_0) ).
thf(1890,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(969,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(391,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ( A = D )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ( A = D )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(593,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( D @ ( D @ ( A @ ( C @ c_COMBK ) ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= C )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP__const_0) ).
thf(2024,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( D @ ( D @ ( A @ ( C @ c_COMBK ) ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= C )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(483,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ~ ( A @ ( D @ hAPP ) @ hBOOL )
| ( B @ ( B @ ( D @ c_Collect ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_2) ).
thf(1773,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ~ ( A @ ( D @ hAPP ) @ hBOOL )
| ( B @ ( B @ ( D @ c_Collect ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(501,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(1815,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(530,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
thf(1875,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Otop__class_Otop ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
thf(1100,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Otop__class_Otop ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(181,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( D @ ( D @ ( A @ ( C @ c_COMBK ) ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= C )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__const_0) ).
thf(1087,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( D @ ( D @ ( A @ ( C @ c_COMBK ) ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= C )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(367,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Olinorder__class_OMin ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__singleton_0) ).
thf(1514,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Olinorder__class_OMin ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(353,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_in ) ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ hAPP ) @ c_Finite__Set_Ofinite ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__INT_0) ).
thf(1479,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_in ) ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ hAPP ) @ c_Finite__Set_Ofinite ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(412,axiom,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(1609,plain,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(470,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(1741,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(92,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( A @ c_in ) ) @ hBOOL )
| ~ ( F @ ( E @ ( C @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__D_0) ).
thf(881,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( A @ c_in ) ) @ hBOOL )
| ~ ( F @ ( E @ ( C @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(585,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( D @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(2007,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( D @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(357,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( A @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__subtractf_0) ).
thf(1489,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( A @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(559,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1946,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(594,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
| ( A @ ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).
thf(2027,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
| ( A @ ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(340,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( c_and @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) )
= ( A @ ( C @ c_Collect ) @ ( A @ ( B @ c_Collect ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conj__eq_0) ).
thf(1450,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( c_and @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) )
= ( A @ ( C @ c_Collect ) @ ( A @ ( B @ c_Collect ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(545,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(1911,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(326,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__2 ) @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__1 ) @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq1_1) ).
thf(1418,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__2 ) @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__1 ) @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(834,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(508,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
thf(1828,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(207,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(1151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(397,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(1581,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(66,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( G @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Fun_Ocomp ) ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) )
= ( F @ ( G @ ( D @ ( C @ ( D @ ( G @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Ocomp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).
thf(821,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( G @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Fun_Ocomp ) ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) )
= ( F @ ( G @ ( D @ ( C @ ( D @ ( G @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Ocomp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).
thf(905,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(273,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ~ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(1302,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ~ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(437,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( E @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).
thf(1664,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( E @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(160,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__Un_0) ).
thf(1040,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(191,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).
thf(1109,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = G )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1334,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_1) ).
thf(646,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(265,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( B = E )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(1283,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( B = E )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(614,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( F @ c_in ) ) @ hBOOL )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__I_0) ).
thf(2073,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( F @ c_in ) ) @ hBOOL )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(551,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(1928,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(86,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( F @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).
thf(866,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( F @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(1526,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(296,axiom,
tc_bool @ class_Lattices_Olattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(1351,plain,
tc_bool @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(293,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(1345,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(333,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(1433,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(229,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(1201,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(407,axiom,
tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(1600,plain,
tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(849,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(370,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Otop )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
thf(1521,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Otop )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(389,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
thf(1564,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(215,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(1169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(687,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(418,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
thf(1622,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(774,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(524,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(1863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(175,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF1__D_0) ).
thf(1074,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(448,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1691,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(661,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(110,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( F @ ( E @ hAPP ) @ ( F @ ( D @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBS__def_0) ).
thf(925,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( F @ ( E @ hAPP ) @ ( F @ ( D @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(275,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(1306,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
thf(1199,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(603,axiom,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).
thf(2047,plain,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(622,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
thf(2093,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(487,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( C @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__le_0) ).
thf(1783,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( C @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(618,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(2083,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(609,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_fequal @ hAPP ) @ c_The ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__sym__eq__trivial_0) ).
thf(2061,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_fequal @ hAPP ) @ c_The ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(481,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(1768,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(526,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(1868,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(465,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(1730,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(57,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( E @ ( C @ hAPP ) @ ( A @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__leI_0) ).
thf(798,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( E @ ( C @ hAPP ) @ ( A @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(168,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = E )
| ( C = D )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(1057,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = E )
| ( C = D )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(261,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(1274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(239,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(1223,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(369,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(1519,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(396,axiom,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(1580,plain,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(253,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(1255,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(1217,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(362,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
thf(1502,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(438,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
thf(1666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(53,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( F @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( C @ ( C @ ( E @ ( F @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__inj__on_0) ).
thf(788,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( F @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( C @ ( C @ ( E @ ( F @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(246,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1238,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(312,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( C @ ( A @ ( B @ ( c_and @ ( D @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_List_Ofilter ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__filter_0) ).
thf(1387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_List_Ofilter ) ) @ ( A @ c_List_Ofilter ) ) )
= ( D @ ( C @ ( A @ ( B @ ( c_and @ ( D @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_List_Ofilter ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(462,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( F @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).
thf(1723,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( F @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(104,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( F @ ( B @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( E @ ( C @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
thf(910,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( F @ ( B @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( E @ ( C @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(1021,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(48,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
thf(778,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(161,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__2 ) ) ) @ ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_0) ).
thf(1042,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__2 ) ) ) @ ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(122,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).
thf(952,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(217,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
| ( B @ ( D @ ( E @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_1) ).
thf(1174,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
| ( B @ ( D @ ( E @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(1676,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(638,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__binary_0) ).
thf(2133,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(555,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( t_a @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__1 ) ) ) @ ( D @ hAPP ) @ c_COMBK ) ) @ ( C @ ( t_a @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__2 ) ) ) @ ( tc_bool @ ( tc_Com_Ostate @ ( tc_Com_Ostate @ ( tc_Com_Ostate @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_COMBK ) ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_escape_1) ).
thf(1938,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( t_a @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__1 ) ) ) @ ( D @ hAPP ) @ c_COMBK ) ) @ ( C @ ( t_a @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__2 ) ) ) @ ( tc_bool @ ( tc_Com_Ostate @ ( tc_Com_Ostate @ ( tc_Com_Ostate @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_COMBK ) ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(548,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(1920,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).
thf(852,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(343,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(1457,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(210,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(1159,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(434,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(1656,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(1027,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(264,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).
thf(1281,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(314,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
| ( D
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold1 ) ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_below__fold1__iff_0) ).
thf(1392,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
| ( D
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold1 ) ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(75,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(842,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(1032,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(409,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(1602,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(612,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( E @ ( D @ ( G @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__2 ) ) ) @ ( F @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( G @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__3 ) ) ) @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_1) ).
thf(2068,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( E @ ( D @ ( G @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__2 ) ) ) @ ( F @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( G @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__3 ) ) ) @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(503,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( c_or @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) )
= ( A @ ( C @ c_Collect ) @ ( A @ ( B @ c_Collect ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__disj__eq_0) ).
thf(1819,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( c_or @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) )
= ( A @ ( C @ c_Collect ) @ ( A @ ( B @ c_Collect ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(419,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(1624,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(512,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(1836,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(489,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(1787,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(682,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(226,axiom,
( ( v_Q @ ( t_b @ ( t_a @ ( v_P @ c_COMBK ) ) @ hAPP ) )
= v_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def__raw_0) ).
thf(1195,plain,
( ( v_Q @ ( t_b @ ( t_a @ ( v_P @ c_COMBK ) ) @ hAPP ) )
= v_P ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(321,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
thf(1407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(393,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) )
= ( A @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__insert_0) ).
thf(1573,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) )
= ( A @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(132,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( A @ ( C @ c_Finite__Set_Osetsum ) @ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ tc_fun ) @ ( A @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) )
= ( E @ ( F @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ ( C @ ( B @ ( D @ c_COMBC ) ) ) @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ tc_fun ) @ ( A @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( C @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__commute_0) ).
thf(974,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( A @ ( C @ c_Finite__Set_Osetsum ) @ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ tc_fun ) @ ( A @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) )
= ( E @ ( F @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ ( C @ ( B @ ( D @ c_COMBC ) ) ) @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ tc_fun ) @ ( A @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( C @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(554,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(1936,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(575,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBK__def_0) ).
thf(1983,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(874,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(492,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(1794,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(497,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(1804,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(285,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
thf(1328,plain,
! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_COMBK ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__empty2_0) ).
thf(1064,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_COMBK ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).
thf(1227,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(135,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(980,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(531,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(1878,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
thf(869,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(476,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(1755,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(194,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(1118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(316,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
thf(1397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(445,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(1683,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(286,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( E @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) @ ( C @ ( A @ hAPP ) @ c_in ) ) @ hBOOL )
| ( E @ ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).
thf(1329,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( E @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) @ ( C @ ( A @ hAPP ) @ c_in ) ) @ hBOOL )
| ( E @ ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(592,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(2023,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(301,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
thf(1361,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(753,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(220,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( G @ ( E @ ( B @ ( D @ ( C @ c_Hoare__Mirabelle_Opeek__and ) ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( G @ ( F @ ( B @ ( tc_Com_Ostate @ ( tc_bool @ ( tc_bool @ ( D @ ( c_Not @ c_Fun_Ocomp ) ) ) ) @ ( C @ c_Hoare__Mirabelle_Opeek__and ) ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( G @ ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_OIf_0) ).
thf(1182,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( G @ ( E @ ( B @ ( D @ ( C @ c_Hoare__Mirabelle_Opeek__and ) ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( G @ ( F @ ( B @ ( tc_Com_Ostate @ ( tc_bool @ ( tc_bool @ ( D @ ( c_Not @ c_Fun_Ocomp ) ) ) ) @ ( C @ c_Hoare__Mirabelle_Opeek__and ) ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( G @ ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(469,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ ( E @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1739,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ ( E @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(329,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).
thf(1424,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(617,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).
thf(2080,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(235,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( B
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( A @ ( B @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMax ) @ c_in ) ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__in_0) ).
thf(1214,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( B
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( A @ ( B @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMax ) @ c_in ) ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(599,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( tc_bool @ ( A @ ( A @ ( A @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_The ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__eq__trivial_0) ).
thf(2038,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( tc_bool @ ( A @ ( A @ ( A @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_The ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I46_J_0) ).
thf(679,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(23,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( E @ ( D @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I45_J_0) ).
thf(706,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( E @ ( D @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(567,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(1964,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(557,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(1942,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(435,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( B = C )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
thf(1659,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( B = C )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(269,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ~ ( E @ ( C @ ( D @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).
thf(1292,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ~ ( E @ ( C @ ( D @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(113,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(933,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( A @ c_Collect ) @ ( B @ c_in ) ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectD_0) ).
thf(1414,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( A @ c_Collect ) @ ( B @ c_in ) ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(605,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).
thf(2053,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(149,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(1016,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(1207,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__constant_1) ).
thf(997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(1297,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(439,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( I @ ( H @ ( G @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( K @ ( H @ ( J @ ( E @ ( D @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) )
| ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
!= ( F @ ( E @ hAPP ) @ ( D @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).
thf(1668,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( I @ ( H @ ( G @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( K @ ( H @ ( J @ ( E @ ( D @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) )
| ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
!= ( F @ ( E @ hAPP ) @ ( D @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(494,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
thf(1799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(249,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ ( tc_Com_Ocom @ ( D @ c_Com_Obody @ c_Option_Othe ) @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( D @ c_Com_Ocom_OBODY @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ ( D @ c_Com_Ocom_OBODY @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_BodyN_0) ).
thf(1246,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ ( tc_Com_Ocom @ ( D @ c_Com_Obody @ c_Option_Othe ) @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( D @ c_Com_Ocom_OBODY @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ ( D @ c_Com_Ocom_OBODY @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(460,axiom,
tc_bool @ class_Orderings_Otop,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
thf(1720,plain,
tc_bool @ class_Orderings_Otop,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(573,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__apply_0) ).
thf(1979,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(506,axiom,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty_0) ).
thf(1825,plain,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(283,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__constant_0) ).
thf(1324,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).
thf(1114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(400,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(1588,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
thf(985,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(374,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) )
= ( A @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__insert__idem_0) ).
thf(1530,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) )
= ( A @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(378,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( C @ ( D @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).
thf(1539,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( C @ ( D @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
thf(1382,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(1266,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(509,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(1831,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(1060,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(1050,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ ( A @ c_fequal @ hAPP ) @ ( c_and @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conv__if2_0) ).
thf(1002,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ ( A @ c_fequal @ hAPP ) @ ( c_and @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(520,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(1852,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(522,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(1857,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(579,axiom,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( A @ ( tc_bool @ ( c_False @ c_COMBK ) ) @ c_Collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__def_0) ).
thf(1991,plain,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( A @ ( tc_bool @ ( c_False @ c_COMBK ) ) @ c_Collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(792,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(115,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(938,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(247,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
thf(1241,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(450,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(1695,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(108,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF1__iff_0) ).
thf(921,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(1286,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(174,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(1071,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(620,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( C @ ( F @ ( E @ ( D @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
thf(2089,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( C @ ( F @ ( E @ ( D @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(415,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( D @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).
thf(1616,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( D @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(222,axiom,
! [A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
thf(1185,plain,
! [A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(466,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(1732,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(607,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(2057,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(517,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(1846,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(539,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(1895,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(1167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(634,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(2121,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(543,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
thf(1906,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(430,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ hAPP ) @ hBOOL )
| ~ ( A @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(1648,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ hAPP ) @ hBOOL )
| ~ ( A @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(583,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( D @ ( E @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) )
= ( E @ ( C @ hAPP ) @ ( D @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_0) ).
thf(2001,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( D @ ( E @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) )
= ( E @ ( C @ hAPP ) @ ( D @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(1146,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(444,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(1680,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(597,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).
thf(2033,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(237,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
thf(1219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(473,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(1747,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Set_Ocontents ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_contents__eq_0) ).
thf(856,plain,
! [B: $i,A: $i] :
( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Set_Ocontents ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
thf(745,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( c_Com_Ocom_OSKIP @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).
thf(1595,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( c_Com_Ocom_OSKIP @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Collect ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).
thf(689,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(306,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(1374,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(38,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I44_J_0) ).
thf(750,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( E @ ( D @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(365,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(1510,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(451,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( F @ ( A @ ( E @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( G @ ( A @ ( tc_bool @ ( E @ tc_fun ) @ ( B @ ( F @ ( A @ ( E @ tc_fun ) @ ( A @ ( E @ tc_fun ) @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( A @ ( A @ c_COMBB ) ) @ ( B @ ( A @ ( E @ tc_fun ) @ ( A @ ( E @ tc_fun ) @ tc_fun ) @ ( A @ ( A @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( E @ c_Finite__Set_Osetsum ) @ ( B @ ( A @ ( tc_bool @ ( E @ tc_fun ) @ tc_fun ) @ ( A @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__product_0) ).
thf(1698,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( F @ ( A @ ( E @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( G @ ( A @ ( tc_bool @ ( E @ tc_fun ) @ ( B @ ( F @ ( A @ ( E @ tc_fun ) @ ( A @ ( E @ tc_fun ) @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( A @ ( A @ c_COMBB ) ) @ ( B @ ( A @ ( E @ tc_fun ) @ ( A @ ( E @ tc_fun ) @ tc_fun ) @ ( A @ ( A @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( E @ c_Finite__Set_Osetsum ) @ ( B @ ( A @ ( tc_bool @ ( E @ tc_fun ) @ tc_fun ) @ ( A @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(565,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__empty_0) ).
thf(1959,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(188,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(1103,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(422,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( A @ ( c_or @ ( B @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( B @ ( A @ c_Collect ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__disjI_0) ).
thf(1631,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( C @ ( A @ ( c_or @ ( B @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( B @ ( A @ c_Collect ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(733,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( C @ ( B @ ( A @ ( t_a @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ hAPP ) )
= ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_HOL_Ominus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
thf(1154,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( C @ ( B @ ( A @ ( t_a @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ hAPP ) )
= ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_HOL_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(145,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(1007,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(534,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( D @ ( E @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) )
= ( E @ ( C @ hAPP ) @ ( D @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__ring_0) ).
thf(1884,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( D @ ( E @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) )
= ( E @ ( C @ hAPP ) @ ( D @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(313,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( B @ hAPP ) )
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).
thf(1389,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( B @ hAPP ) )
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(417,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1620,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(475,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(1752,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(432,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(1652,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(588,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(2016,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(376,axiom,
tc_bool @ class_Lattices_Olower__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(1535,plain,
tc_bool @ class_Lattices_Olower__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(452,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( C @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut_0) ).
thf(1701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( C @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( C @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
thf(1124,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( C @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I15_J_0) ).
thf(826,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) )
| ~ ( D @ ( B @ ( A @ ( C @ c_Fun_Oinj__on ) ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).
thf(711,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) )
| ~ ( D @ ( B @ ( A @ ( C @ c_Fun_Oinj__on ) ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(958,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(319,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(1403,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(331,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).
thf(1428,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(202,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(1139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(595,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(2029,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(455,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(1707,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(277,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( F @ c_in ) ) @ hBOOL )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).
thf(1312,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( F @ c_in ) ) @ hBOOL )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(424,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 ) ) ) @ ( F @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( G @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 ) ) ) ) ) @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_1) ).
thf(1635,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 ) ) ) @ ( F @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( G @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 ) ) ) ) ) @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
thf(1107,plain,
! [B: $i,A: $i] :
( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(1332,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(606,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ c_Set_Oinsert @ c_COMBC ) ) ) @ hAPP ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__singleton_0) ).
thf(2055,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ c_Set_Oinsert @ c_COMBC ) ) ) @ hAPP ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(804,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(299,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( A @ c_Collect ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_in ) ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_1) ).
thf(1356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( A @ c_Collect ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_in ) ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(11,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_2) ).
thf(672,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = F )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(260,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ c_in ) ) @ hBOOL )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
thf(1271,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ c_in ) ) @ hBOOL )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(305,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(1371,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(713,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(525,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(1865,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(480,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(1765,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(1090,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(346,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(1464,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(120,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).
thf(947,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(134,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
thf(979,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
thf(900,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I17_J_0) ).
thf(831,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(538,axiom,
! [A: $i] : ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( c_False @ c_COMBK ) ) @ c_COMBK ) ) @ c_Wellfounded_OwfP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfP__empty_0) ).
thf(1894,plain,
! [A: $i] : ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( c_False @ c_COMBK ) ) @ c_COMBK ) ) @ c_Wellfounded_OwfP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(784,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(147,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( F @ ( E @ ( D @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( F @ ( E @ ( D @ c_Set_Oimage ) ) ) @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) )
= ( E @ ( F @ ( A @ ( B @ ( D @ ( C @ c_Fun_Ocomp ) ) ) ) @ ( A @ ( F @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__reindex_0) ).
thf(1011,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( F @ ( E @ ( D @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( F @ ( E @ ( D @ c_Set_Oimage ) ) ) @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) )
= ( E @ ( F @ ( A @ ( B @ ( D @ ( C @ c_Fun_Ocomp ) ) ) ) @ ( A @ ( F @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(164,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(1048,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(295,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(1349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(358,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(1492,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(379,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
thf(1542,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(1144,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(632,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(2116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(495,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(1801,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(196,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
thf(1122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(569,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ c_Collect ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_0) ).
thf(1969,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ c_Collect ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(233,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(1209,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(633,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( C @ ( B @ c_Collect ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectI_0) ).
thf(2119,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( C @ ( B @ c_Collect ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(401,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(1589,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(553,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
| ~ ( D @ ( E @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff_0) ).
thf(1933,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
| ~ ( D @ ( E @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(482,axiom,
( ( v_P @ ( tc_bool @ c_HOL_Oord__class_Oless @ hAPP ) )
= ( v_P @ ( c_Not @ hAPP ) @ ( c_and @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__bool__def__raw_0) ).
thf(1771,plain,
( ( v_P @ ( tc_bool @ c_HOL_Oord__class_Oless @ hAPP ) )
= ( v_P @ ( c_Not @ hAPP ) @ ( c_and @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(737,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(392,axiom,
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( t_a @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
thf(1571,plain,
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( t_a @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(307,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(1376,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(611,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
thf(2065,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(96,axiom,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
thf(890,plain,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(811,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= ( C @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__insert_0) ).
thf(1471,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= ( C @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(82,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( E @ ( C @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__lower_0) ).
thf(858,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( E @ ( C @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(630,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
thf(2111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(580,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_Set_Oimage ) ) ) )
= ( B @ ( A @ ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ c_Set_Oimage ) ) ) @ ( D @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__composition_0) ).
thf(1993,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_Set_Oimage ) ) ) )
= ( B @ ( A @ ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ c_Set_Oimage ) ) ) @ ( D @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(504,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( F @ ( D @ ( C @ ( B @ ( A @ ( D @ ( F @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).
thf(1821,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( F @ ( D @ ( C @ ( B @ ( A @ ( D @ ( F @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(544,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).
thf(1909,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(513,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(1838,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(106,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( I @ ( C @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).
thf(915,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( I @ ( C @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(118,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Obounded__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(943,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Obounded__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(218,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(1177,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(561,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(1952,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(447,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).
thf(1688,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(758,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(1339,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(1149,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(127,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( C @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
!= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I1_J_0) ).
thf(964,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( C @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
!= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(1556,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(344,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).
thf(1460,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(105,axiom,
! [A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Orderings_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
thf(912,plain,
! [A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Orderings_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(514,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(1841,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(351,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( tc_bool @ ( F @ tc_fun ) @ ( C @ ( E @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( D @ c_in ) ) @ hBOOL )
| ( F @ ( A @ ( E @ hAPP ) @ ( D @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__E_0) ).
thf(1474,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( tc_bool @ ( F @ tc_fun ) @ ( C @ ( E @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( D @ c_in ) ) @ hBOOL )
| ( F @ ( A @ ( E @ hAPP ) @ ( D @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).
thf(768,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(162,axiom,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
thf(1044,plain,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(619,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(2086,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(591,axiom,
tc_bool @ class_Finite__Set_Ofinite_Ofinite,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(2022,plain,
tc_bool @ class_Finite__Set_Ofinite_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(626,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(2101,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( C @ ( A @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold1 ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__belowI_0) ).
thf(653,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( C @ ( A @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold1 ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(571,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
thf(1973,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).
thf(658,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(388,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( A @ ( B @ ( c_Not @ ( A @ ( tc_bool @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__not_0) ).
thf(1562,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( A @ ( B @ ( c_Not @ ( A @ ( tc_bool @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(136,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 ) ) ) @ ( F @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( G @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 ) ) ) ) ) @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_1) ).
thf(983,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 ) ) ) @ ( F @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( G @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 ) ) ) ) ) @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(615,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).
thf(2075,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(172,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(1066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(1445,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(373,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(1528,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(780,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(428,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).
thf(1643,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(640,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
thf(2139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(93,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( E @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(883,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( E @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(484,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(1775,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(1000,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(334,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Odistrib__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(1435,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Odistrib__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(463,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(1726,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(302,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( F @ c_in ) ) @ hBOOL )
| ~ ( E @ ( F @ ( C @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__I_0) ).
thf(1364,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( F @ c_in ) ) @ hBOOL )
| ~ ( E @ ( F @ ( C @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(1250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(176,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(1076,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(420,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
thf(1626,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
thf(722,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(157,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
thf(1034,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(398,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1583,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(499,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Olinorder__class_OMax ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__singleton_0) ).
thf(1809,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Olinorder__class_OMax ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(436,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
thf(1662,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set__sing_1) ).
thf(1203,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(347,axiom,
! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
thf(1467,plain,
! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( D @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I54_J_0) ).
thf(795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( D @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(327,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(1420,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(111,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = E )
| ( B = E )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(927,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = E )
| ( B = E )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(201,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).
thf(1134,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(178,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).
thf(1081,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I49_J_0) ).
thf(823,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(274,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( t_a @ ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_K__record__comp_0) ).
thf(1304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( t_a @ ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(529,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_List_Olistsp ) ) @ hBOOL )
| ~ ( A @ ( D @ ( C @ c_List_Olistsp ) ) @ hBOOL )
| ( A @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_List_Olistsp ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp__infI_0) ).
thf(1873,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_List_Olistsp ) ) @ hBOOL )
| ~ ( A @ ( D @ ( C @ c_List_Olistsp ) ) @ hBOOL )
| ( A @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_List_Olistsp ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(477,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(1758,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(213,axiom,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(1166,plain,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(262,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(1277,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(635,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(2124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(72,axiom,
! [A: $i] :
( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
| ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV_0) ).
thf(836,plain,
! [A: $i] :
( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
| ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(383,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(1551,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(516,axiom,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
thf(1845,plain,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(776,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(406,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( B @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( B @ ( D @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).
thf(1598,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( B @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( B @ ( D @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(566,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(1961,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(1025,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(413,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__2 ) @ ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__1 ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq2_1) ).
thf(1611,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__2 ) @ ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__1 ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(887,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(971,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(410,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(1605,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(486,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).
thf(1780,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(186,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(1098,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(240,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(1225,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(471,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( D @ hAPP ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__insert_0) ).
thf(1743,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( D @ hAPP ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(390,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( t_a @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( v_x @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__def_0) ).
thf(1566,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( t_a @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( v_x @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(642,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__range__imageI_0) ).
thf(2143,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(1230,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(355,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1484,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(361,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( B
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( A @ ( B @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ c_in ) ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__in_0) ).
thf(1499,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( B
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( A @ ( B @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ c_in ) ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(1188,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(159,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(1038,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I47_J_0) ).
thf(717,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(256,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
thf(1262,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(541,axiom,
! [B: $i,A: $i] :
( ( t_a @ ( v_x @ ( B @ ( A @ ( c_and @ ( t_a @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( t_a @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_List_Olistsp ) ) )
= ( t_a @ ( v_x @ ( B @ c_List_Olistsp ) ) @ ( t_a @ ( v_x @ ( A @ c_List_Olistsp ) ) @ ( c_and @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp__conj__eq_0) ).
thf(1901,plain,
! [B: $i,A: $i] :
( ( t_a @ ( v_x @ ( B @ ( A @ ( c_and @ ( t_a @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( t_a @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_List_Olistsp ) ) )
= ( t_a @ ( v_x @ ( B @ c_List_Olistsp ) ) @ ( t_a @ ( v_x @ ( A @ c_List_Olistsp ) ) @ ( c_and @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(180,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__2 ) @ ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__1 ) @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq2_0) ).
thf(1085,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__2 ) @ ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__1 ) @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(103,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(907,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(577,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(1987,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(458,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(1716,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(341,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(1452,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(425,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(1637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(840,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(488,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( tc_bool @ ( A @ ( A @ ( A @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__def_0) ).
thf(1785,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( tc_bool @ ( A @ ( A @ ( A @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(1317,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(479,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ c_in ) ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1763,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ c_in ) ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(300,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(1358,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(238,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__2 ) @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__1 ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq1_0) ).
thf(1221,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__2 ) @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__1 ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(1052,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I58_J_0) ).
thf(727,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(493,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( E @ ( B @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(1797,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( E @ ( B @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(596,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(2030,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(90,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( C @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).
thf(876,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( C @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(540,axiom,
! [A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__UNIV_0) ).
thf(1898,plain,
! [A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(1257,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(631,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).
thf(2113,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(703,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(1141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(377,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
thf(1536,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(574,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(1981,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(496,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(1802,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
thf(1023,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(563,axiom,
! [A: $i] :
( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ ( tc_bool @ ( A @ ( A @ ( A @ c_HOL_Oord__class_Oless @ c_COMBC ) ) ) @ ( tc_bool @ ( A @ ( A @ ( A @ c_lessequals @ c_COMBC ) ) ) @ ( A @ c_Complete__Lattice_OInf__class_OInf @ ( A @ c_Complete__Lattice_OSup__class_OSup @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dual__complete__lattice_0) ).
thf(1955,plain,
! [A: $i] :
( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ ( tc_bool @ ( A @ ( A @ ( A @ c_HOL_Oord__class_Oless @ c_COMBC ) ) ) @ ( tc_bool @ ( A @ ( A @ ( A @ c_lessequals @ c_COMBC ) ) ) @ ( A @ c_Complete__Lattice_OInf__class_OInf @ ( A @ c_Complete__Lattice_OSup__class_OSup @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(643,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(2145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(556,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( F @ ( E @ hAPP ) @ ( D @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(1940,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( F @ ( E @ hAPP ) @ ( D @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(587,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(2013,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(279,axiom,
! [B: $i,A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Nitpick_Osko__Nitpick__XEx1__def__1__3 ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).
thf(1316,plain,
! [B: $i,A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Nitpick_Osko__Nitpick__XEx1__def__1__3 ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(602,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( C @ ( A @ hAPP ) @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(2045,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( C @ ( A @ hAPP ) @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(384,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1553,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(560,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(1949,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(502,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Ofold1 ) ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).
thf(1817,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Ofold1 ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(515,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( C @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
thf(1844,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( C @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(368,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ ( B @ ( B @ c_fequal @ ( A @ ( tc_bool @ ( B @ c_COMBB ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( c_and @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( A @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( A @ c_Ex @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_Collect ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__image__set_0) ).
thf(1517,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ ( B @ ( B @ c_fequal @ ( A @ ( tc_bool @ ( B @ c_COMBB ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( c_and @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( A @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( A @ c_Ex @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_Collect ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(198,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( A @ ( A @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__left__distrib_0) ).
thf(1126,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( C @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( A @ ( A @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ ( B @ ( A @ ( A @ tc_fun ) @ ( A @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( B @ c_Finite__Set_Osetsum ) @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(339,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
| ( A @ ( A @ ( B @ ( c_Not @ ( A @ ( tc_bool @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_Collect ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__not_1) ).
thf(1448,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
| ( A @ ( A @ ( B @ ( c_Not @ ( A @ ( tc_bool @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_Collect ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(582,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
thf(1998,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(209,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
thf(1157,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(511,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(1834,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(433,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
= ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
thf(1654,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
= ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__constant_0) ).
thf(1412,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(268,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Nitpick_Osko__Nitpick__XEx1__def__1__3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).
thf(1289,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Nitpick_Osko__Nitpick__XEx1__def__1__3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(76,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(844,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(498,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(1807,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I19_J_0) ).
thf(771,plain,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(429,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(1646,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(284,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( F @ c_in ) ) @ hBOOL )
| ~ ( E @ ( F @ ( C @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__iff_2) ).
thf(1326,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( F @ c_in ) ) @ hBOOL )
| ~ ( E @ ( F @ ( C @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
| ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(352,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= ( C @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
thf(1476,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= ( C @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(542,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( C @ ( B @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__absorb_0) ).
thf(1903,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( C @ ( B @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(364,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(1508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(354,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(1481,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(472,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Set_Ocontents ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ c_Set_Oinsert @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_fequal @ hAPP ) @ ( B @ ( tc_bool @ ( tc_bool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_The ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_contents__def_0) ).
thf(1745,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Set_Ocontents ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ c_Set_Oinsert @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_fequal @ hAPP ) @ ( B @ ( tc_bool @ ( tc_bool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_The ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(786,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(252,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(1253,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(20,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Oinj__on ) ) ) )
| ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__imageI_0) ).
thf(699,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Oinj__on ) ) ) )
| ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Com_Ocom_OBODY )
!= ( B @ c_Com_Ocom_OBODY ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
thf(813,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Com_Ocom_OBODY )
!= ( B @ c_Com_Ocom_OBODY ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(311,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( H @ ( I @ ( F @ ( G @ ( E @ ( C @ ( A @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( D @ ( I @ ( H @ ( G @ ( F @ ( tc_bool @ ( D @ ( D @ ( E @ c_COMBC ) ) ) @ ( tc_bool @ ( D @ ( D @ ( C @ c_COMBC ) ) ) @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).
thf(1385,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( H @ ( I @ ( F @ ( G @ ( E @ ( C @ ( A @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( D @ ( I @ ( H @ ( G @ ( F @ ( tc_bool @ ( D @ ( D @ ( E @ c_COMBC ) ) ) @ ( tc_bool @ ( D @ ( D @ ( C @ c_COMBC ) ) ) @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(461,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(1721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(896,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(624,axiom,
tc_bool @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(2098,plain,
tc_bool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(441,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(1674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(426,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(1639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(421,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(1629,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(584,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = D )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(2004,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = D )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(371,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(1523,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(637,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(2130,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(140,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
| ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_Finite__Set_Ofinite ) )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UN_0) ).
thf(995,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
| ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_Finite__Set_Ofinite ) )
| ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(386,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__UNIV_0) ).
thf(1558,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ( A @ ( A @ ( C @ ( B @ ( c_and @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__conjI_0) ).
thf(1030,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ( A @ ( A @ ( C @ ( B @ ( c_and @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(485,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Otop__class_Otop ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
thf(1777,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Otop__class_Otop ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(336,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(1440,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ ( tc_bool @ ( A @ ( A @ ( A @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ ( c_and @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conv__if_0) ).
thf(1045,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ ( tc_bool @ ( A @ ( A @ ( A @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ ( c_and @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I59_J_0) ).
thf(667,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(270,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(1294,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(454,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).
thf(1706,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(225,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( G @ ( D @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( F @ ( E @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( F @ ( E @ ( D @ c_Com_Ocom_OSemi ) @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comp_0) ).
thf(1193,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( G @ ( D @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( F @ ( E @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( F @ ( E @ ( D @ c_Com_Ocom_OSemi ) @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(411,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(1607,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(43,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_1) ).
thf(763,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(623,axiom,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
thf(2095,plain,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(15,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( E @ ( D @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I52_J_0) ).
thf(684,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( E @ ( D @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(598,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( A @ ( C @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ( A @ ( A @ ( C @ ( B @ ( c_or @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__disjI_2) ).
thf(2036,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( A @ ( C @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ( A @ ( A @ ( C @ ( B @ ( c_or @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(276,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(1309,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(211,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(1161,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(800,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(193,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(1116,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(427,axiom,
tc_bool @ class_HOL_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
thf(1642,plain,
tc_bool @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(366,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(1512,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(443,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( F @ ( E @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 ) ) ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_2) ).
thf(1678,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( F @ ( E @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 ) ) ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(128,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( E @ ( B @ ( D @ ( C @ c_Hoare__Mirabelle_Opeek__and ) ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( B @ ( tc_Com_Ostate @ ( tc_bool @ ( tc_bool @ ( D @ ( c_Not @ c_Fun_Ocomp ) ) ) ) @ ( C @ c_Hoare__Mirabelle_Opeek__and ) ) @ ( E @ ( D @ c_Com_Ocom_OWhile ) @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Loop_0) ).
thf(967,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( E @ ( B @ ( D @ ( C @ c_Hoare__Mirabelle_Opeek__and ) ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( B @ ( tc_Com_Ostate @ ( tc_bool @ ( tc_bool @ ( D @ ( c_Not @ c_Fun_Ocomp ) ) ) ) @ ( C @ c_Hoare__Mirabelle_Opeek__and ) ) @ ( E @ ( D @ c_Com_Ocom_OWhile ) @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(185,axiom,
tc_bool @ class_Lattices_Obounded__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(1097,plain,
tc_bool @ class_Lattices_Obounded__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(381,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
thf(1546,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(315,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).
thf(1395,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(65,axiom,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).
thf(818,plain,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(854,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(85,axiom,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_Set_Oinsert @ c_COMBC ) ) ) @ hAPP ) @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__singleton_0) ).
thf(865,plain,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_Set_Oinsert @ c_COMBC ) ) ) @ hAPP ) @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
thf(735,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(395,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(1578,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(564,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( F @ ( E @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 ) ) ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_2) ).
thf(1957,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( F @ ( E @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 ) ) ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(403,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_2) ).
thf(1593,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(309,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(1380,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(250,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
thf(1248,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(790,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(604,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( B @ c_Collect ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).
thf(2050,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( B @ c_Collect ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(278,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).
thf(1314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(1495,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(61,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( D @ ( C @ ( C @ ( E @ ( F @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__compose_0) ).
thf(807,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( D @ ( C @ ( C @ ( E @ ( F @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(387,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
thf(1561,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(216,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(1172,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(621,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(2091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(960,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(29,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( A @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
thf(720,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( A @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).
thf(955,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(107,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( C @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
thf(918,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( C @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(578,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(1989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(449,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).
thf(1693,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(613,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( A @ ( C @ ( D @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( A @ ( C @ ( E @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( C @ ( D @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).
thf(2070,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( A @ ( C @ ( D @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( A @ ( C @ ( E @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( C @ ( D @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(490,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(1789,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
thf(664,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(456,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).
thf(1710,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(227,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ( A @ ( A @ ( C @ ( B @ ( c_and @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__conjI_1) ).
thf(1197,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ c_Collect ) @ c_Finite__Set_Ofinite ) )
| ( A @ ( A @ ( C @ ( B @ ( c_and @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(600,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(2040,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I55_J_0) ).
thf(696,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(294,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( B @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(1346,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( B @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(610,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(2063,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(36,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_0) ).
thf(740,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( F @ ( E @ ( D @ c_Com_Ocom_OCond ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(1352,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(199,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(1129,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(83,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(860,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(308,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).
thf(1378,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(150,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Ominus )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
thf(1019,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Ominus )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__constant_1) ).
thf(992,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(549,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).
thf(1923,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(550,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(1925,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(457,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(1713,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(532,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
thf(1880,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(272,axiom,
! [A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__empty_0) ).
thf(1299,plain,
! [A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_0) ).
thf(691,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ ( A @ c_fequal @ hAPP ) @ ( c_and @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conv__if2_1) ).
thf(871,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ ( A @ c_fequal @ hAPP ) @ ( c_and @ ( A @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( A @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ c_Collect ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(195,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
thf(1120,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(183,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( E @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(1093,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( E @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(552,axiom,
! [A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).
thf(1930,plain,
! [A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(244,axiom,
tc_bool @ class_Lattices_Odistrib__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(1236,plain,
tc_bool @ class_Lattices_Odistrib__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(138,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).
thf(987,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
!= ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(636,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(2127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(572,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(1976,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(1,negated_conjecture,
~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( v_b @ ( c_Not @ ( tc_Com_Ostate @ ( tc_bool @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_a @ ( v_P @ ( c_and @ ( tc_Com_Ostate @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ ( t_a @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_Com_Ostate @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( tc_Com_Ostate @ c_COMBS ) ) @ ( t_a @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_Com_Ostate @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_c @ ( t_a @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( tc_Com_Ostate @ ( tc_bool @ ( c_False @ c_COMBK ) ) @ c_COMBK ) ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(644,plain,
~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( v_b @ ( c_Not @ ( tc_Com_Ostate @ ( tc_bool @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_a @ ( v_P @ ( c_and @ ( tc_Com_Ostate @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_bool @ c_COMBB ) ) @ hAPP ) @ ( t_a @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_Com_Ostate @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_bool @ ( tc_Com_Ostate @ c_COMBS ) ) @ ( t_a @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ tc_fun ) @ ( tc_bool @ ( tc_bool @ tc_fun ) @ ( tc_Com_Ostate @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ c_COMBC ) ) ) @ hAPP ) @ ( v_c @ ( t_a @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( tc_Com_Ostate @ ( tc_bool @ ( c_False @ c_COMBK ) ) @ c_COMBK ) ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( v_G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(363,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ c_Finite__Set_Olinorder__class_OMax ) @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMax ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__mono_0) ).
thf(1505,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ c_Finite__Set_Olinorder__class_OMax ) @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMax ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(317,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(1399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1331,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(281,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(1320,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(221,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(1184,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(589,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(2018,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(325,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).
thf(1416,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(628,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
thf(2106,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(348,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(1468,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(558,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( tc_bool @ ( F @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF1__E_0) ).
thf(1944,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( tc_bool @ ( F @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(116,axiom,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(940,plain,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(114,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(935,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(146,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).
thf(1009,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(923,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(468,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( F @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ ( B @ ( D @ ( A @ ( F @ c_Set_Oimage ) ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I10_J_0) ).
thf(1737,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( F @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ ( B @ ( D @ ( A @ ( F @ c_Set_Oimage ) ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(518,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( A @ ( C @ c_Finite__Set_Olinorder__class_OMax ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__ge_0) ).
thf(1848,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( A @ ( C @ c_Finite__Set_Olinorder__class_OMax ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(608,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(2059,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(547,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( B
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( C
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) )
= ( A @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__Un2_0) ).
thf(1917,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( B
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( C
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) )
= ( A @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I14_J_0) ).
thf(755,plain,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(1204,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(500,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(1812,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
thf(1014,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(527,axiom,
tc_bool @ class_HOL_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(1870,plain,
tc_bool @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(3231,plain,
$false,
inference(e,[status(thm)],[1322,1036,1469,760,2109,1633,1995,1105,893,1850,941,1179,1549,1686,1586,809,1337,1718,1369,1823,1190,1237,846,1083,962,1211,1005,1068,1443,1618,1401,1422,1544,1728,1269,677,1437,1486,1855,2077,1750,977,1596,1406,2104,730,1882,2099,1591,878,655,1971,1533,1497,1671,1735,1164,715,2141,1233,1260,945,2042,1354,930,670,1078,1426,1761,1342,1063,1954,898,1914,1243,1576,782,709,2020,1613,2010,1650,1601,1366,1967,1887,651,829,1095,973,885,2136,1703,1287,1985,1871,838,802,1826,1279,1455,1832,949,1055,1409,1792,1430,1860,1264,1462,1132,902,1892,1890,969,1568,2024,1773,1815,1875,1100,1087,1514,1479,1609,1741,881,2007,1489,1946,2027,1450,1911,1418,834,1828,1151,1581,821,905,1302,1664,1040,1109,1334,646,1283,2073,1928,866,1526,1351,1345,1433,1201,1600,849,1521,1564,1169,687,1622,774,1863,1074,1691,661,925,1306,1199,2047,2093,1783,2083,2061,1768,1868,1730,798,1057,1274,1223,1519,1580,1255,1217,1502,1666,788,1238,1387,1723,910,1021,778,1042,952,1174,1676,2133,1938,1920,852,1457,1159,1656,1027,1281,1392,842,1032,1602,2068,1819,1624,1836,1787,682,1195,1407,1573,974,1936,1983,874,1794,1804,1328,1064,1227,980,1878,869,1755,1118,1397,1683,1329,2023,1361,753,1182,1739,1424,2080,1214,2038,679,706,1964,1942,1659,1292,933,1414,2053,1016,1207,997,701,1297,1668,1799,1246,1720,1979,1825,1324,1114,1588,985,1530,1539,1382,1266,1831,1060,1050,1002,1852,1857,1991,792,938,1241,1695,921,1286,1071,2089,1616,1185,1732,2057,1846,1895,1167,2121,1906,1648,2001,1146,1680,2033,1219,1747,856,745,1595,689,1374,750,1510,1698,1959,1103,1631,733,1154,1007,1884,1389,1620,1752,1652,2016,1535,1701,1124,826,711,958,1403,1428,1139,2029,1707,1312,1635,1107,1332,2055,804,1356,672,1271,1371,713,1865,1765,1090,1464,947,979,900,831,1894,784,1011,1048,1349,1492,1542,1144,2116,1801,1122,1969,1209,2119,1589,1933,1771,737,1571,1376,863,2065,890,811,1471,858,2111,1993,1821,1909,1838,915,943,1177,1952,1688,758,1339,1149,964,1556,1460,912,1841,1474,768,1044,2086,2022,2101,653,1973,658,1562,983,2075,1066,1445,1528,780,1643,2139,883,1775,1000,1435,1726,1364,1250,1076,1626,722,1034,1583,1809,1662,1203,1467,795,1420,927,1134,1081,823,1304,1873,1758,1166,1277,2124,836,1551,1845,776,1598,1961,1025,1611,887,971,1605,1780,1098,1225,1743,1566,2143,1230,1484,1499,1188,1038,717,1262,1901,1085,907,1987,1716,1452,1637,840,1785,1317,1763,1358,1221,1052,727,1797,2030,876,1898,1257,2113,703,1141,1536,1981,1802,1023,1955,2145,1940,2013,1316,2045,1553,1949,1817,1844,1517,1126,1448,1998,1157,1834,1654,1412,1289,844,1807,771,1646,1326,1476,1903,1508,1481,1745,786,1253,699,813,1385,1721,896,2098,1674,1639,1629,2004,1523,2130,995,1558,1030,1777,1440,1045,667,1294,1706,1193,1607,763,2095,684,2036,1309,1161,800,1116,1642,1512,1678,967,1097,1546,1395,818,854,865,735,1578,1957,1593,1380,1248,790,2050,1314,1495,807,1561,1172,2091,960,720,955,918,1989,1693,2070,1789,664,1710,1197,2040,696,1346,2063,740,1352,1129,860,1378,1019,992,1923,1925,1713,1880,1299,691,871,1120,1093,1930,1236,987,2127,1976,644,1505,1399,1331,1320,1184,2018,1416,2106,1468,1944,940,935,1009,923,1737,1848,2059,1917,755,1204,1812,1014,1870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV834-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/5.63 % Computer : n010.cluster.edu
% 0.13/5.63 % Model : x86_64 x86_64
% 0.13/5.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.63 % Memory : 8046.5625MB
% 0.13/5.63 % OS : Linux 6.8.0-71-generic
% 0.13/5.63 % CPULimit : 300
% 0.13/5.63 % WCLimit : 300
% 0.13/5.63 % DateTime : Sat Sep 26 15:02:52 UTC 2026
% 0.13/5.63 % CPUTime :
% 0.13/5.63 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.12/6.44 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.36/7.09 % [INFO] Parsing done (646ms).
% 3.36/7.11 % [INFO] Running in sequential loop mode.
% 4.91/7.68 % [INFO] eprover registered as external prover.
% 4.91/7.70 % [INFO] Scanning for conjecture ...
% 6.33/8.08 % [INFO] Found a conjecture (or negated_conjecture) and 643 axioms. Running axiom selection ...
% 7.79/8.49 % [INFO] Axiom selection finished. Selected 642 axioms (removed 1 axioms).
% 9.72/9.00 % [INFO] Problem is propositional (TPTP CNF).
% 9.72/9.05 % [INFO] Type checking passed.
% 10.39/9.05 % [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 ...
% 70.04/24.15 % External prover 'e' found a proof!
% 70.04/24.15 % [INFO] Killing All external provers ...
% 70.04/24.15 % Time passed: 18345ms (effective reasoning time: 17026ms)
% 61.35/24.16 % Axioms used in derivation (642): cls_atLeastatMost__subset__iff_2, cls_the__sym__eq__trivial_0, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_subset__insert_1, cls_Diff__iff_2, cls_bot__fun__eq_0, cls_order__le__less__trans_0, cls_inj__image__mem__iff_1, cls_top__fun__eq_0, cls_inf__sup__absorb_0, cls_Int__Un__distrib_0, cls_com_Osimps_I55_J_0, clsarity_fun__Lattices_Olower__semilattice, cls_inf__sup__aci_I2_J_0, cls_finite__Collect__disjI_1, cls_Diff__cancel_0, cls_INT__extend__simps_I4_J_0, cls_Int__absorb2_0, cls_com_Osimps_I18_J_0, cls_sup__ge1_0, cls_image__constant_0, cls_insertE_0, cls_Un__Diff_0, cls_com_Osimps_I3_J_0, cls_Un__subset__iff_0, cls_order__less__le__trans_0, cls_equalityI_0, cls_insert__inter__insert_0, cls_order__eq__iff_0, cls_com_Osimps_I5_J_0, cls_sup__top__left_0, cls_inj__on__Un_2, cls_setsum__diff_0, cls_xt1_I12_J_0, cls_COMBC__def_0, cls_subset__empty_1, cls_subset__image__iff_2, cls_finite__insert_0, cls_inj__on__image__Int_0, cls_empty__is__image_1, cls_com_Osimps_I14_J_0, cls_image__mono_0, cls_Un__empty__left_0, cls_le__funD_0, cls_inj__image__eq__iff_0, cls_com_Osimps_I44_J_0, cls_sup__bot__right_0, cls_fold1__insert_0, cls_insert__code_1, cls_INT__D_0, clsarity_bool__Lattices_Olower__semilattice, cls_le__SUPI_0, cls_linorder__neqE_0, cls_inf__sup__aci_I6_J_0, cls_Un__upper1_0, cls_Un__commute_0, cls_listsp__infI_0, cls_COMBK__def_0, cls_image__Int_0, cls_UnCI_1, cls_distrib__sup__le_0, cls_Int__mono_0, cls_le__iff__inf_1, cls_complete__lattice_OSup__singleton_0, cls_conseq_0, cls_UN__extend__simps_I10_J_0, cls_fold1Set__sing_1, clsarity_fun__Orderings_Oorder, cls_finite__Un_2, cls_listsp__conj__eq_0, cls_Diff__Un_0, cls_Int__insert__left_0, cls_triple_Oinject_1, cls_finite__Collect__disjI_0, cls_Int__subset__iff_2, cls_le__inf__iff_1, clsarity_bool__HOL_Ominus, cls_Diff__subset__conv_0, cls_Int__Un__distrib2_0, cls_mem__def_1, cls_Int__Collect_1, cls_Inf__lower_0, cls_insert__absorb_0, cls_empty__iff_0, cls_Min__le_0, cls_inj__on__image__set__diff_0, cls_less__supI1_0, cls_inf1E_1, cls_com_Osimps_I5_J_1, cls_Diff__triv_0, cls_insert__iff_1, cls_insert__subset_0, cls_Collect__conj__eq_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_sup__inf__distrib2_0, cls_K__record__comp_0, clsarity_fun__Lattices_Oupper__semilattice, cls_inj__image__subset__iff_0, cls_com_Osimps_I4_J_2, cls_le__sup__iff_0, cls_inj__on__Un__image__eq__iff_0, cls_inf__sup__distrib1_0, cls_order__less__trans_0, cls_Int__absorb1_0, cls_conseq12_1, cls_Diff__insert_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_inf__left__commute_0, cls_COMBB__def_0, cls_INT__absorb_0, cls_CollectI_0, cls_inj__image__mem__iff_0, cls_subset__insert__iff_2, cls_fold1__Un2_0, cls_mult__less__cancel__right__disj_3, clsarity_fun__Orderings_Otop, cls_hoare__derivs_OSkip_0, cls_finite__insert_1, cls_contents__eq_0, cls_inf__commute_0, cls_com_Osimps_I47_J_0, cls_Min__singleton_0, cls_Comp_0, cls_Un__left__commute_0, clsarity_bool__Finite__Set_Ofinite_Ofinite, cls_com_Osimps_I54_J_0, cls_INF__leI_0, clsarity_bool__HOL_Oord, cls_inj__singleton_0, cls_set__mp_0, cls_setsum__diff1_1, cls_COMBS__def_0, cls_Un__Int__distrib2_0, cls_BodyN_0, cls_finite__Int_1, cls_Int__empty__right_0, cls_INT__extend__simps_I3_J_0, cls_fold1__def_0, cls_com_Osimps_I45_J_0, cls_Collect__empty__eq_0, cls_le__supI_0, cls_INT__empty_0, cls_UN__extend__simps_I1_J_0, cls_CollectD_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_INT__subset__iff_0, cls_UN__singleton_0, cls_class__semiring_Osemiring__rules_I7_J_0, cls_order__less__asym_0, cls_inf__fun__eq_0, cls_linorder__not__less_0, cls_Inf__singleton_0, cls_Un__subset__iff_1, cls_Inf__binary_0, cls_empty__is__image_0, cls_order__le__less_0, cls_rangeI_0, cls_order__less__asym_H_0, cls_inj__on__Un_3, cls_rev__image__eqI_0, cls_linorder__antisym__conv1_0, cls_triple_Oinject_2, cls_class__semiring_Omul__c_0, cls_le__supE_1, cls_UN__iff_2, cls_linorder__antisym__conv2_0, cls_le__iff__sup_0, cls_UN__extend__simps_I3_J_0, cls_order__eq__refl_0, cls_finite__image__set_0, cls_SUP__const_0, cls_inj__on__insert_0, cls_finite__range__imageI_0, cls_range__composition_0, cls_SUP1__I_0, cls_UN__absorb_0, clsarity_fun__Orderings_Obot, cls_INT__constant_0, cls_Diff__UNIV_0, cls_Sup__UNIV_0, cls_image__constant__conv_1, cls_Un__UNIV__right_0, cls_setsum__product_0, cls_finite__Int_0, cls_conseq1_1, 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_less__le__not__le_2, cls_xt1_I10_J_0, cls_com_Osimps_I48_J_0, cls_sup__eq__bot__eq2_0, cls_hoare__derivs_Ointros_I6_J_0, cls_Un__upper2_0, cls_Int__insert__right_1, cls_conseq_2, cls_not__less__iff__gr__or__eq_0, cls_UN__Un_0, cls_Max__mono_0, cls_inf__top__right_0, cls_Sup__singleton_0, cls_com_Osimps_I6_J_0, cls_UnCI_0, cls_UN__constant_0, cls_comp__inj__on_0, cls_escape_0, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_inj__on__imageI_0, cls_subset__iff_0, cls_insert__code_2, cls_INT__extend__simps_I10_J_0, cls_com_Osimps_I58_J_0, clsarity_fun__HOL_Oord, cls_Diff__idemp_0, cls_subset__empty_0, cls_rev__predicate1D_0, cls_wfP__empty_0, cls_complete__lattice_OInf__UNIV_0, cls_inf__eq__top__eq1_0, cls_insert__Diff__single_0, cls_UN__simps_I10_J_0, cls_ATP__Linkup_OCOMBC__def_0, cls_singleton__iff_1, cls_atLeastatMost__empty__iff_1, cls_finite_0, cls_complete__lattice_OInf__empty_0, cls_image__insert_0, cls_UN__subset__iff_0, cls_finite__Diff_0, cls_SUP1__iff_2, cls_inf__absorb2_0, cls_atLeastatMost__empty__iff2_0, clsarity_bool__Lattices_Oupper__semilattice, cls_class__semiring_Osemiring__rules_I15_J_0, cls_UNIV__not__empty_0, cls_doubleton__eq__iff_2, cls_diff__single__insert_0, clsarity_fun__Finite__Set_Ofinite_Ofinite, cls_Sup__binary_0, cls_Int__Collect_0, cls_Un__insert__left_0, cls_inf__sup__ord_I2_J_0, cls_com_Osimps_I59_J_0, cls_subset__insert__iff_3, cls_class__semiring_Osemiring__rules_I19_J_0, cls_inj__image__subset__iff_1, cls_xt1_I8_J_0, cls_finite__surj_0, cls_finite__UnI_0, cls_inf__sup__aci_I3_J_0, cls_set__eq__subset_2, cls_Un__mono_0, cls_less__infI1_0, cls_Int__insert__left_1, cls_insert__subset_1, cls_Int__empty__left_0, cls_class__semiring_Osemiring__rules_I16_J_0, cls_Inf__insert_0, cls_mult__left__idem_0, cls_INT__iff_0, cls_INT__extend__simps_I2_J_0, cls_ex__in__conv_0, cls_sup__commute_0, cls_class__semiring_Osemiring__rules_I17_J_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_le__inf__iff_0, cls_Int__subset__iff_1, cls_COMBK__def__raw_0, cls_not__leE_0, cls_Collect__conv__if_1, cls_INT__lower_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_Int__assoc_0, cls_conseq12_2, cls_com_Osimps_I46_J_0, cls_inf__le2_0, cls_insert__is__Un_0, cls_order__antisym_0, 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% 61.35/24.16 % No. of inferences in proof: 1287
% 61.35/24.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 18345 ms resp. 17026 ms w/o parsing
% 64.20/24.82 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 64.20/24.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------